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This question presupposes that you believe the two to be in opposition - I don't. Math fluency is developed through practice, of the drill and kill variety; it's harder to say how mathematical creativity is developed (and yes, creativity is of immense value in mathematical research -- we don't just sit around thinking about the Really Big Numbers, as one of my grandmothers thought).

But the two really do coexist -- they have to. Mathematical creativity is hard to express when you have to go back to first principles every time you add fractions. But drilling algorithms can be pretty boring. How does the tedium of drilling algorithms coexist with creativity in solving word problems or engineering problems or Fermat's last theorem?

I think learning math is a lot like practicing the viola, which I could never stand to do.

I personally think the tedium of practicing computations is nothing compared to that of practicing viola, or any other instrument, but that's just me. Still, noone doubts that all violists, even the great ones -- especially the great ones -- have had to put in thousands of hours of practice, and probably noone would argue that they weren't necessary.

And how does the need for practice coexist with creativity and inspiration in playing the viola?

Well, pretty much everyone who practices the viola hard, over a number of years, is going to be a competent violist. The concert violists are going to be some subset of those who practiced their fannies off -- in fact, in terms of hours spent practicing, really inspired instrumentalists beat out their merely awesomely competent competitors. That's how you get to Carnegie Hall, after all, and here's a chart to prove it.

How do we deal with the fact that musical practice is boring for most of us? Well, if we don't like to practice, we don't have to play. We opt out if we don't like the arrangement - as I did long ago, and as Ben did this year (although the instrument he is spurning, after a perfect record of non-practice in fifth grade, is actually the cello).

The problem with math is that nobody can opt out of learning it: we all need to be competent at it. An understanding of quantities and numbers and rates and growth are the basis of a lot of thinking in our society. It would be nice if there were a royal road to mathematical fluency, but there isn't one that we've yet found; it takes years for even the most mathematically able child to pick up all the mathematics they'll need as an adult.

Even a merely competent violist has pushed his knowledge of the mechanics of his instrument down out of his conscious brain and into his fingers. This has to happen before a violist can even dream of being creative, because if it hasn't, then his conscious brain is still working on mechanics.

Here is what I saw in my college algebra and calculus classes: people still struggling with the mechanics of math, years after they ought to have had the basic moves down. They didn't practice long and hard enough, and if they ever had the moves down, they'd lost them by then.

So how do you get your kid to practice? You get him into the habit. You provide carrots in the form of praise, trips to Chuck E Cheese, movies, video game time, whatever turns him on. You also provide a stick if necessary. You do what it takes to ensure that your kid does this thing that he needs to do, even if you have to fight with him (this is what Bernie calls being a brick wall, and what Catherine calls being your kid's frontal lobes). You clear out his schedule, if necessary, to ensure he has the time he needs to practice.

And you try to make sure he is taking a line of study that isn't going to let him down in the end.

comments...

But all that other stuff can wait!

I'm going to be quick, which means this is off the top of my head:

1. Carolyn's friend Gerry on multiplication

For what it's worth, I think he's dead right about the value of mental multiplication.

I've mentioned that I taught a little after-school class in Singapore Math this winter. In every class I had the kids do mental math.

We did a lot of mental multiplication with the explicit purpose of implanting the distributive property inside everyone's heads.

I'm constantly pushing Christopher to do mental multiplication for this very reason.

He now 'knows' the distributive property; I think he can actually write it out in its 'letter form,' i.e. a(b + c) = ab + ac. (I think.)

He also, I think, knows -- and understands -- that the multiplication algorithm is based on the distributive property.

He knows that when you're doing a problem like:

21
x23

(sorry for the funky alignment; neither Carolyn nor I has been able to figure out how to insert extra spaces in the text thus far . . . )

. . . anyway . . . Christopher knows that when you take the 3 times the 2 you are multiplying 3 x 20; he knows that you are splitting the problem up into smaller multiplication problems and then adding the products together, which you can do because of the distributive property.

But even though he knows all this, I swear he's not as good at mental multiplication as the kids in my Singapore Math class (which Christopher boycotted). Nor does he seem to understand mental multiplication.

He didn't get the practice my Singapore Math kids did, and he's still not really making the connection that the same thing that lets you do the standard multiplication algorithm can be used to multiply numbers in your head or to very quickly multiply numbers horizontally.

His knowledge is still inflexible; he's not generalizing it to other situations and contexts. He's not seeing the connections.

This brings me to --

2. Carolyn's post on practice

This is a HUGE subject, but here are my first thoughts.

I've found that practice per se isn't such a hard thing to get kids to do.

My Singapore Math kids loved the timed worksheets I gave them. (I used the 'Fast Facts' worksheets from Saxon Math.) They used to ask to do more of them, because they made it into a competition. They were revved!

I'd have my timer out, and the kids would call out Done! when they finished the sheet; then I'd call their time & they'd subtract it from the starting time of 5 minutes and write it down on their score sheets.

(I gave each child his own 'Singapore Math' notebook with a Saxon score sheet in the front. So each week they could compare their new score to their previous scores.)

Now, you'd think this could go seriously awry, with the slow kids feeling defeated. I was worried about this myself, since I had kids ranging all the way from a fourth grader who may have been classified with some level of special needs (I have no idea--the parent seemed to indicate this) to a fifth grader whose parents immigrated from China and who's probably one of the best math students in the school.

That's a range.

But nobody's ego got crushed. Exactly the opposite.

Since they all had their own score sheets, they were competing against themselves as well as against the class. They also did different worksheets, depending on whether they'd hit the 5-minute mark on the worksheet from the week before.

As soon as somebody could do the 'Fast Facts' addition sheet, he or she moved on to the 'Fast Facts' subtraction sheet. So the faster kids were doing harder worksheets, and the slower kids were doing easier worksheets.

I guess that's like handicapping in golf, right? (I don't play golf, so I don't know.)

Let's just say that levelled the field considerably, and no one seemed to feel remotely humiliated because they were still doing subtraction when someone else was doing multiplication. They just liked the race.

And they all picked up speed incredibly quickly; I was amazed.

I had one child who, the first time he did a 5-minute addition worksheet, took -- gosh, I don't know -- upwards of 8 or even 10 minutes to get through it.

This child has perfect handwriting and is painstaking when he writes numbers, which was slowing him down, so the second day I actually wrote the answers for him so he wouldn't lose time just on penmanship.

But here's the miracle.

This kid did zero practicing in between classes, and yet by the third class he was coming in under the 5-minute deadline.

I couldn't believe it, and I don't know how he did it. He just . . . got faster. They all did.

They were achieving personal bests every week.

This gets back to Carolyn's post on group learning and Wichita Boy's post about competition: under the right circumstances, practice is fun.

I think the problem for Christopher & Ben is that they're sitting at a table with their mom who is forcing them to do math.

If they were sitting at a table with their friends, and everyone was doing math, it would be different. I happen to know for a fact that this is true, because a couple of times Christopher's friends Drew & Marc, who are fraternal twins, have done a Saxon Math lesson with us. Their mother told them they had to, so they did.

When the three of them are doing Saxon Math together, they peddle.

I've been thinking about group learning ever since Carolyn wrote about it, and I'm turning into a believer.

But more on that later.


+ + +


I see I've gotten off-track.

I meant to talk about Carolyn's observations on practice and expertise.

I'll have to do that later, but in the meantime the single best article I've seen on this subject is here.


+ + +


I wonder if you could get kids to practice the viola if you put 3 of them in a room together and set the timer.


ATeachersStory
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)

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MathInTheBloodPart3 28 May 2005 - 02:16 CarolynJohnston

Carolyn's side of the story

Third in a series: Part 1, Part 2

Catherine talked me into doing something about my own misgivings about the Everyday Math program: starting Ben on a course of Saxon math. I didn't pull him out of his Everyday Math classes at school, although I could have, because I wanted him to remain in class with his peers.

So we started doing the two curricula side by side.

Saxon Math homeschool has a very regular format: there are warmup exercises, a short and simple lesson, a targeted practice set consisting of exercises from the lesson, and a much more extensive practice set consisting of problems that may come from any portion of the text leading up to that lesson.

The Saxon problems aren't easy, but the problem sets are very well designed; there are never any huge leaps, never anything that's clearly over a child's head: no 'discovery' problems requiring the child to intuit the meaning of something he hasn't been taught yet.

Saxon may not be inspired, but it's solid, and as Catherine posted here, it does build mathematical intuition. It is an excellent choice for a homeschooling parent who wants a solid foundation in mathematics for their child.

But I didn't stick to Saxon Math as religiously as Catherine did. I'm not as disciplined as she is, and I kept finding things I wanted to skip, and things I thought I could teach better in my own way.

But although I taught mathematics at the college level for a number of years -- and encountered all too often the results of an inadequate preparation for math at that level -- I never taught elementary mathematics until I tried to teach my own son. And that turned out to be very different from anything I've ever done before.

I remember the night I decided to teach my son how to solve a linear equation. A linear equation is any equation of the form ax+b=c, where a, b and c are numbers, and x is the number to be solved for. I just can hardly imagine anything simpler and more straightforward than a linear equation.

But I was wrong. It turns out there are a lot of skills that go into being able to solve a linear equation.

You need to understand that if two things are on the opposite sides of an equals sign, they are the same, even if they don't look the same. You need to know that if you do something to one side of an equation, you have to do the same thing to the other in order for the equation still to hold. You need to know that you can undo the addition of b on the left hand side by subtracting b, and that it's okay to do that, and a whole host of other things, as long as you do it on both sides of the equation.

That was too much understanding to impart in one night. The poor kid's head was swimming, and I quickly realized I'd made a big mistake, but I wasn't going to just drop it completely; one thing I think I know about how my son learns is that he needs to end every lesson with a small bit of success in order to stay motivated.

And so I needed to leave him with a little more understanding about equations than he'd started with. I told him that an equation was like a balancing scale, something that he'd had experience with in primary school science.

"What happens if you have a scale with weights on each side, and it's balancing, and you take one of the weights off one side?" I asked him.

"It goes 'thunk' on the other side," he said.

"Right! And what can you do to balance it again?"

"Put the weight back."

"Uh, yeah. But another thing you can do is to take an equal weight off the other side. What happens then?"

"It balances again," he said.

"Right!" I said. "An equation is just like that. If you subtract a number on one side, and then subtract the same number on the other side, that's like taking the same weight off of both sides."

And then I showed him how to solve one, just one, very simple equation: x+6=10. And then he did one on his own. And then we had high fives and we were done.

And I felt daunted, because for the first time I realized that there was knowing mathematics, and there was teaching mathematics, and they weren't the same. I might have the former down, but not the latter.

And right about then, at Catherine's urging, I read Knowing and Teaching Elementary Mathematics.

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FrenchCalculatorForKids 16 Jun 2005 - 10:42 CatherineJohnson

Naturally, I was thinking, Excellent!

1st graders can Practice Their Math Facts AND Learn French at the same time!

Unfortunately, I have no idea what language this person is speaking.

(Click on 'Magic Maths.')


+ + +


The addition & multiplication tables are cute, though.


SpeakingOfTheFrench
SpeakingOfTheFrenchPart2
StillSpeakingOfTheFrench
FrenchPrincipalSaysWakeUp
SchoolsInMexico

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SpeakingOfTheFrench 16 Jun 2005 - 10:41 CatherineJohnson

Just a couple of days ago I was talking about clandestine teaching.

Now today I find Instructivist has linked to a raft of anti-constructivist books published in France in the past couple of years, one of them being:





Je suis une jeune institutrice : ma troisième année d’enseignement vient de se boucler. Je sais, le terme de " clandestine " peut faire sourire. Pourtant, j’insiste. J’efface soigneusement le tableau quand je quitte ma classe pour qu’on ne voie pas trace de mon travail, je fais recouvrir de papier kraft les manuels avec lesquels mes élèves apprennent à lire - et que j’ai achetés sur mes deniers. Je tais soigneusement mes convictions et beaucoup de mes méthodes. Elles n’ont pas l’heur de plaire à certains de mes collègues et, en tout cas, elles répugnent franchement aux membres de l’inspection.

En fait, dès mon entrée à l’Institut universitaire de formation des maîtres (IUFM), j’ai presque aussitôt compris que je n’avais rien à en attendre. Nous avons passé en tout et pour tout six heures sur l’année à l’enseignement de la lecture et de l’écriture ! Le credo des formateurs se résumait à : " Le maître ne doit pas être un reférent pour l’apprenant [l’enfant]."

J’ai donc résolu de me comporter en reporter clandestin. De septembre à janvier j’ai tenu un journal tous les soirs, pour résumer mes journées et mes impressions.


roughly:

I am a young teacher: my 3rd year of teaching is about to end. I know, the term 'clandestine' might make people smile. However, I insist. I carefully hide the blackboard when I leave my class so that no one can see a trace of my work, I cover the handbooks from which my students learn to read - and which I bought witih my own money - with 'kraft' paper. I carefully hide my convictions and above all my methods. They're not the sort of things that will please certain of my colleagues and, in any case, they frankly repel members of the inspection team. [I gather that in France inspection teams visit classrooms to monitor quality.]

In fact, since my entrance in the teacher's college I learned almost at once that I should expect nothing from them. We spent a total of six hours in one year on the teaching of reading and writing! The creed of the trainers could be summarized as: "The teacher shouldn't be a 'referent' [probably a source of knowledge] for the student.

So I resolved to [conduct myself as a clandestine reporter ??]. From September to January I kept a diary every night, to record my days and my impressions.



FrenchCalculatorForKids
SpeakingOfTheFrenchPart2
StillSpeakingOfTheFrench
FrenchPrincipalSaysWakeUp
SchoolsInMexico

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SpeakingOfTheFrenchPart2 16 Jun 2005 - 10:46 CatherineJohnson

Spiked (another Instructivist find) translates 'clandestine' as 'illegal.'

[update: Instructivist thinks 'illegal' is wrong. His translation of 'clandestine' in this context is 'stealth.' Diary of a Stealth Teacher.]

[update 2: My husband, who is fluent in French, says 'illegal' is completely wrong. He says 'underground,' 'hidden,' and 'stealth' all capture the meaning.]

Diary of an Illegal Teacher


FrenchCalculatorForKids
SpeakingOfTheFrench
StillSpeakingOfTheFrench
FrenchPrincipalSaysWakeUp
SchoolsInMexico

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StillSpeakingOfTheFrench 16 Jun 2005 - 10:47 CatherineJohnson



I love this one:




Spiked translation:
And Your Children Will Not Be Able To Read ... Nor Count!


FrenchCalculatorForKids
SpeakingOfTheFrench
SpeakingOfTheFrenchPart2
StillSpeakingOfTheFrench
FrenchPrincipalSaysWakeUp
SchoolsInMexico

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FrenchPrincipalSaysWakeUp 01 Nov 2005 - 14:09 CatherineJohnson

Et vos enfants ne sauront pas lire . . . ni compter!
Editions Stock
Avril 2004
Marc Le Bris

« Pendant vingt ans, l'Éducation nationale m'a empêché de faire mon métier. À ma sortie de l'école normale, en 1977, j'étais un jeune instituteur progressiste et militant, convaincu de la supériorité de la méthode de lecture dite "naturelle".

J'ai tout cru. J'ai tout fait, des groupes, des activités d'éveil, de la grammaire fonctionnelle, de la lecture naturelle, des mathématiques modernes, de l'animation, de l'auto-apprentissage, de l'histoire des objets, du décloisonnement, de la créativité, des études dirigées . . .

Pourtant, les élèves des maîtres plus anciens, qui osaient continuer à faire des dictées ou à apprendre la lecture par syllabage systématique, obtenaient de meilleurs résultats. Les miens, dorlotés par les méthodes modernes, ont subi un handicap scolaire dont j'ai honte aujourd'hui. Honte? Pas tant que ça... Car, comme bon nombre d'entre nous, j'ai corrigé le tir.

J'écris ce livre pour alarmer les parents, pour qu'ils sauvent leurs enfants, pour qu'ils fassent le travail de l'école à la maison. La pédagogie moderne ne sert plus qu'à justifier l'abandon des ambitions que nous avions pour nos enfants. Nous avons devant nous une véritable catastrophe culturelle. »

Marc le Bris, 50 ans, est instituteur et directeur d'école à Médréac, en Ille-et-Vilaine. Il est membre de l'association Sauver les lettres.

roughly:

For twenty years the national education system prevented me from doing my job. When I graduated from education school, in 1977, I was a young instructor, progressive and activist, convinced of the superiority of the method of teaching reading known as ‘natural.’

I believed everything. I did everything, I did groups, I did [icebreaking] activities, functional grammar, natural reading [probably whole language], the new math, student participation [l’animation = interaction], self-teaching [self-directed teaching, probably], ‘history of objects’ [l’histoire des objets], taking down the walls, creativity, directed studies . . .

However, the students of the oldest teachers, who dared to continue to do dictée^* or teach reading with phonics, obtained the best results. My students, guilded by modern methods, had endured an academic handicap of which I am ashamed today. Shame? Maybe not completely . . . because, like many of us, I compensated for some of the worst excesses.

I wrote this book in order to wake parents up, so they can save their children and teach their children their school work at home. All modern pedagogy does is justify the abandonment of the ambitions we have had for out children. We have ahead of us a veritable cultural catastrophe.

Marc le Bris, 50 years old, is a teacher and principal of d'école à Médréac, en Ille-et-Vilaine. He is a member of Sauver les letters.




^*Le dictée is the classic exercise in which the teacher dictates a passage of prose and the students write it down. This was traditionally an important part of French language arts, because so many French words sound alike. My husband did it when he was first learning French, and said it was incredibly hard. All the adjectives have to agree in gender & number with the nouns, and you can’t hear any of this in the spoken language.

French is still being taught using le dictee in other countries. Recently there was an international dictee contest judged by Bernard Pivot, the famous moderator of the book review show Apostrophes.



FrenchCalculatorForKids
SpeakingOfTheFrench
SpeakingOfTheFrenchPart2
StillSpeakingOfTheFrench
SchoolsInMexico

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HowNotToTeachMath 29 May 2005 - 15:39 CatherineJohnson


While we're on the subject of illegal teaching, one of my favorite personal stories of a teacher closing the door and teaching is Matthew Clavel's How Not to Teach Math in City Journal.

Clavel was teaching in a Manhattan School that had phased in Everyday Math four years before he arrived; his fourth graders had used the curriculum since Kindergarten.


The curriculum’s failure was undeniable: not one of my students knew his or her times tables, and few had mastered even the most basic operations; knowledge of multiplication and division was abysmal. Perhaps you think I shouldn’t have rejected a course of learning without giving it a full year (my school had only recently hired me as a 23-year-old Teach for America corps member). But what would you do, if you discovered that none of your fourth graders could correctly tell you the answer to four times eight?

[snip]

Instead of rote learning and memorization, students move haphazardly from one seemingly unconnected topic to another. In Fuzzy Math lingo, it’s called “spiraling.” On this view, teachers shouldn’t use a single method to get addition across to students; they should try lots of approaches—like adding the left-most digits first. That way, the Fuzzy Math approach says, you have a better chance of getting students to understand the concept of addition. In practice, however, trying to teach a host of different methods if students haven’t sufficiently mastered any specific one—as is all but inevitable, since they haven’t spent much time practicing any specific one—can be very confusing.

[snip]

Teachers frustrated by this incoherent approach got little sympathy from school administrators. District officials told us that we should just keep going—even if not a single child in our rooms understood what we were talking about. We were going to spiral back to each topic later in the year, they reassured us.

[snip]

According to a 2000 Brookings Institute study, fourth graders who used calculators every day were likely to do worse in math than other students. But it’s minority kids like those in my class who are turning to calculators the most. The Brookings study reports that half of all black school children used calculators every day, compared with 27 percent of white school kids.

[snip]

Then there is the bizarre recommended homework. According to Everyday Mathematics, I should have assigned my students extra-hard material to struggle with at home. Here’s an example from the updated fourth-grade workbook: “Homer’s is selling roller blades at 25 percent off the regular price of $52.00. Martin’s is selling them for one-third off the regular price of $60. Which store is offering the better buy?”

Now put yourself in the place of kid who hasn’t learned how to multiply quickly, who isn’t sure about what a percentage is, and whose knowledge of fractions is meager.

[snip]

I certainly wasn’t alone in hating it. Indeed, I never heard a good word for it from my fellow teachers. At a grade conference one day, one our most respected fourth-grade teachers, a veteran who worked hard and cared deeply about the achievement of her students, summed up the general frustration with the new program: “I can’t teach it.”

[snip]

A third-grade teacher objected to the intimidating complexity of some of Everyday Mathematics’s word-heavy mandatory activities, mentioning by way of example one of her totally lost students, who could not yet read or write. I had a few students in my class who were in the same boat, so there was nothing unusual about her statement. Yet the district official, smiling, just responded, “I don’t believe you.”

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InflexibleKnowledge 29 May 2005 - 05:17 CarolynJohnston

In HowNotToTeachMath, Catherine posted an example of a fourth grade Everyday Math homework problem:

Homer's is selling roller blades at 25 percent off the regular price of $52.00. Martin's is selling them for one-third off the regular price of $60. Which store is offering the better buy?

I remember this sort of problem from last year, when Ben was in fourth grade. There were a whole series of such problems, more or less just like this. They were the sort of word problems you'd more typically see in a 7th-grade pre-algebra class; fortunately, they were all more or less the same. There was only one way to teach them, and that was to train the kids to do this sort of problem, step-by-step; what you might call by rote. I'm pretty sure this defeated the intention of the Everyday Math curriculum designers, who were trying to get the kids to think creatively about real world problems.

That's the idea behind many of the new-new math curricula. We can skip the tedium of teaching the standard algorithms, and emphasize estimation instead; we can skip teaching algebraic symbol manipulation independently, and teach algebra in the context of the word problems that adults really have to solve. Adults have to work with data, and so in the Everyday Math curriculum, there is enormous emphasis on statistics; kids start learning the median, mode and range before they are even capable of calculating the average. Calculating statistical landmarks is a topic that my son's classes have 'spiraled back to' any number of times in the two years my son has been doing Everyday Math.

And I don't think Everyday Math is even the most extreme of the new curricula: noone gets out of Everyday Math without at least knowing something about how to do multiplication and long division. I credit my son's teachers with taking the extra time needed to ensure that this was the case.

The intent of Everyday Math is to teach kids how to think flexibly about mathematics from the get-go. It's a laudable goal. But apparently it's a misguided one, because that's simply not how people learn new material.

When we're learning something completely new to us, we go through a phase where we understand the new material only in a very inflexible way; we can't generalize it very well, and we find it difficult to apply to new situations.

And that's okay. It's the way our minds work, apparently; we start out with inflexible knowledge, that we can gradually apply more flexibly as we gain more familiarity with it. That's why beginning violinists play stiffly, and why kids learning to read read small words, slowly. Inflexible knowledge isn't the same as rote knowledge, which leads nowhere; it's a necessary precursor to expertise.

This is something Catherine and I will harp on, over and over, because it's really important to understand this hard fact about how humans learn if you want to teach your little humans how to do math, or anything else.

This article from American Educator on inflexible learning, and its relation to expertise, is a must-read.

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ConcernedParentsOfReading 29 May 2005 - 20:22 CatherineJohnson

Carolyn and I have not yet systematically found and posted all the parents' groups (on the to-do list, obviously).

Just yesterday I discovered that I had somehow missed Concerned Parents of Reading, so I wanted to get this link up at once.

Dr. Robert Mandell and his wife, Jackie, seem to be either founders or mainstays of the group (please correct if I've got this wrong!), and Dr. Mandell has been kind enough to send me material on the goings-on in MA--including news articles on the pilot program of Singapore Math which I've been reading about in the AIR report (this links to the press release; you can download the full report from there. The report is quite long--well over a hundred pages--but well worth reading.)

Links:
analysis of 1997 scores
local news article on math scores & Everyday Math
Suggestions of Concerned Parents of Reading, MA


+ + +


I chuckled when I saw this item on the 'Suggestions' list:

You ask the principal about test scores and are told the tests don't measure skills your children will need in the 21st century.

I had been wondering about that phrase, 21st century skills.

It's everywhere in the Singapore report.

You're reading along, growing more enlightened & inspired with each passing page, and then--BAM--you slam into 21st century skills again.

Now I know where it comes from.

TO BE CONTINUED

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ParentPundit 27 Jun 2006 - 13:49 CatherineJohnson

Carolyn just spotted an incredibly kind post about KTM at Parent Pundit.

Neat!

Parent Pundit also has a number of posts on Everyday Math, which is her daughter's math curriculum, as well as discussion of an online tutoring program I had never heard of: ALEKS A Better State of Knowledge.

Parent Pundit's daughter has just moved to the advanced math class in her school, so I'm going to check out ALEKS right away (maybe for my own use at some point).

Her story of discovering that her daughter had fallen behind in math knowledge while getting A's in her math classes is here: If your school has Everyday Math.





a parent's experience with ALEKS
ALEKS Graphic
formative assessment on wheels
ParentPundit uses ALEKS to fix Everyday Math
ALEKS question
ALEKS assessment coming right up

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BadInternetDay 30 May 2005 - 03:58 CarolynJohnston

Service from Comcast has actually been intermittent for the last couple of days, which is very frustrating. It's Memorial Day: what better time to be on the internet?

Sadly, though, it seems a lot of people share my vision of the perfect holiday weekend.

I do want to sneak this post on, however. Parent Pundit's article on Everyday Math, to which Catherine linked a couple of posts ago, is the best short summary of objections to the Everyday Math curriculum that I've ever seen.

I don't want to rant about Everyday Math indefinitely -- my main goal on KTM is to collect and share useful methods and ideas for teaching math, and there are, incredibly, even crazier math curricula to target. So ParentPundit's post will stand as the absolute last word on the failings of Everyday Math, as far as I am concerned.

And don't fail to check out her list of supporting links at the end of the post, especially if you're looking for ammunition to prevent an Everyday Takeover.

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HappyMemorialDay 29 May 2006 - 21:27 CatherineJohnson

Memorial Day 2005
Memorial Day 2006
Leigh Ann Hester

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BlameTheTeacher 30 May 2005 - 20:38 CarolynJohnston

Reading over ParentPundit's post about Everyday Math, I encountered the following in the comments section, left by aschoolyardblogger. It's an argument one frequently hears to counter parents' and teachers' complaints about reform curricula.

It is a difficult task for teachers to begin any reform mathematics projects - their own math learning at first is being tested and reformed. One of the key ingredients, in my mind, is support provided through teacher training, but almost and maybe more important is the support of parents. One way to understand a math program like EM is to read through and do the exercises in the curriculum consecutively, openmindedly as a learner, not a an assessor. Play with the manipulatives, perhaps even borrow a teaching guide. These programs are much different, and much more exciting than the way we were taught. They are also very hard to describe. With some study, you might find yourself a great parent contributor to something your children's school is attempting to perfect.

Open your mind, Grasshopper: play with the manipulatives. Wax on, wax off.... I think teachers (and parents) need some sticking up for.

Math itself doesn't change much, and neither do people. Teachers who know how to teach math weren't invented by new curricula (for that matter, reform math curricula aren't a new invention, either). Nor have the rare teachers who take pleasure in humiliating children been stopped by the adoption of new curricula.

The truly exceptional teachers aren't the ones who need a supportive curriculum most; they can always roll their own. The whole purpose of a curriculum is to guide the process of teaching and learning for the majority of people. To argue that a curriculum fails only because of the failings of the teachers who must implement it is specious -- like arguing that Communism fails only because of the fallible people who must implement it.

Not to mention that the argument is insulting. God, teachers must get sick of these insinuations that their understanding needs 'reforming'. I know that parents do.

Learning to be a good teacher of math, like learning math itself, is very challenging. There is a depth of domain knowledge and pedagogical understanding that one can acquire over the course of a career in mathematics education; this pedagogical understanding should be what guides a teacher's explanation of mathematics in the classroom, not a 'Teaching Guide'. Only a teacher with a flexible approach that comes from deep understanding can come up with the fifth explanation that meets the needs of an individual child, when the first four have failed.

I've noticed that there are topics where Everyday Math does not offer cool new teaching methods, and they tend to be the topics that have always been difficult to teach: for example, division by fractions. These things are difficult to teach and understand because, well, they just are, no matter whose method you're using.

A math curriculum should be the foundation of a kid's math education. A teacher who has an exciting activity to try can supplement a curriculum, but the curriculum should provide enough guidance to ensure that the ground that needs to be covered, gets covered. The cool techniques that Everyday Math uses to enhance understanding can then serve as grace notes.

And it may sound absurdly pedestrian, but the second valuable thing that a good math curriculum can provide is a good set of problems for the children to work. A good problem set design is worth its weight in gold. Saxon has one. I'm not always crazy about Saxon math's explanations of methods, but its problem set is awesome.

A teacher who is motivated to try to acquire and pass on what Liping Ma refers to as Profound Understanding of Fundamental Mathematics -- and who is respected for trying -- can and must provide the rest.

comments...

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GreatMindsThinkAlike 30 May 2005 - 21:16 CatherineJohnson

Good Grief.

Apparently Carolyn and I were not the first people on the planet to think up 'Kitchen Table Math'.

(Scroll down.)

comments...

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ProfoundUnderstandingFundamentalMathematics 31 May 2005 - 01:57 CatherineJohnson






Carolyn mentioned Liping Ma's concept of 'profound understanding of fundamental mathematics' (PUFM).

This chart is Ma's map of the 'knowledge package' Chinese teachers possess for the topic of subtraction. This is what Chinese mathematics teachers know and understand about subtraction.

I don't happen to have this knowledge package inside my own head, and neither does any other parent I know.

This is why it won't do to say:

One way to understand a math program like EM is to read through and do the exercises in the curriculum consecutively, openmindedly as a learner, not as an assessor. Play with the manipulatives, perhaps even borrow a teaching guide. These programs are much different, and much more exciting than the way we were taught. They are also very hard to describe. With some study, you might find yourself a great parent contributor to something your children's school is attempting to perfect.


+ + +


Chinese math teachers develop pedagogical content knowledge over the course of many years teaching and studying elementary mathematics.

There are no shortcuts.

How long does it take to acquire a profound understanding of fundamental mathematics?

I'm guessing 10:

Some evidence that a great deal of practice, and not just talent, is a prerequisite for expertise is the "ten year rule," which states that individuals must practice intensively for at least 10 years before they are ready to make a substantive contribution to their field. What about prodigies like Mozart, who began composing at the age of six? Prodigies are very advanced for their age, but their contributions to their respective fields as children are widely considered to be ordinary. It is not until they are older (and have practiced more) that they achieve the works for which they are known.


+ + +


No parent is going to pick up a copy of Everyday Math, read through the book, work the exercises, and be ready to teach or tutor the curriculum effectively.

That's not the way it works.

Parents have a fighting chance of teaching or tutoring effectively with a direct-instruction curriculum like Saxon Math. We have that chance because the books are written so that anyone who's been through grade school can understand what the lessons are about.

None of us is going to do a brilliant job teaching math using Saxon. Becoming brilliant at anything takes 10 years.

But we can help our children learn math.

It's not just children who need direct instruction. Parents need it, too. We parents need to be able to pick up our child's mathematics textbook, read the lesson, and know what it's talking about.

That school districts consciously select unproved mathematics curricula they know parents will not understand and will not be able to teach or tutor from is, to me, unconscionable.

It's not up to us to go begging for a peek at the teacher's guide.

It's up to our schools to bring us into the loop.

comments...

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TeacherGuideEverydayMath 25 Mar 2006 - 23:35 CatherineJohnson


Wow.

Speaking of sneaking a peak at the teacher's guide, it just so happens that I have open, on my desktop, a bunch of pdf files from the Everyday Mathematics Teacher's Reference Manual, Grades 4-6, The University of Chicago School Mathematics Project, Everyday Learning Corporation, Chicago, IL, 1999, ISBN 1-57039-515-2, pages 127-139, courtesy of one Tsewei Wang, Ph.D., Associate Professor, Department of Chemical Engineering, University of Tennessee and Concerned Parent.

Have I mentioned how much I love the internet?

Interesting to see that Everyday Math teaches the same Guess-and-Check algorithm for long division that's in Trailblazers.

Only, Trailblazers calls it 'Forgiving Division' (pdf file; search for 'forgiving division'):

Forgiving Division Method
(URG Unit 4 pp. 5, 6, 53; SG p. 113)

A paper-and-pencil method for division in which successive partial quotients are chosen and subtracted from the dividend, until the remainder is less than the divisor. The sum of the partial quotients is the quotient.

+ + +


So say you're dividing 239 by 3.

Instead of using math facts to know that 3 goes into 23 seven times, you start by guessing how many times 3 goes into 239.


+ + +


OK, let's divide 239 by 3 using forgiving division!


'I'm ready!'



I'm going to start by guessing the number . . . 7!

I guess 7!

3 x 7 is . . . 21!

I write down 21 underneath 239, then I subtract, and I get . . . 218.

Whoa.

That's a lot.

OK, I'm going to use a strategy.

I'm going to guess . . . 10, because 10 is a friendly number.

10 x 3 is . . . 30!

I write 30 underneath 218, then I subtract----188.

Wow.

188 is big.

OK. 188. I'm down to 188.

. . . I'm going to try 10 again.

10 x 3 is 30, subtract 30 from 188, get . . . 158.

158?

Wait.

Wait.

I'm lost.

What number am I down to?

Oh. 158. I'm at 158.

OK, I'm going to try 20.

20 x 3 is 60, subtract from 158, get . . . 98.

Oh good! 98! That's really good! 98 is below 100!

Maybe I could try 30 this time.

30 x 3 is 90, subtract from 98, get 8!

Fantastic!

8!

8 is a really friendly number!

Now I can use my math facts and find that 8 divided by 3 is 2.

2 x 3 is 6, subtract from 8, get 2; 2 is less than 3, I'm done!

Yay!

Finally!

Now I add up all my partial quotients and the answer is------

7 + 10 + 10 + 20 + 30 + 2 = 79 remainder 2.

79 remainder 2!

That's the answer!

That's it!

All done!

Bye Bye!

The end!

Forgiving Division

see:
The Many Faces of the Bitter Single Guy

and:

BlameTheTeacher
ProfoundUnderstandingFundamentalMathematics
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
ILoveTheWorldWideWeb
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
WhoSaysLongDivisionIsHard
Everyday Math alternate division algorithm

keywords: Sponge Bob Bitter Single Guy




comments...

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AssessYourChildForFreePart2 16 Jun 2005 - 17:53 CatherineJohnson



I've just added this post to ThingsWeHaveLearned:


David Klein developed these Practice Problems for the California Mathematics Standards Grades 1-8 for the Los Angeles County Board of Education.

For me, these problem sets are precious. That is none too strong a word.


And here's Carolyn, in an email to David:

It's wonderful that you put together those assessment questions. Those practice problems are golden. One of the most difficult things for a parent to do is to get a solid idea of what kids ought to know -- what it means for them to be on track. CA's state standards are good, but too dense. There could be nothing more succinct than a set of problems that the kids must know how to do, year by year. Kitchen.Catherine and I want to post links to them front and center, and to continually refer parents to them (because, of course, repetition is key :)).


"Golden" is right. A consultation with an educational psychologist can run into the thousands of dollars.

If you suspect that your child has specific learning problems, wrangling a consult from your school may be a very good idea.

But if your question is simply: where does my child's math achievement stand today? then these grade-by-grade problem sets are all you need (I think) to find your answer.

At least, they've worked for me and Christopher.

AssessYourChildForFree
DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

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ATeachersStory 24 Mar 2006 - 01:35 CatherineJohnson

Carolyn (J) has just alerted me to the fact that there are comments under some of our posts . . . so apparently my Next Action vis a vis KTM is: ask Carolyn how to keep track of comments.

('Next Action' is Getting-Things-Done-speak. Carolyn and I are both fans of David Allen's Getting Things Done, and in fact last week Carolyn tipped me off to a whole Getting-Things-Done blog that I am hoping will change my life.)






Anyway, this is a comment from a teacher who has a fascinating situation with Saxon Math.

(I've inserted extra paragraph breaks to make this easier to read):

I teach in a private Christian School. My 5th graders continue to score above all other grades on SAT's.

I am now the only teacher who teaches Saxon, although when I came 11 years ago, all grades used Saxon.

It was felt that there were gaps in the Saxon program for lower grades, so they changed to another program for K-3. That program didn't work, so they are now trying another curriculum. They also felt there were gaps in Saxon for high school, so that has changed. Then they changed 7-8 grades to Mc Dougal-Littell's Passport to Algebra and Geometry, leaving only 4,5,6 using Saxon. Then, they added Passport to Mathematics in 6th. Now, this year they have changing 4th grade to the K-3 curriculum. After three years of complaints from parents and after losing many families, they realized they were going to have to do something about the problems between 5th and 6th grades.

But because of my success in Saxon, they are allowing me to remain with the curriculum.

I know this is a long story, but I find this incredible: one grade in the school continues to be at the top on SAT's, year after year, no matter the class's Math abilities and strengths -- it's my 5th grade class and I use Saxon.

Now, I do use Saxon as it is designed to be used (students make corrections and corrections until they get it right) and that's very important. And I require all the proof, rather than merely answers. Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful.

The bottom line is: Saxon, when used properly and as designed, works.

Then, the students go into Passport and good students make F's. I'm trying to determine if Passport is considered to be "constructivist" but can find no informatiion on that. I've read the reports from Mathematically Correct's seventh grade review. Passport to Algebra/Geometry is given an A, Passport to Mathematics is given a C. That's all I have found. I see no reference to its being constructivist.

All I know is this: students fall apart, parents ask me to help tutor them, yet it does little good.

Our new secondary principal describes the two programs (Saxon and Passport) as being very different, so I'm guessing that our students are having to go from a very traditional, incremental approach that is successful to a very non-traditional approach. I'm very glad that I found your blog site. I'm going to refer parents to you. Perhaps, they can get insights that I can't yet offer them because I can only teach the "old fashioned, traditional (and successful) way". Thanks for listening and God bless.

I'm pulling these lines out for emphasis:

Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful.

This is absolutely my own experience.

When I started teaching Christopher math, in the wake of his two failed Unit exams, I was hearing 'math is for geeks,' 'math is for nerds,' 'I hate math,' 'math stinks,' and 'I'm not from Singapore.'

A few weeks into the program all that went away. He was getting As on his tests, he understood the lessons, and suddenly math wasn't for geeks after all.

Self-esteem comes from being able to do something. If a child can do math, he feels good about math. It's that simple.

The other day Christopher actually said to me, spontaneously, in the midst of doing his Saxon homework when he could have been outside shooting baskets or upstairs playing WWE Here Comes the Pain on his PlayStation, "I like math, I just don't like doing math problems."

I had to stop what I was doing and check this out.

"You like math?"

"I like the idea of math."

He's not ready to Commit, but he sounded happy.


ILikeMathPart2
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)

BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
BonusPreTeenPost
SummerSupplementTimePart2
SundaySchool
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids

comments...

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TakingABreak 31 May 2005 - 22:43 CatherineJohnson

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AboutLongDivision 14 Jun 2005 - 01:29 CarolynJohnston

(I actually wrote this post a couple of days ago, when my internet connection was down!).

Ben's half-brother is visiting for Memorial Day Weekend. It's always wonderful when Colin comes; in spite of their size difference (Colin, who is 16 and about 6'2", is more than a foot taller than Ben) there is a lot that they can do together; watch movies, play Nintendo, play basketball.

But, of course, learning still has to go on, and last night I insisted that Ben had to get some long division practice in. He knows the long division algorithm, and a few months ago I taught him how to divide by decimals. So now I am trying to get Ben to overlearn decimal long division, and the best way to do that is to get him to practice it.

So I handed him a sheet of paper with some long division problems on it and asked him to do them. He did them too fast -- too eager to get back to Colin and the Nintendo game -- and got most of them wrong. Not surprising, perhaps, but I'm looking for his long division skills to be so automatic that he can do them when most of his conscious attention is elsewhere.

I want long division to be a no-brainer for him, literally. It should be in his fingers.

He did the problems over again this morning; I stood looking over his shoulder to try to figure out what had gone wrong the night before. I was surprised at how good he actually is at the long division algorithm. He is, in fact, working out the few bugs left before he achieves mastery, and the distraction of Colin's presence had driven them out into the light.

If your kid is at or near the mastery point in long division, here are a few problems to look out for, and some sample problems that might help diagnose them.

• Uncertainty about what to do if the divisor does not divide the current number, after you bring the next digit down. For example, this occurs in the second step of dividing 92.0 by 9. The answer to this problem is 10.2222... a child who does not have this down cold will typically get 12.222222 for an answer, skipping over that lone zero.

• Uncertainty about what to do with a problem where the dividend has fewer decimal places than the divisor. One example of this is the problem 34/.21. In setting up this long division algorithm, the divisor and dividend should both be multiplied by 100: i.e., the decimal should move to the right by two places for both values, and the division problem should become 3400/21. A kid who does not completely have this nailed may get confused about what to do with the 34.

• Uncertainty about where to stop the long division process. Division problems that do not terminate should read, in general, something like "find the value of 213/14 to the nearest tenth (or hundredth, or whole number) ". A kid needs to be taught explicitly how to handle answering these questions. For example, suppose a problem reads: find 92.17 divided by 13 to the nearest tenth. Then the child should actually calculate the quotient out to the hundredth place, and round the answer to the nearest tenth. In the case of this problem, the child will get 7.09 as an answer through long division, and should round this answer to 7.1.

I would strongly advise against doing what I did last night -- that is, handing him ten juicy long division problems to do in a chunk. When faced with a lot of problems like that, my kid tends to lose hope of ever finishing, and despair makes him careless. Better to give him only three or four at a time, which I plan to do from now until he has long division down cold.


StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

comments...

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PaperFractions 16 Jun 2005 - 17:50 CatherineJohnson

Success!

I'd been trying to find one of my favorite Math Wars quotes, without luck.

Then this morning it popped up unannounced in the middle of a different quest altogether.

Here is David Klein, speaking at a 2002 AEI seminar called DOES TWO PLUS TWO STILL EQUAL FOUR? WHAT SHOULD OUR CHILDREN KNOW ABOUT MATH?:


DR. KLEIN: The NCTM standards actually have deep mathematical flaws. The 1989 version was worse than the present one, but the present one does have some serious problems. For one thing, the quadratic formula, a major topic in eighth grade algebra, isn't even mentioned in the document.

But when the NCTM standards attempt to explain how to divide fractions for middle school, they don't even do it correctly. The method that they give there is they suggest repeated subtraction and analogy with whole numbers. Try that with 5/8 divided by 3/4 using the NCTM methods, and you'll be cutting paper all day and all night.


I don't think 5/8 is a very friendly fraction.



DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

comments...

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FriendlyFractions 16 Jun 2005 - 17:49 CatherineJohnson

Want to know what comes up when you Google friendly fractions?


Visit Fraction Town and meet Friendly Fractions and Fractions Not So Friendly, even see a Fraction Frenzy as students learn about fractional parts. Dividing and multiplying by one and two digits and determining the probability of events occurring finish up the school year. Have a great summer!


Day 151 sounds especially fun!

Fraction lesson created for day 152 of the 180 day sequence of lesson plans. Students will use their knowledge of fractions to create a map of Fraction Town and decorate their map using what they've learned about fractions.


See also:
DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions





comments...

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SlowOnTheUptake 14 Jun 2005 - 14:32 CatherineJohnson

It's 2:30, and I've managed to miss the big news of the day 'til now.

Joanne Jacobs has links to Jay Mathews' 10 Myths (Maybe) About Learning Math as well as to NYC HOLD's response.


ILikeMathPart2
ILikeMath

comments...

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CulturalEvolution 02 Jun 2005 - 14:40 CatherineJohnson

NYC HOLD has posted a talk by Fred Greenleaf, Professor of Mathematics at NYU, called High School Programs That Work (pdf file).

This passage jumped out at me, because Temple and I talked about this in Animals in Translation:


Since prehistoric times, human beings have survived and prospered by being able to pass on the accumulated knowledge of our species to our children. In the present era we have vast bodies of information to deal with; some areas (medicine, mathematics) have taken hundreds or even thousands of years of patient exper- iment, observation, and false starts to evolve into their present forms. Passing all this knowledge from one generation to the next requires efficient and effective methods, namely flexible and innovative direct instruction by teachers who are highly competent in their subjects. Having students sit around re-inventing the wheel in endless trial-and-error “discovery projects” is not an option.



Professor Greenleaf is talking about cultural evolution.

Temple and I spent some time on this subject because, at the time we were writing, no one had seen cultural evolution in nonhuman animals.

(Since we finished the book, cultural evolution may have been demonstrated in the New Caledonian crow -- and, for what it's worth, I personally won't be surprised if we find cultural evolution in other nonhuman animals. But that's beside the point. Cultural evolution is the hallmark of the 'human animal,' and is certainly the hallmark of our own culture.)

Here is M. Tomasello on cultural evolution:

Cumulative cultural evolution is thus the explanation for many of human beings' most impressive cognitive achievements. . . . Most importantly, cumulative cultural evolution ensures that human cognitive ontogeny takes place in an environment of ever-new artifacts and social practices which, at any one time, represent something resembling the entire collective wisdom of the entire social group throughout its entire cultural history. Each child who understands [other people] as intentional/mental beings like herself . . . can now participate in the collectivity known as human cognition, and so say (following Isaac Newton) that she sees as far as she does because she "stands on the shoulders of giants."


For the sake of argument, let's agree that we want our children to develop 21st century skills.

What does this mean?

It means we want them to go beyond us, to discover knowledge we have not discovered ourselves.

We want them to stand on our shoulders.

If our children spend their childhoods re-discovering the wheel, it is possible they will not be able to discover what comes after.

We need to pass our knowledge on to them now, while they are young, and their minds are like little sponges.

We need to do this now, because time is always short.

Childhood is fleeting, and one day we will be gone.







(I'll upload the complete article shortly.)

comments...

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FreshHorses 01 Jun 2005 - 21:14 CatherineJohnson

I had never seen this before:


It is a profoundly erroneous truism repeated by all copybooks, and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of operations which we can perform without thinking about them. Operations of thought are like cavalry charges in battle - they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.

- Alfred North Whitehead, Introduction to Mathematics

quoted by Ethan Akin, In Defense of 'Mindless Rote'



I love it!

'Fresh horses' and 'cavalry charges' are much more fun to think about than working memory and automaticity!

comments...

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HowCouldIForget 02 Jun 2005 - 02:41 CatherineJohnson

I just remembered.

I haven't posted anything about the fact that I have two kids with autism.

Christopher isn't the only child around here who needs Serious Intervention.

There are 3 of them! Jimmy, Andrew, and Christopher. Jimmy and Andrew are autistic.

Andrew is Christopher's twin, and he's just started to learn some math this year. I'm going to Have At Him this summer. (So if anyone has any ideas, or knows anyone who has any ideas, please. Chime in.)

comments...

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TheBomb 02 Jun 2005 - 00:59 CatherineJohnson

There.

I've done it.

I've dropped the autism bomb.






MoreAutismBomb

comments...

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TheBombPart2 02 Jun 2005 - 14:57 CatherineJohnson



So yesterday, some of the moms on the aqueduct were debating whether anyone from our school ever gets into Harvard.

One of them said, "The only reason to go there is so you can spend the rest of your life dropping the Harvard bomb."


MoreHarvardBomb

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SpotTheFallacy 02 Jun 2005 - 01:41 CarolynJohnston

There's a new book out called "National Differences, Global Similarities: World Culture and the Future of Schooling", by two education professors at Penn State, and published by Stanford University Press. It was discussed in yesterday's PhysOrg.com newsletter (hat tip: bernie).

They analyzed data from the Third International Study of Mathematics and Sciences, which in 1994 and 1999 collected a lot of data on educational effectiveness in 41 countries. From the article:

Their findings indicated a frequent lack of positive correlation between the average amount of homework assigned in a nation and corresponding level of academic achievement. For example, many countries with the highest scoring students, such as Japan, the Czech Republic and Denmark, have teachers who give little homework. "At the other end of the spectrum, countries with very low average scores -- Thailand, Greece, Iran -- have teachers who assign a great deal of homework," [author] Baker noted.

Their conclusion is that homework is actually bad for learning, proving that even education researchers can be tripped up by the correlation implies causation fallacy.

But worse than that, homework is not politically correct:

If schools expect every family to reinforce the child's learning process at home, they need to realize that, when families are unequal to the task, students will not receive the same quality of education. The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.

"Those families that are better able to marshal resources to support outside school learning will likely gain disproportionate advantage," he added.

Fixing this problem will put us one step closer to the year when everyone will finally be equal.

comments...

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SuitablyHorrified 02 Jun 2005 - 14:55 CatherineJohnson



That's me. Suitably horrified:

The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.

"Those families that are better able to marshal resources to support outside school learning will likely gain disproportionate advantage," he added.


While we're playing Spot the Fallacy, how about a round of Identify the Logical Inconsistency?

I'll go first.

a) homework has no effect on learning

b) homework will increase educational inequality because white children will do it, and black children will not

Both statements cannot be true.

comments...

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SuitablyHorrifiedPart2 02 Jun 2005 - 01:48 CatherineJohnson



OK, this is maybe not the best criticism for me to be raising after my 50% of 10 is one-half of 5 fiasco, but isn't there a problem with the math here?


The addition of homework will only exacerbate existing inequities within a nation's student population and pull down overall scores, said Baker.


So the way this works is . . . homework unfairly raises the scores of kids in high-functioning families, while the scores of kids in low-functioning families remain in the cellar, thus increasing Grade Inequality.

So how exactly do you get decreased overall scores in that scenario?

Doesn't the mean go up when the top scores go up?

Isn't that the whole point of disaggregating the data?



MoreDisaggregatedData

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FromAReader 11 Jun 2005 - 16:39 CatherineJohnson

My daughter was tutored for six months at the Sylvan Learning Center in [name of town omitted]. The . . . owners of the Center . . . said that Everyday Mathematics was great for their business. The program being used in several communities near the Center. [Name of town omitted] now has a Kumon! Of course this data never shows, because they dont want to know! My daughter went from two grades below grade level to two grades above grade level in the six months she was tutored. When she took the Stanford 9 she scored in the 90 percentile. No credit to Chicago Math but to her tutoring. She also did Saxon at home.

spaced repetition:

My daughter went from two grades below grade level to two grades above grade level in the six months she was tutored. When she took the Stanford 9 she scored in the 90 percentile.


ATeachersStory
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)

comments...

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IHaveAPlanAndImStickingToIt 02 Jun 2005 - 14:47 CatherineJohnson



I'm going to clean off my desk today.





ImNotKidding

comments...

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ADifficultChild 16 Jun 2005 - 17:42 CatherineJohnson



Barry Garelick told me to go find Ralph Raimi's web site and read his articles.


This is an excerpt from the one I started with:

If I were asked what seriously could be done to teach something useful in the name of math to this kid, I would advise starting with the arithmetic of fractions, i.e. what she failed to learn in the 5th and 6th grades and since, and their applications and meaning of course. I believe this could be made interesting to her once she knew she didn't have to learn all those symbol manipulations she has been plagued with these last five years. But there is nobody to do this for her, and there is no clear incentive, since all she thinks she needs is to pass the next few exams.

Even with time and a knowledgeable teacher as private tutor, fractions might not make it past the starting gate, since she has been persuaded that her calculator has rendered them unnecessary.


Read the whole thing.


ADifficultChildPart2
TeachUsMath
PenfieldParents
DontRelyOnStateTests
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

comments...

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LiveBloggingTheSpellingBee 02 Jun 2005 - 15:40 CatherineJohnson



Joanne Jacobs says Throwing Things is liveblogging the Spelling Bee.

Spelling is our other big obsession around here.







BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory

comments...

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ProgressReportPart2 02 Jun 2005 - 15:37 CatherineJohnson



I can't say my desk is looking a whole lot better.


comments...

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NewAndImproved 02 Jun 2005 - 16:44 CatherineJohnson

OK, progress.

I have stacked, and I have dusted.

Stacking is good.



The area beneath my desk, however, looks NothingLikeThis.

Nor do I envision a day when it will.

comments...

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DavidKleinAtAEI 06 Jul 2005 - 16:52 CatherineJohnson

I've learned from David Klein that the American Enterprise Institute posted his hand-out materials, not the speech he gave.

go here to read it

excerpt:

While he was president of the NCTM, Jack Price said that minority groups and women do not learn math the same way as white males. He stated:

"... women have a tendency to learn better in a collaborative effort when they are doing inductive reasoning."

This was in contrast to the way white males learn math. According to Jack Price,

"males ... learn better deductively in a competitive environment."

This attitude toward women and minorities is consistent with the NSF funded math books. They rely heavily on superficial repetitive patterns, a form of inductive reasoning, rather than logical deduction, which is the core of mathematics.

The NCTM has attempted to redefine mathematics itself in order to support a notion of learning styles in math associated with skin color and gender.

This is misguided in the extreme.

I'll say.

comments...

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CanAnyonePlayThisGame 02 Jun 2005 - 19:10 CatherineJohnson


re: DavidKleinAtAEI


I'm interested in the subject of sex differences in math learning & achievement. (I think the whole idea that Blacks, Hispanics, and Women all Learn The Same Way is ludicrous on the face of it.)

I don't personally have a problem with the idea that men may have a biological advantage when it comes to learning math (or to very high achievement in math, I should probably say).

Nor do I have a problem with the idea that if they do have an advantage, it has to do with spatial ability.

I find this notion pretty interesting, as a matter of fact, and have now spoken to two women with degrees in mathematics who went out and learned how to draw specifically to increase their spatial ability.

(When I finally learned to draw last summer, something I had wanted to do all my life, I was in the class for about 5 seconds before I realized: this is math. More on that another day.)

Anyway, it may or may not be true that spatial reasoning has something to do with high achievement in mathematics, and it may or may not be true that men tend to be better at spatial tasks. As far as I can tell, the evidence for these two propositions is reasonably strong at this point, though I could be wrong. I'm not doing a review of the literature here.

What I do know is that: I want to learn real math whether I'm good at rotating figures inside my head or not. (I stink at rotating figures inside my head.)

I certainly do not want the NCTM to decide, on my behalf, that I need to learn a kind of math that isn't really math, because I'm a woman, so therefore I'm out of the running for the standard deductive math (white) boys and (white) men get to know.

Furthermore, if the ability to solve certain spatial tasks is useful to learning and understanding math, then I want to develop spatial ability.

I want to learn deductive math, and I want to 'remediate' anything in my own way of thinking and learning that will help me to do that.

comments...

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DolcianiStructureAndMethod 02 Jun 2005 - 20:11 CatherineJohnson


Yay!

My copy of Algebra Structure and Method Book 1, by Brown, Dolciani, Sorgenfrey, & Cole, just came. I discovered Dolciani in Barry Garelick's article on math ed:


Accomplished mathematicians wrote many of the texts used in that earlier era , and the math—though misguided and inappropriate for the lower grades and too formal for the high school grades—was at least mathematically correct. Some of the high school texts were absolutely first-rate, and new-math–era textbooks like Mary Dolciani’s “Structure and Method” series for algebra and geometry continue to be used by math teachers who understand mathematics and how it is to be taught.


I obsessively tracked down an edition from 1994, because that is the edition The Principal's Guide to Raising Math Achievement cites, but I have no idea whether the 1994 matters if the title and all four authors are the same.



I just came across a site that sells the teacher's edition as well. At least, it does today (click on the book):

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TeachUsMath 14 Jun 2005 - 21:44 CatherineJohnson



Eventually Carolyn and I will get links to all the parents' sites & education blogs.

Here is Penfield, NY's parent group, Teach Us Math.

Be sure to check their blog. Commenters have left links to terrific sites.


PenfieldParents
ADifficultChild
ADifficultChildPart2

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ParentAtTeachUsMath 02 Jun 2005 - 20:41 CatherineJohnson

Oh my goodness.

I'm reading through the comments at Teach Us Math.


Our 7th grade, straight A math student, came home approximately five weeks ago and very proudly informed me that she finally got it. The fraction 1/4 equals .25 which equals 25%. I told her I was very proud of her, and when she left the room I cried. Of all the school districts we have had our children in, only Penfield has allowed children to pass math without knowing any math.

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SayItAgain 02 Jun 2005 - 20:46 CatherineJohnson

Another commenter at Teach Us Math.


I teach math now at a university. The most significant barrier to students mastering calculus is poor symbol manipulation skills - especially with respect to fractions. These skills are acquired over many years with practice. First with paper and pencil calculations, then with operations with fractions, then with the first year of algebra. I have never met a student who was skilled at symbol manipulation who had any difficulty digesting the basic concepts of calculus. Students who stumble all over themselves doing basic algebra never really grasp the fundamental ideas. Unfortunately, at the university level they will never get enough practice to make up for the deficits they bring from K-12.


This is a universal perception. I have yet to meet a college-level mathematics professor who did not immediately bring up students' inability to handle fractions as a barrier to all future achievement.

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TakingABreakPart2 02 Jun 2005 - 22:15 CatherineJohnson

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WebmasterApologizes 03 Jun 2005 - 01:12 CarolynJohnston

To Catherine, who couldn't change the name on one of her posts; and to all who tried and were unable to comment today: I'm sorry. It was my fault.

Pick an excuse:

a. I gotta stop webmastering when I'm drowsy.

b. I'm a novice at this, so sue me!

Anyway, the problem is all fixed now.

Please note our new 'anonymous login' feature! Enter a comment, and when the system prompts you for a username, give:

username: KtmGuest

password: guest

So if you're shy, now you can leave us a comment anyway, and we hope you will!

comments...

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HappyFaceMath 03 Jun 2005 - 02:12 CatherineJohnson



See? I told you math is fun.

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SummerSupplement 27 Jun 2005 - 17:25 CarolynJohnston

Ive been looking around a bit for an alternative to Saxon 76 for summer math practice. This was mainly because we only have 3 months, and Saxon homeschool books have well over a hundred lessons in them -- I would have had to go through it, picking what lessons to skip, and I'd rather not.

I decided to take the opportunity to introduce the math series Ben is going to be using in his middle school math classes: Prentice-Hall Mathematics. Our school district has widely adopted Connected Math for grades 6-8, and I fought hard to get Ben into one of the two remaining schools in our district that use a standard curriculum. But it occurred to me the other day that I know very little about this school's curriculum choice: subconsciously, I guess I'd decided that any school with the sense not to jump on the CMP bandwagon could be trusted to choose a decent math curriculum.

But of course, there's no being sure about that. The world isn't black and white, and there's more than one way to mess up a math curriculum. But I did as well as I could do within this district, and now I need to find out what we're in for.

So I ordered a copy today of Prentice-Hall Mathematics, Course 1.

I must say, the table of contents is right up my alley:

1. Decimals
2. Algebra: Patterns and Variables
3. Number Theory and Fractions
4. Adding and Subtracting Fractions
5. Multiplying and Dividing Fractions
6. Ratios, Proportions, and Percents
7. Data and Graphs
8. Tools of Geometry
9. Geometry and Measurement
10. Algebra: Integers
11. Exploring Probablilty
12. Algebra: Equations and Inequalities


Short and to the point, with an early emphasis on the critical topic, fractions. Though we could probably do with a break of a year or two from Exploring any more Probability, but that's just too much to hope for.

FreeWorksheets
TreadingWater

SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

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NoComment 07 Jul 2005 - 02:04 CatherineJohnson

Increasingly, the nation's richest are spending their money on personal services or exclusive experiences and isolating themselves from the masses in ways that go beyond building gated walls.

These Americans employ about 9,000 personal chefs, up from about 400 just 10 years ago, according to the American Personal Chef Association. They are taking ever more exotic vacations, often in private planes. They visit plastic surgeons and dermatologists for costly and frequent cosmetic procedures. And they are sending their children to $400-an-hour math tutors, summer camps at French chateaus and crash courses on managing money.

When the Joneses Wear Jeans


also see:
MoneyTalks
SpecialEdReferralsEverydayMath

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BrianLehrerOnNYCScoresNow 01 Oct 2006 - 17:17 CatherineJohnson



The Brian Lehrer show is covering the NYC score increase now

Definitely worth listening; they're giving the Mayor's guy a lot of trouble at this point.

He's giving them the run-around, IMO.

His point: it's sad that, instead of celebrating all the hard work and great scores, people are looking for Bad Stuff.

Brian Lehrer's response: we're journalists. We look for Bad Stuff.


Ed just called with something I missed; apparently the mayor's guy said that there is a widening gap between high and low scorers. The kids who were already at 3 or 4 scored higher; the kids at 1 and 2 scored lower. [IIRC, scores of 1 and 2 are 'below proficiency'; 3 is 'proficient'; 4 means the student scored above proficiency.]

The mayor's guy (sorry, I didn't catch his name) said this pattern was seen across the board, at both high- and low-performing schools.

He also says they didn't take a 'significant' number of non-English speakers out of the testing pool.

OK, just caught his name: Dennis Walcott, Deputy Mayor for Policy



Now they've got Eva Moskowitz on.

I can't say she's doing too well.

She's not going to be 'pushed into an analysis' . . . something like that.



Bob Tobias from NYU (yay Hometeam) is up next, expert on testing.

'much more in-depth analysis of the data before we can' say what's what etc. etc.

Brian Lehrer: what do you really think?

[Thank you, Brian Lehrer.]

'To me that says that something other than the policies in . . . [NYC] is responsible . . '

'I don't see evidence for the efficacy of the reforms . . . ' UPDATE 9-30-2006: Bob Tobias was right.

'We have nothing to compare the city data to.'

State scores went up everywhere. He's firm on this: if scores went up everywhere, then the rise we see in NYC scores isn't attributable to Bloomberg reforms.

[I don't understand the ins and outs of NYC testing. City students apparently take two sets of tests: the state tets, and a unique set of tests only NYC takes. Apparently next year, because of NCLB, these tests will be given across the state, not just in the city.]

Back to Tobias; I think it's fair to say he thinks the scores are flukey. 'I've been looking at scores for 30 years and I've never seen rises like this; These rises are really incredible, etc.'




The folks at Everyday Math must be writing up their press releases right this minute.




Now they're onto political analysis: Mayor Bloomberg told voters he'd do for education what Rudy did for crime, and now he can say he did it.

I hope Diane Ravitch is surrounded by Good Friends and Soothing Music, seeing as how her view of Mayor Bloomberg can pretty much be summarized as:




(click on the Mayor for the article)


'It looks nit-pickey to the public to be raising questions.'

Are we teaching to the test? Parents worry. We are as a society so solely focused on the tests that there are schools not teaching art as much as they used to. [this is not a concern for me now that math has become a branch of English Language Arts]



NYC HOLD on 'Children First', which seems to be the all-constructivist-all-the-time program Bloomberg & Klein instituted top-down



Next up on the Brian Lehrer show: chick lit . . . 'I am proud to admit I write chick lit . . . I try to empower myself to write chick lit . . .It's about being a single woman and owning that . . . '

Etc.



hoo boy. wait til you've got a coupla kids in the public school system, honey.

ok, back to math.



Here's Bob Tobias in the Post: UPDATE 10-1-2006: sorry, link no longer working; NY Sun link good

Robert Tobias, director of the Center for Research on Teaching and Learning at NYU, wasn't certain how much credit to assign to Bloomberg's reforms.

He noted that districts with the highest fourth-grade gains had the highest number of third-graders held back last year.

In District 9, which posted a huge 17.5-point gain, more than 430 kids were held back, and roughly 12 percent fewer pupils took the tests this year.

"I'm not saying that the policies aren't working — however, I think we've got to put it in perspective," Tobias said.

"I would expect that [retention] would have an impact on the achievement gap."




Brian Lehrer Show on NYC scores 2005
stupid mayor trick
Thank you, whole language
guess and check reading
stupid mayor trick part 3: the good news
The Spin Doctors reading scores 2006

National Reading Panel (official website)
The Partnership for Reading
(govt website: "bringing scientific evidence to learning")
National Reading Panel report full text (pdf file)

comments...

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TakingABreakPart3 03 Jun 2005 - 17:48 CatherineJohnson










(click on the painting for artist info)

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TeenageBrain 20 Jan 2006 - 00:45 CatherineJohnson

Jerry Becker has posted TIME MAGAZINE's article on the teenage brain over at The Math Forum.

I'm especially interested in this subject, because, last I checked, researcher Jay Giedd seemed to have found a second window of very active brain growth in adolescence -- a discovery I interpret to mean that 'Birth to 3' is not the only period in a child's life that can benefit from intensive intervention.

(I could be wrong; this is what I remember of the first coverage of his research a few years ago.)

One of these days I'll get around to reading The Myth of the First 3 Years: A New Understanding of Early Brain Development and Lifelong Learning, and while I'm at it I'll re-read Malcolm Gladwell's review.

I've seen special ed programs that simply give up on middle schoolers, because the window has closed.

I'm against that.




update 1-19-2006

FRONTLINE interview with Giedd:

The most surprising thing has been how much the teen brain is changing. By age six, the brain is already 95 percent of its adult size. But the gray matter, or thinking part of the brain, continues to thicken throughout childhood as the brain cells get extra connections, much like a tree growing extra branches, twigs and roots. In the frontal part of the brain, the part of the brain involved in judgment, organization, planning, strategizing -- those very skills that teens get better and better at -- this process of thickening of the gray matter peaks at about age 11 in girls and age 12 in boys, roughly about the same time as puberty.

After that peak, the gray matter thins as the excess connections are eliminated or pruned. So much of our research is focusing on trying to understand what influences or guides the building-up stage when the gray matter is growing extra branches and connections and what guides the thinning or pruning phase when the excess connections are eliminated.

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PatternLearning 06 Jul 2005 - 11:26 CarolynJohnston

see also: SummerSupplement.

Another reason I want to supplement from the Prentice Hall text this summer is to familiarize Ben with the style of his middle school math series, so we can skip the format shock period at the beginning of the school year. This is the period when the style of the book seems so new and strange, and he can't find the problems he's supposed to do, and he can't focus on the topic just because of the strangeness of the book.

This is definitely something that has to be taken into account in Ben's learning. He copes better with transitions of all sorts over time, but there is still a cost to making changes.

Besides, he is starting middle school this fall. He doesn't know what's about to hit him, and his teachers keep assuring me that my concerns about his managing lockers, his homework, the transitions between classes, are all pointless. I hope they're right about that; I think they're crazy, but I hope I'm wrong.

At least, if all goes well this summer, Prentice-Hall Mathematics will be a familiar friend in the fall.

Catherine and I both have a lot of familiarity with 'format shock', because it's a characteristic that everyone has to one degree or another, and people on the autism spectrum have extreme cases. Transitions of any sort are just hard for people with autism disorders, even mild ones.

One of the things that autism affects is the ability to extract the main idea from something. This is why transitions are difficult; because in the prior learning experience, the person may have focused on, and felt supported by, something that wasn't central to the topic. When the support vanishes -- which it may at any time, if it's not central to the topic -- it's disruptive. The support itself can be something very insignificant, like the color or font of a 'highlights' box on the corner of a page.

But we all rely on incidental supports to some extent, when learning something new. Non-central props help support us as we move to the next stage in our learning. At the other extreme, imagine how frustrating it would be if you were trying to learn something really new and difficult -- like Mandarin, say -- and the font, style, and problem set layout were dramatically different from day to day.

When Ben was taking Saxon Math in grades 1-3, he became very comfortable with the predictable format of its worksheets: a word problem at the top (usually with a rectangle to do little drawings in), followed by problems attacking the central feature of the lesson from different angles, all laid out similarly from day to day, and always with the same font.

As long as it is actually helping Ben's learning instead of derailing it, I'm fine with Ben's depending on a predictable format. I want the book itself to be out of the way of his learning, not to hinder it by providing continual little shocks.

Still, pattern learning can really derail real learning, by preventing a kid from generalizing what he knows. Consider, for example, a kid who always does subtraction problems oriented vertically, and when introduced to a subtraction problem that's oriented horizontally, can't do the problem. It could happen; but most math books take great care to avoid introducing fixed patterns like that.

A little variation nudges a student toward full mastery, by whittling away what's unessential.

Most textbook writers know this. It's a much more common problem these days for the format, and the desired response, to be unpredictable.


PatternLearningPart2
PatternTraining





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PatternTraining 06 Jul 2005 - 11:25 CatherineJohnson



I think I first learned about pattern training from Temple.

Pattern training is a big problem with animals, and also with autistic people . . . but now that I’m trying to teach my son math I realize it’s a huge problem for me, too.

I just didn’t know it.

The best way to understand pattern training is to think about dogs.

Pattern training happens when you always train your dog in the same place at the same time using the same sequence of commands.

The dog learns the pattern, not the individual commands, so he can’t generalize what he knows about sit in the training situation to a whole new situation.

If you ask him to ‘sit’ outside of a training session, he doesn’t know what you’re talking about.

The same thing happens training service dogs.

You can’t just train a dog to cross a corner.

You have to train him to cross lots of different corners, in lots of different places.

Otherwise he only knows how to cross the one corner, and that’s it. Take him to another corner a block away and he’s stumped.

He doesn’t generalize.

This is a huge problem in autism, and it’s the heart of Temple’s & my book, Animals in Translation. Autistic kids don’t generalize well, and neither do animals, and Temple and I argued that this gives autistic people like her unique insight into the behavior of animals.

I believe this is true, but since we wrote the book I think I overestimated just how great we ‘typicals’ are at generalizing.

TO BE CONTINUED





PatternLearning (format shock)
PatternLearningPart2
SummerSupplement





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RussianMathPart2 08 Jul 2005 - 23:24 CatherineJohnson

My copy of Mathematics 6 came yesterday, and it is incredible. A beautiful, beautiful book. The design is exquisite (in my next life I'm going to be a graphic designer) and I've learned things just reading the first 5 pages.

I'm pretty attached to the Saxon books, but I actually feel love for this one.

[Now I'm thinking . . . do I sound completely nuts? Well, if I do, the beauty of a Bliki is that I can DELETE THIS POST later on today, after I've come to my senses.]

I'm going outside right now to do the problems in Chapter 1.1 Factors and Multiples.



Our Favorite Supplements
RussianMath
RussianMathPart3
WhyILoveCarolynh
ItTakesChops
Mike McKeown comment
IndusAcademy

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BasBraams 04 Jun 2005 - 19:44 CatherineJohnson

I'm a big fan of Bas Braams.

I'm just realizing I haven't read all of his posted works, so I'm getting started.


update: oh my gosh! I've just discovered Bas Braams has a blog! It's called Scientifically Correct.


update 2: He is writing Scientifically Correct with Ze'ev Wurman.

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HowToGetParentBuyIn 10 Oct 2006 - 01:58 CatherineJohnson


The TRAILBLAZERS teachers' guide devotes a number of sections to strategies for neutralizing incensed parents.

I had planned to quote some of these passages, and then, tonight, found an online TRAILBLAZERS document (PDF file) that's chock-ful of them:

Be pro-active with parents. Don’t wait until complaints hit. People have done a lot of things to involve parents, from math nights to big math carnivals, where the kids teach the activities to the parents. There are letters in the program that go home to parents.

When this teacher says 'there are letters in the program that go home to parents,' she doesn't mean that her school writes letters to parents once a month.

She means that her school has purchased, as part of the TRAILBLAZERS 'package' (which is enormous, I've seen it; worse yet, I've lifted it) a set of special TRAILBLAZERS Dear-Parent letters to be photocopied and sent home in the backpack at regular, designated intervals.

What the parent sees is a friendly letter from the school about her child’s math program.

What the school sees is a professionally-developed public relations campaign targeted to dissenting moms & dads.

The TRAILBLAZERS Dear Parent letters are not intended to serve an educational purpose. At least, no educational purpose is mentioned in any of the supporting materials I've seen as yet.

The explicit and openly stated purpose of the TRAILBLAZERS Dear Parent letters is to promote parent buy-in.

All of which means that not only am I paying for a program I don't like and don't want, I am paying for the press kit to persuade me I'm wrong. Maybe this isn't exactly the kind of thing the Boston Tea Party was about, but it's getting there.


+ + +


And here is another strategy for dealing with parents!

This strategy was developed by one Barbara Martin, principal of the Holmes Elementary School in Chicago:

[For parents] we do also have a math day, and on that math day, we invite parents to be in the room. The kids do math all day. In order to get the parents in the room, I offer them a little stipend. I only offer the stipend to the parents who can stay in the room all day—they’re helping the teacher, because they’re doing math all day, with Trailblazers and all the manipulatives. At the same time, they’re also getting to see what kids do. There are other parents that visit math day and leave because they can’t stay all day. We have a good turnout.

Ms. Martin has had fantastic success with TRAILBLAZERS ---

"For some of my children, our feeder schools are saying, “Please, please send us more like these.”

+ + +


So let's see how Holmes Elementary School children are faring in the high-stakes world of standardized testing.


+ + +


Oh dear.

Third grade: 30% of the kids meet state standards.
Fifth grade: down to maybe 27%.
Eighth grade: down to 5% meeting state standards.

This is an all-black, poor school, so they've got a lot to contend with. Maybe they'd have a 95% fail rate in 8th grade no matter what curriculum you gave them.

But look at their reading scores.

3rd grade: maybe 17 or 18% meet standards.
5th grade: up to 36 or 37%meeting standards.
8th grade: they're up to around 44% meeting standards.

Math goes down, reading goes up. Same kids, same school, same period of time.


EverydayMathDoesItToo
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
NoCommentPart2
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers

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ADifficultChildPart2 16 Jun 2005 - 17:44 CarolynJohnston

In ADifficultChild, Catherine linked to a story that Ralph Raimi told about a high school girl he evaluated, on behalf of her mother, who was becoming concerned about her problems in math class.

He talks about specific problems with her math education, which begin with her great confusion about basic fraction manipulation and the operations of algebra, but in the end are dwarfed by her resentment of math.

She had never heard of "the number line", and when I suggested a yardstick she said she had never used one. She didn't know what numbers appeared on a yardstick, or what I was talking about when I wanted to know the position of the markings between inch or foot labels. So I drew a picture and got a reluctant agreement that there must be such things.

His conclusion about her future vis a vis mathematics is pretty dismal.

She is scheduled to take a non pre-college math next year (some- thing like statistics one term and business math the other, but I've forgotten what she told me on that), and she could probably pass that one now. It is cruel and inhuman to push algebra and trig on her, and truth tables forsooth, this year, given her background and her school's attitude towards textbooks and other such unnecessary explanations. Can I recommend she spend extra time on math, besides the torture of a meaningless class every day? But I haven't found out if it is even legal for her to stop her present course at all. I'll have to ask around.

If I were asked what seriously could be done to teach something useful in the name of math to this kid, I would advise starting with the arithmetic of fractions, i.e. what she failed to learn in the 5th and 6th grades and since, and their applications and meaning of course. I believe this could be made interesting to her once she knew she didn't have to learn all those symbol manipulations she has been plagued with these last five years. But there is nobody to do this for her, and there is no clear incentive, since all she thinks she needs is to pass the next few exams.

Now here is the part I find desperately sad.

She livened up considerably when we talked about things which were not mathematics. She wants to grow up to be an emergency room nurse. She likes her biology class and her "history and music" class, where she learns about "classical" and "baroque" music. She says she can't take chemistry, which I had suggested as useful for a nurse, because she wasn't going to take Math III. There was lots of math needed for the chem course, she said, more than for the physics. (Yet she asked irritably several times during our interview "what good was all this math" for her.)

She didn't know, and apparently Ralph didn't either, that the certification examination for a registered nurse in most if not all states (and certainly in New York, where 'Sarah' lives) contains algebra questions, and nursing school requires students to be able to pass a college algebra course. They like RNs to be able to do basic calculations of dosages and mixtures and the like; careless errors by an RN can be dangerous.

I've had nursing students who hated math as much as 'Sarah' did, who suddenly found that they had to take a college algebra class in hand and try to get a passing grade in order to get a job in their chosen career path. All of them suffered hugely; some of them couldn't do it at all. I knew one student who, having long since finished most of the coursework required to graduate from her nursing program, had been working for several years as an aide in a nursing home while taking college algebra over and over, trying vainly to get a passing grade.

In order to avoid any more mathematics, this girl has already shut the door on chemistry. Will she shut the door on her chosen career just as casually?

[ Afterword: I may have to eat my words. After I wrote this, I went looking online for information about nursing licensure requirements and nursing programs. The national licensure test for RNs is the NCLEX-RN. On a brief review of some practice questions from the NCLEX, I did not find any specifically relating to math (although I did find some relating to chemistry). Most of the nursing schools I found did have some kind of algebra requirement, although often high school algebra was sufficient. It may be that requirements were once stiffer at Binghamton University's nursing school, where I encountered my struggling students; it may be that requirements have been relaxed. If anyone can fill me in on the status of math in nursing education, I'd like to know more about it. -- CarolynJohnston ]


ADifficultChild
TeachUsMath
PenfieldParents
DontRelyOnStateTests
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

comments...

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ATeacherUsingTrailblazers 10 Nov 2005 - 01:19 CatherineJohnson

One of the things that I’ve learned is what homeworks are good homeworks to send home and what homeworks we really need to do in class because of parent frustration. Last year, not yet knowing this, I sent a homework home and got back such venomous mail: “What is this? Why are you asking my 3rd grader to do this? If you ever send another magic square home, I am pulling my child out of the school. I can’t do this, and neither can he.” So now I’m just making better choices on what to send home.

I think we can all agree that it's important for teachers to make good choices (pdf file).

But why any parent would object to an 8-year old child being asked to construct a magic square for homework is beyond me.

After all, think how much conceptual knowledge that child will have after his mom has looked up Magic Squares on the internet and helped him draw one.


HowToGetParentBuyIn
EverydayMathDoesItToo
ILoveTheWorldWideWeb
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers

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TeacherAppreciationWeek 31 Oct 2005 - 14:51 CatherineJohnson

This is obviously the time to say that Christopher's math teacher for the second half of the year, Nancy Woeckener, told one of the other moms way back in September: "I don't believe in giving kids homework their parents are going to have to do."

Mrs. Woeckener has been a terrific teacher for Christopher, and for me.

Not only did she not assign homework for Christopher's parents to do, but when she taught a unit that stumped the moms (on figuring compound interest, and, yes, I am embarrassed)—she wrote out a precise mathematical explanation of what she was teaching and sent it home to all of us.

I now know how to figure compound interest the easy way, using the commutative property, thanks to Mrs. Woeckener!

(I know that I know how to figure compound interest the easy way, because another friend of mine, whose son is in a different math class, had to ask me the other day how to do it. She'd forgotten, probably because she hadn't quite gotten the concept back when her son's teacher was going over it. Not only did I remember how to do it, I could explain why the formula worked. Thanks to Mrs. Woeckener, I have Gained Conceptual Knowledge!)

Mrs. Woeckener answered emails instantly, telling me exactly when tests would be given & what would be on them.

Last but not least, she kept an eye out for Christopher when he joined her class mid-year. It's rare for a child in this district to move up a level in the middle of the year. The district is looking to cut children from the Phase 4 class, not add. Christopher was the only child who made the jump (as far as I know) and I've already mentioned more than once that, going into the fall, he wasn't the kid anyone would have pegged to be 'the one.'

He had to come from behind.

Not long after Christopher had moved to Phase 4, Mrs. Woeckener sought me out on a field trip and introduced herself. She told me she was keeping track of Christopher, that he was doing fine, and that she'd get hold of me right away if she had concerns.

She also gave me the feeling that her plan was to see to it there wouldn't be any concerns.

And that's exactly the way things worked out.

Christopher was a lucky boy to have Mrs. Woeckener as his math teacher this year.


ILikeMath

comments...

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EverydayMathDoesItToo 22 Jun 2005 - 14:18 CarolynJohnston

Regarding Catherine's awesome post, HowToGetParentBuyIn:

It's just occurred to me that for two years now, since our school started using Everyday Math, little math pamphlets about the Everyday Math units have been coming home on Xerox copy paper, like everything else coming from the school. And come to think of it, there are always little helpful hints for parents on how to do the homework.

I should have realized I was being public relationed. The school never sent home little parent hints on how to help with Saxon homework.

So that's three points of reference: Trailblazers and Everyday Math are actively trying to manage their relationships with parents. Saxon is not.

My question is: why would school districts turn themselves inside out to adopt these programs, when the publishers acknowledge that they are potentially putting themselves at odds with parents? What's in it for them?

I have my theory about why reform math programs roll through the educational world. More to come: stay tuned.


HowToGetParentBuyIn
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
NoCommentPart2
AnotherGemFromMathForum

comments...

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ILoveTheWorldWideWeb 22 Jun 2005 - 14:19 CatherineJohnson

I knew if I just kept looking I'd find them.

Somebody would have made helpful pdf files of all the TRAILBLAZERS PARENT LETTERS and posted them on the web.

Sure enough, somebody did.


HowToGetParentBuyIn
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
EverydayMathDoesItToo
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
CompareAndContrast

comments...

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ForgivingDivision 14 Jun 2005 - 01:33 CatherineJohnson

It's official.

TRAILBLAZERS does not teach the standard algorithm for long division at all:

The paper-and-pencil method that Math TrailblazersTM uses to do long division is somewhat different from the way long division is traditionally taught in the United States. This method, called the forgiving division method, is often easier for students to learn. They do not have to erase as much, and they learn more about division and estimation.

from:
Letter Home (pdf file)
page 6
Division and Data


+ + +


If you were wanting to see what forgiving division looks like, page six shows a forgiving division of 644 by 7.

I'm surprised they actually tell parents this is what they're doing.

Of course, by the time you get the Division and Data letter you've been receiving TRAILBLAZERS PARENT LETTERS for years and you're still in the school. They probably figure they've worn you down.



AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
ILoveTheWorldWideWeb
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

comments...

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ForgivingDivisionPart2 14 Jun 2005 - 01:40 CatherineJohnson

This is pretty droll.

Here's a parent asking Math Forum for help on his son's forgiving division homework:

From: Dan Bruce
Subject: Solving division problems using the "forgiving" method

My son has been asked to solve his division problems using the forgiving method, but he doesn't recall what this process is, and judging by the answers he's arriving at, he's way off base. Have you ever heard of this method and could you demonstrate it using the example 100/6?

Thanks.


And here's the answer:

Date: 05/15/2002 at 09:49:17
From: Doctor Mitteldorf
Subject: Re: Solving division problems using the "forgiving" method

I'd never heard of the forgiving method, and couldn't find references to it in our archives. From a reference that I found in a discussion group on the net, I gather that it's about piecing together whatever multiplication facts you are comfortable with to solve the problem at hand.

Suppose you want to know how many 6's there are in 100. You can remember that 7*6=42, so you write down the 7 as part of your answer, then take the 42 away from 100 and have 58 left.

Next step: you might say the same thing. There's another 42 in there, so there's another 7 sixes. Write down another 7 under the first one, and subtract 42 from 58.

Now you've got 16 left, and you know you can squeeze 2 sixes out of 16, but not 3. So you write down the 2 under your 7's and add them up: 7+7+2=16.

You've pulled 16 sixes out of 100 (with 4 left over that wasn't enough to make another 6). You did it in groups of 7, 7 and 2, but someone else might have done 5 and 5 and 5 and 1, and the "standard" method would have been to do 10 + 6. The method is forgiving in the sense that your partial guesses don't have to be anything in particular, as long as you don't overshoot.

- Doctor Mitteldorf, The Math Forum


+ + +


Yup.

I can just see all the extra learning about division and estimation that's going on here.

And so much less erasing, too!


ForgivingDivision
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ILoveTheWorldWideWeb
HowNotToTeachMath
ThirteenQuartersInTerc
MathInTheBlood
StrugglesWithLongDivision
AboutLongDivision
WhoSaysLongDivisionIsHard

comments...

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TryThisWithForgivingDivision 14 Jun 2005 - 01:45 CatherineJohnson



Go ahead.

Try it.

ForgivingDivision
ForgivingDivisionPart2
TeacherGuideEverydayMath
EverydayMathEpilogue
ILoveTheWorldWideWeb
ThirteenQuartersInTerc
HowNotToTeachMath
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
WhoSaysLongDivisionIsHard

comments...

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SingaporeMathPlacementTest 24 Apr 2006 - 15:35 CatherineJohnson

The placement test for Singapore Math is here, along with basic info about the curriculum.

A very useful Quick Guide is here.

Boiling it down:

• The series they recommend for grade school kids is Primary Mathematics US edition.
  

• Each grade uses two textbooks (and corresponding workbooks) per grade, labeled A & B. 'A' is used in the fall semester, 'B' in the spring semester.

I think it's a terrific idea to order, as well, one of the Challenging Word Problems books, and ask your child to do one bar model a day. That's what I'm doing with Christopher, and with me, too.

I finished the entire 3rd grade book of Challenging Word Problems -- all 268 of them -- on Saturday!

[update: When I say 'I,' I mean me, Catherine. I did the problems myself. I've only managed to haul Christopher through 10 or 15 bar models so far.]

Now, when I see a problem like 'There were 33 children in Mrs. Jones's class, 5 more boys than girls. How many girls were in Mrs. Jones's class?' an image of a bar model instantly pops into my head.

I think that's a good thing.

On the other hand, I'm having serious trouble summoning a bar model for a rate-and-distance problem in the opening review material in Mathematics 6, the newly translated Russian text.

Sigh.


There are a couple of other Singapore Math books for parents that I think are terrific. More on that later.



FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides

TeachYourChildToTypeThisSummer

advice on Singapore Math 6-2005
Singapore Math book recommendations in a nutshell





comments...

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TakingABreakPart4 07 Jun 2005 - 01:54 CatherineJohnson

Off to Playland today, where I will not be riding this.

comments...

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DontRelyOnStateTests 05 Oct 2005 - 00:28 CatherineJohnson

A quick note on state tests.

I'm sure both Carolyn and I will have more to say about this, but since Instructivist has raised the question of 'what's on the tests?' I wanted to post these links.

I read fairly often that 'math scores have risen over the past decade, but reading scores have remained flat.'

Assuming I understand Tom Loveless's research correctly, we should probably all drop what we're doing right this minute and send a letter to our respective newspapers urging the staff to delete the 'math scores have risen' macro from their word processors:

Despite sharply rising test scores on both the NAEP Math and most state math tests, the Brown Center's analysis of the difficulty of the math items at fourth and eighth grade demonstrates that the NAEP test fails to assess essential arithmetic skills that are required for success in algebra and higher mathematics.

"The good news is that NAEP scores have risen dramatically in mathematics over the past decade," noted Tom Loveless, director of the Brown Center on Education Policy and author of the 2004 Brown Center Report on American Education. "But, given our findings, it is unclear whether this is a significant accomplishment in terms of substantial gains in mathematics skills and knowledge."

The National Assessment of Educational Progress, or NAEP as it is commonly known, assesses fourth, eighth, and twelfth grade students in math and reading. Scores on the math assessments have risen dramatically over the last 10 years, indicating that U.S. students are becoming more adept at mathematics.

But the Brown Center analysis shows that the NAEP math assessments rely on arithmetic skills that are far below the grade levels of the students being assessed. The analysis finds that almost all problem solving items use whole numbers and avoid fractions, decimals, and percentages – forms of numbers that students must know how to use to tackle higher order mathematics like algebra.

The press release from Brookings is here.

The full study is here. (pdf file)

David Klein's California standards assessment problems are an excellent way to assess your children yourself. I used them with Christopher this year.

Carolyn says they're 'golden' and I agree.

There are other good sources for assessment problems parents can use. We'll get to those as soon as we can.

Another thought: you might want to give your child the very short Singapore Math 'placement exam'.

The Singapore tests are an eye-opener, because you see exactly how far behind our kids really are.

If we had moved to Singapore at the end of 4th grade, Christopher would have been placed in second semester 3rd grade. That's a gap of 18 months by the age of 10.

Having seen the kinds of questions kids in Singapore are answering in 8th grade (we'll post those, too) I can tell you that the 'Singapore gap' gets bigger, not smaller.


+ + +


quick note:

The Singapore tests aren't upsetting; at least they weren't for Christopher. He'd never even seen some of the material, so he certainly didn't feel bad about not being able to do it.



BonusOnlineAssessmentQuestions



See also:
NewYorkStateMathCurricula
PenfieldParents
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions
sample NAEP questions

comments...

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BonusPreTeenPost 29 Jun 2005 - 02:41 CatherineJohnson



I just asked Christopher if he thought this joke was funny:





He said, "No."

Then he said, "I just put down Who cares? for everything."

I love this age.





BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
SummerSupplementTimePart2
SundaySchool
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids

comments...

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ConcreteThinking 06 Jul 2005 - 11:18 CatherineJohnson

NCTM Standards-based curricula consistently claim to enhance students’ conceptual understanding, a goal typically touted as a revolutionary advance over traditional adherence to “blind rote manipulation.” This is nonsense. When NCTM curricula such as TERC’s Investigations use the term “understanding,” they often refer merely to the obvious and pedagogically useful technique of furnishing concrete models for simple arithmetical examples, e.g. by using fraction strips to picture fractions such as 3/4 and 2/3. Every competent parent or educator knows that this is a good way to start. Unfortunately, a principal failing of Standards-based curricula is that students never move beyond, and so are forced to rely on, simple models and representations. As a result, when students confront purely symbolic representations that are not attached to physical models, they simply freeze. Their reaction, perhaps best characterized as “symbol shock,” is, in my experience, a primary cause of students’ failure to succeed in college mathematics.

read the whole thing

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WhyILoveCarolyn 08 Jul 2005 - 23:22 CatherineJohnson

Carolyn just told me she's known a few Russian mathematicians, and 'they have chops.'



Our Favorite Supplements
RussianMath
RussianMathPart2
RussianMathPart3
ItTakesChops
Mike McKeown comment
IndusAcademy

comments...

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ItTakesChops 08 Jul 2005 - 23:23 CatherineJohnson

It takes chops to solve this when you're eleven:

Two cars leave simultaneously at 9 a.m. heading toward one another from different cities that are 210 km apart. The average speed of one car is 50 km/h while the other car averages 70 km/h. Come up with an appropriate question and answer it.

This problem appears on page 5, 'Review,' of Mathematics 6: an award-winning textbook from Russia, by Enn Nurk and Aksel Telgmaa.

The 6 in the title stands for 6th grade.


+ + +


update: OK, I solved it.

But I couldn't think of a bar model.



Our Favorite Supplements
RussianMath
RussianMathPart2
RussianMathPart3
WhyILoveCarolyn
Mike McKeown comment
IndusAcademy

comments...

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WhyMathReformHappens 07 Jun 2005 - 03:57 CarolynJohnston

In EverydayMathDoesItToo, I said that I have a theory about why math reform happens.

I think math reform movements happen largely because it's boring for most teachers to teach the same math class over and over.

If you teach history, you can do it a little differently every time. If you teach the Civil War, then one year you can emphasize the Northern perspective, next year the Southern. If you teach English, you can have the kids read different books; even if you have to teach the same book every year, the discussion takes you in a different direction every time.

But fractions don't change much, and the struggles that kids have to go through to understand them don't change much either. It doesn't take too long for a teacher to get to the point where they can teach the material, and then they can get very bored with it.

And then these are teachers who care about kids; and the kids complain about how hard and tedious math can be; and the teachers want to fix that problem. They want to take away the hardness and the tedium. Why should they be bored teaching the same old dry stuff over and over, they think, when the kids are struggling and unhappy anyway? Can't we make the whole experience better for all of us?

And so math reform movements fall on fertile ground, always.

As Catherine observed in NotTheWholeStoryPart2, math reform dates back in the United States to at least 1923. The 1923 brand of math reform has come and gone, and New Math in the 1960s came and went. Math reform movements that eschew teaching standard material generally have a long half-life -- long enough to do a lot of damage -- but in the end, they fail.

The people who really go on to be able to use math in their lives -- to understand their taxes, their checkbooks, their investments, or accounting, finance, engineering, and science -- all have learned how to do calculations, how to manipulate fractions, and how to do algebra, without the aid of calculators or computers. They don't usually do it without calculators and computers, but to a man they could.

So how to alleviate boredom in the classroom, on the part of both teachers and students?

In order to stay engaged, teachers have to focus on something other than the material alone. Of course, they have to know the material cold; but they have to be interested in the process by which kids learn mathematics, get stuck, and get unstuck. Math teaching (all teaching, for that matter) takes expertise in the cognitive psychology of children; some kids will just get it, and some few will always get stuck, and you have to cast about looking for a way to help them understand. It's continually striving for a deeper understanding of the material, and a deeper understanding of the students, that can keep teaching interesting.

The book Knowing and Teaching Elementary Mathematics was a really enlightening read for me, because it showed how a teacher's understanding of mathematics at even the elementary levels can really be deepened over time, just by the challenge of trying to help many different kids understand it.

And what can keep the students interested? It's quite simple: getting it will charge a kid up. Kids love to acquire skills; they correctly see that skills bring power in the grownup world. It's repeated failure -- knowing that they're not getting it, and falling farther behind -- that will sicken a kid on math.

comments...

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SummerSupplementTime 11 Jan 2006 - 22:53 CatherineJohnson

Too much going on today!

I'm eager to think about 'teacher boredom' and ed reform . . . plus I have a terrific email from a teacher on the subject of summer regression that needs a few identifying details deleted before I can post --- and I have a life beyond this bliki, too, or at least I used to.

But all that can wait!

summer regression

I've just stumbled across what I think may be a good source of information (pdf file) on summer regression.

Tilley, Cox, and Staybrook47 studied summer regression in achievement for students receiving no educational services for three months. They found that most students experience some regression during the summer recess. Cooper et al.48 reviewed 39 such studies and found that achievement test scores do indeed decline over the summer vacation. Their meta-analysis revealed that the summer loss equaled about one month on a grade-level equivalent scale, or one tenth of a standard deviation relative to spring test scores. The effect of summer break was more detrimental for math than for reading and most detrimental for math computation and spelling. Also, middle-class students appeared to gain on grade-level equivalent reading recognition tests over summer while lower-class students lost on them. Possible explanations for the findings included the differential availability of opportunities to practice different academic material over summer (reading is much more easily practiced than mathematics) and differences in the material’s susceptibility to forgetting (factual knowledge is more easily forgotten than conceptual knowledge).

The critical points bear repeating:

• Summer loss equaled about one month
• The effect of summer break was more detrimental for math than for reading and most detrimental for math computation and spelling
  

Think about it.

One month's loss, for kids who are already at least a year behind their peers in high-achieving countries.

I think it's important to keep up your child's math skills in the summer!

(Carolyn and I have been brain-storming ways to use KTM to help-----)

TO BE CONTINUED


FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
HowToSpell
HowToSpellPart2
MoreSpelling
TheSaxonMathOfSpelling

Summer Supplement Time
linking decline in high school scores to elementary school
research on summer regression
the time costs of not teaching to mastery
U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra

comments...

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OverAtJoanneJacobs 07 Jun 2005 - 17:30 CatherineJohnson

Definitely check out Joanne Jacobs' post on MBA-types encountering educational bureaucracy.

comments...

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MoneyTalks 07 Jul 2005 - 02:06 CatherineJohnson

Money Talks, and when it does, it says, I will pay you $325 to $475 an hour for really good Direct Instruction:

Adam Fisher remembers walking home from elementary school thinking not about Mister Softee or Ms. Pac Man but about Ms. Grace, his third-grade teacher. Why, he wondered, had she explained a new math concept in such a roundabout way? If only she had laid it out like this, he recalls thinking, reworking the lesson in his head, then we would have understood it immediately.

This was not the first time Mr. Fisher had pondered the art of teaching and learning. In fact, he had been tutoring his classmates since the previous year, having discovered that he had a knack for explaining concepts so the other kids understood them.

A slender fellow with a goatee and a mass of curly hair, Mr. Fisher, 34, still tutors students. Only today his students are seeking higher test scores - and his tutorials cost $375 to $425 an hour.

[snip]

"I earn enough to raise a family in Manhattan," he said. "I'm a teacher who gets paid equitably. I don't feel guilty about that."

In fact, Mr. Fisher feels pretty good about what he does. He argues that test-prep can be much more than rote learning aimed at achieving a superficial score. To him, studying for a school entrance exam is an opportunity for a student to learn not only facts and procedures but also a systematic approach to learning itself. "My job is not to teach a student the trick to getting a high score; my job is getting a student to make the knowledge theirs so it becomes part of them," Mr. Fisher said.

[snip]

Steve Feldman, a 23-year-old Manhattan resident, said that the three months Mr. Fisher tutored him for the law school exam prepared him well for the mental rigors of the law. Originally scoring in the 16th percentile, Mr. Feldman ended up in the 85th percentile. He was accepted to his first-choice school, Tulane University, and credits much of his success to his tutor's method and disposition.

[snip]

"He would sit and watch me take a practice test and figure out, just by watching me, what I was having trouble with. Then we'd work on that until I had it down."

[snip]

Vanessa Gottlieb, on the other hand, started out with a high SAT score. Still, Mr. Fisher helped her raise it enough to gain early admission to Georgetown University.

"He's great at breaking down the fundamentals and brought my math to a whole new level," she said.

[snip]

Indeed, Mr. Fisher glows when he talks of the mental gymnastics he must perform, confessing that his favorite part of the job is when a student gets really stuck. It is then, he says, that he gets to exercise his creativity. How to get this technique through to this kid? How to break down a complicated concept so each part is small enough to digest? That's what excites him.

"You can't imagine how rewarding it is to see a kid finally get it," he said. "They get that giddy feeling. You can see it on their faces, and half the time they wind up walking out of my office so distracted they forget their coat."

update: I just found this line in a NYC Math Forum email:

Have you heard any ads for "Hooked on Whole Language" and "Hooked on Fuzzy Math"? No, and you won't because no parent would knowingly pay for such. But parents, as taxpayers, pay for it every day across America.

also see:
NoComment
SpecialEdReferralsEverydayMath

comments...

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WelcomeJoanneJacobsFolks 08 Jun 2005 - 01:37 CatherineJohnson

Thanks for coming by!

If you're especially interested in constructivist math curricula, check out:

MathInSalinaKansas
CompareAndContrast
HowToGetParentBuyIn
EverydayMathDoesItToo
ATeacherUsingTrailblazers


If you want to know how bad things are in France:

SpeakingOfTheFrench
SpeakingOfTheFrenchPart2
FrenchPrincipalSaysWakeUp


If you are interested in teaching math to your children, or helping with homework, see any and all of Carolyn's posts.

comments...

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GirlVsCalculator 08 Jun 2005 - 04:26 CarolynJohnston

Calculators aren't actually so reliable. Actually, if you were to compare calculations done with calculators to those done by humans one to one, I'd bet that calculators produce a much higher error rate; it's so easy to mess up and hit the wrong button, or to get a complex sequence of operations in the wrong order.

My husband has a story that illustrates one of the consequences of overreliance on calculators in math classes.

He was teaching a probability unit in a freshman college course in finite math, and most of the kids were struggling with it. These kids came into class every day clutching their calculators fearfully, as though they were talismans to ward off math demons (embodied by their professors, I guess).

The unit test in probability happened, and one of the problems was as follows:

John flips a penny repeatedly. If the probability of its turning up heads is .5, then how many times must John flip the penny in order to have a 90% chance of its coming up heads 100 times?

One girl in the class -- a bright girl -- set up the problem, banged on her calculator for a while, and came up with an answer of .00001. When she went in to get help with the problem, my husband told her that she'd basically set up the problem correctly; the problem was with the calculator -- she wasn't getting the keystrokes in the right order.

"You need to use your common sense to check your answer," he told her. "Think about it. In order to have ANY chance of the penny coming up heads 100 times, how many times does he have to flip the coin at least?"

"Oh, yeah!" she said. "At least 100!"

A couple of days later, the class took a retest, and the exact same problem was on the test again. This time, the student performed the same calculation in the same way, and came up with .00001 again. Frustrated, she showed that she had absorbed my husband's lesson about common sense, and put down: 100.00001.

comments...

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MathHorrorStories 09 Jun 2005 - 15:31 CatherineJohnson


re: GirlVsCalculator


I've been keeping a collection of math horror stories for awhile now. (So please! Send yours!)

I got started on this little edu-sideline thanks to a friend of mine who's married to an architectural engineer.

In grad school, she said, he would do pages and pages of calculations by hand, in teeny-tiny little print.

These sheets would come back to him from his professor with equally tiny little red-pencil corrections scattered across the page.

So today her husband is hiring students fresh out of grad school to work for him. These are grad students; they have MAs in architectural engineering.

None of them does calculations by hand, ever. They use architectural engineering software.

They'll bring in printouts of their work for him, and he'll look at it, spot a bunch of errors, and say, 'This is wrong.'

They just stare at him.

They have no idea what he's talking about, or where or what the errors might be.

These are architectural engineers, folks.

They build stuff.

comments...

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AdvertisementsForMyself 08 Jun 2005 - 19:14 CatherineJohnson

My friend Gary Mirkin sent me a pdf file of the NATURE review of Animals in Translation (scroll down).

I was thrilled to get it -- thanks, Gary!

warning: I just noticed that an article on a British documentary about unborn children precedes the review. I think it's OK for children, but check first & let me know if it's not.

[update: Carolyn pointed out I should probably say directly that I am the coauthor of ANIMALS IN TRANSLATION. I think she's right, judging by the fact that I discovered just yesterday that Amazon.com doesn't even list me as the coauthor of Shadow Syndromes, which I am. Sigh.]

comments...

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GreatMindsThinkAlikePart2 08 Jun 2005 - 19:38 CatherineJohnson

I just mentioned $400 hourly fees to masters of direct instruction and today Joanne Jacobs has a link to Zig Engelmann's new web site.

Jacobs also links to a terrifically useful glossary of terms here.

comments...

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GuessAndCheck 31 Oct 2005 - 14:32 CatherineJohnson

So Ed and I were driving the kids into Manhattan the other night, to see their new doctor.

We were on the FDR, passing the Triborough bridge, when we got onto the subject of how engineering types seem to be especially hostile to fuzzy math.

We figured that probably has something to do with the fact that they build stuff for a living.


Oh, look!

The bridge fell into the water!

OK, I'm going to estimate we need twice as much concrete this time.


+ + +


International Red Cross symbol for Guess And Check






update: I mentioned in a Comment that the Grade 6 Phase 4 kids spent a month doing problems they couldn't solve this year. Here is the set of the 'strategies' the kids were supposed to use.

in order of appearance:

• Act Out or Use Objects
• Use or Make a Table, an Organized List, or a Graph
• Guess and Check
• Use or Look for a Pattern
• Use Logical Reasoning
• Make It Simpler
• Work Backwards
• Make a Picture or Diagram

Apparently the Phase 4 class is following the Master Plan.




comments...

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RedLetterDayPart2 08 Jun 2005 - 21:00 CatherineJohnson

KITCHEN TABLE MATH has just receieved its first private donation of a personal Math Horror Story!

I have my own story like this. About 10 years ago I was a working Aerospace Engineer. I was in charge of a project to do the conceptual design of a new transport aircraft. The using command for the Air Force wanted the aircraft to be able to land and takeoff in the length of a football field so obviously takeoff and landing were to be important in this design. In most transport aircraft we don't worry about takeoof and landing at the conceptual level because the air force has 15000 ft runways. Well I told a young engineer just out of college to write a program to do the take off and landing. When he was done he handed me the results for the first design and the takeoff time was 300 seconds. He saw nothing wrong with this since as he said "that's what the computer says it should be." I told him to go to his desk and come back in 300 seconds. Only then did it dawn on him that 5 minutes might be too long for a take off run.



Thank you!

comments...

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NewsYouCanUse 09 Jun 2005 - 01:08 CatherineJohnson

Now this is something I didn't know.

The price for tutors who accompany families on vacation abroad averages about $1,400 a day.


Calculus by the Sea

comments...

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CalligrammeParallogramme 09 Jun 2005 - 15:34 CatherineJohnson

This is adorable. Apparently French children create calligrammes, which seem to be poems in the shape of the object the poem is about.

I stumbled across these at the web site for the Ecole Active Bilingue Jeannine Manuel in Paris.

Here is a calligrame about a parallelogram!




click on caligramme to enlarge




update: calligrammes aren't just for children

update 2: I just asked Martine, who takes care of our kids, about calligrammes. (Martine is French.) She said she had a friend who did them, and that she took a special class to learn how.



comments...

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EverydayMathEpilogue 14 Jun 2005 - 01:48 CarolynJohnston

In which I finally get to graduate from Everyday Math.

I guess I'm just slow on the uptake. I finally figured out why I ended up teaching so much of what I consider basic math to my son in the last two years; it wasn't that he spaced out and missed it, it was that it never was taught at all.

What threw me off was that problems using these skills cropped up in the text anyway. When Ben came home with homework he was unable to do, I assumed he'd just failed to get it.

It turns out, though, that the kids were just supposed to use calculators. Duh.

Ben graduated from elementary school last night, in a two-hour tear-jerking ceremony to end all ceremonies. Every kid got a special award with his diploma: the Math Wizard award, the Most Encouraging award, the Future Leader award, the Social Butterfly award. Ben got the Energizer Bunny award. He really did.

And today I found this discussion of excerpted material from the Everyday Math Teacher's Reference Manual, grades 4-6. It explained so much.

When discussing the Fraction-Addition Algorithm, the authors state: "It is important to note that Everyday Mathematics does not support the traditional emphasis on finding a least common denominator. This approach is excessive, too formal, and without much meaning for many people. In fact, implying the least common denominators are the only permissible denominators is probably harmful to later learning in algebra."

Will someone please explain to me why there is so much fear, in math education, of the harm that learning things might do? How about the damage done when you don't learn things?

The Everyday Mathematics curriculum displays a clear preference for the partial-products algorithm for multiplication, which is extraordinarily cumbersome for all but simplistic calculations, requiring n time m intermediate, or partial, products instead of min(n,m) as required by the standard algorithm. (The numbers n and m represent the number of digits in each number.)

Actually, there is something to Everyday Math's claim that the partial-products algorithm has value because of its similarity to an algorithm taught in high school for multiplying binomials. Remember having to multiply expressions like (x+y)(a+b), using a method that was acronymized as FOIL (first, outer, inner, last)?

To get the result, you first multiply the first factors (x and a), then the outer ones (x and b), then the inner ones (y and a), then the last (y and b). That's the algebraic version of what Everyday math calls the partial products method: 53 times 36 gets multiplied as (50+3)*(30+6)= 50*30 + 50*6 + 3*30 + 3*6.

The problem with using this algorithm for multiplying numbers is that you end up adding 4 terms together, instead of the two you could have if you used the standard algorithm, which is a lot more efficient. If you use the partial-products algorithm to multiply two three-digit numbers, you'll get 9 summands to add instead of 3; but the Everyday Math Teacher's manual would never recommend that you do that. It would tell you that smart people -- sensible people -- use a calculator.

But I really believe in the value of teaching an efficient algorithm. Kids who are growing up to be engineers, computer scientists, physicists, mathematicians, chemists, analysts, statisticians and finance experts need to learn to appreciate efficiency in algorithms.

"The authors of Everyday Mathematics do not believe it is worth the time and effort to fully develop paper-and-pencil long division algorithms for all possible whole number, fraction, and decimal problems. Mastery of the intricacies of these algorithms is a huge undertaking, and one that experience tells us is doomed to failure for many students...."

Frankly, I am shocked to find a statement like that in a teacher's manual. And learning long division is a huge undertaking? Give me a break.

Anyway, this explains why I suddenly found problems like 365/.5 in Ben's homework, without any preamble whatsoever, or any explanation of the meaning of dividing by a decimal. To me, it represented a whole new requirement for understanding and skill; to Everyday Math, it was just an extra keystroke on a calculator. Anyway, I swung into action the night we found that problem, and gave Ben a crash course in decimal division; it was one of my finer moments of reactive teaching.

"It simply does not seem wise to invest 100 hours or more on instruction and practice of algorithms that some students will succeed at doing slowly on paper, with uncertain results, while nearly anyone can quickly and accurately find a quotient with a calculator."

Concerning accuracy and calculators, see GirlVsCalculator.

"This said, the practical needs of students to succeed on outdated standardized tests may require you to teach long division algorithms."

Not to mention their practical needs for passing algebra, calculus and physics later on in their lives.


AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard




comments...

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SummerMathChallenge 09 Jun 2005 - 16:01 CarolynJohnston

I'd like to offer a summer math challenge to all of us who are hoping to help their kids stay level, or advance, in math this summer.

Singapore Math seems to be the curriculum that offers the most challenging word problems, the ones that really grow a kid's higher-level reasoning abilities. But people don't know where to start with the curriculum, and are afraid it might be too hard for them to teach.

So this summer, every day or two, Catherine and I will post a Singapore Math word problem. A day or two later, we'll post a solution. In the process, we'll talk about bar modeling, which is Singapore Math's very clever visual approach to teaching algebraic thinking.

Any kid, even a kid who is determined to spend the summer having a Good Time, can surely take the time to do one measly word problem a day, especially if he is handsomely bribed.

Our kids are 10 and 11, so we'll focus on problems that are about at their level. But we will take requests, too.

comments...

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CompareAndContrastPart2 05 Jul 2006 - 22:12 CatherineJohnson

I've been searching for some good examples of bar models to illustrate Carolyn's SummerMathChallenge post, and I just came across this page from the Primary Mathematics Grade 2A workbook.

Mind you, '2A' is the workbook for the first half of 2nd grade. Second semester is '2B'.

update 7-5-06: The original image has disappeared, so I'm replacing it with this "worked problem" from Challenging Word Problems Primary 2:

CompareAndContrast
CompareAndContrastPart3
CompareAndContrastPart4
CompareAndContrastPart5
CompareAndContrastPart6
CompareAndContrastPart7
MathInSalinaKansas

comments...

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SummerMathChallengePart2 09 Jun 2005 - 19:48 CatherineJohnson

sample BarModels

Bar models, I'd like to add, are not easy.

I think they're a fantastic way of teaching math to kids, and to myself, but they are neither simple nor obvious. That's one of the things I like about them.

The idea behind the Sinaporean bar models is to use an abstract visual representation of number and of word problems as a bridge between the concrete and the abstract.

Speaking only for myself, I think they work. I'll have more to say about that later on.

comments...

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CompareAndContrastPart3 05 Jul 2006 - 22:04 CatherineJohnson

This page is from the Grade 6, second semester workbook for Primary Mathematics.

Children in Singapore do not use calculators to work these problems. update 7-5-06: the page I linked to in June 2005 has disappeared, and I don't remember what was on it. The page shown here now is different...





This answer sheet is no longer relevant:
AnswerSheetFractions6B



CompareAndContrast
CompareAndContrastPart2
CompareAndContrastPart4
CompareAndContrastPart5
CompareAndContrastPart6
CompareAndContrastPart7
MathInSalinaKansas



See also:
DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

comments...

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SummerMathChallengePart3 09 Jun 2005 - 19:46 CatherineJohnson

I've mentioned before that I've been teaching myself how to work word problems using bar models -- and that I have now finished all 270 problems in Challenging Word Problems Grade 3.

I've also been having Christopher do one bar model problem every day, along with his Saxon Math lesson. We've been at this for a few weeks now.

Christopher initially refused to start at the beginning with me, and work the very first bar models Singapore kids would work.

These are simple number problems like:

9 + 7 = __ .

The sum of 9 and 7 is __.

The difference between 9 and 7 is __.

To Christopher, these problems look absurdly easy.

But the point of doing these absurdly easy problems is to make sure the child knows that:

• the expression '9 + 7' means the same thing as the phrase 'the sum of 9 and 7 is'
  
• to show that 9 + 7 and 9 - 7 can be represented by the same model

Both of these goals are terrifically important, and they don't come automatically.

And I have found that the 'revelation' that a 'different' problem can be represented by the exact same model has increased my 'number sense' tremendously. (More on that later--I have an example!)

So if I'd had my druthers, Christopher would have started where the Singapore kids start, with What is the sum of 9 and 7?

But he fought me tooth and nail on this. Whyyyy do I have to draw a barrrrrr model when I already knooooowwwww the ansssswwweeerrrr?????

(I gather there are plenty of kids out there asking the exact same question about the use-many-different-methods-to-solve-the-same-problem approach of fuzzy math, btw.)

He was such a pill about the whole thing that I gave up, and moved to the Grade 4 book (because he insisted that the Grade 3 book, which I was doing myself, was also too easy.)

This approach has not worked out.

Christopher and I do a bar model problem most days, and I don't see much progress at all -- although he does have a pretty good grasp, now, of how to represent addition and subtraction.

But when it comes to multiplication, division, ratio, proportion, and -- horrors -- changing ratio -- forget it.

So I'm going to back him up to much simpler problems, and insist he do them no matter how much he yells (which won't be much at this point, since he's used to doing them by now and he's noticed that the Grade 4 problems are darn hard.)

So I'll be posting starter bar model problems along with Carolyn's more advanced problems, and offering some suggestions about how to sequence your bar model practice at home.

I should add that I taught a little after-school class in Singapore Math this winter, and I had one child who loved bar models. He just got them immediately. He was a real hyper little guy, who wanted lots of stimulation, and he couldn't bear doing an easy problem.

So I brought him in some harder problems, and I think that was fine in his case.

My point being, you have to figure out what (seems to) work for your own child.

If you have a child who naturally takes to drawing bar models, then pick whatever level he or she wants to do.

If you have a child like Christopher, who does not appear to be a Natural Born Visual Modeler, I think it's smart to back up to the beginning and do First Things First.

Like everything else in math, bar modeling appears to be a sequential, hierarchical topic!

Even when you already know how to get the answer!

Have to go get some lunch --- more on this later.

comments...

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NctmEndorsements 09 Jun 2005 - 19:44 CatherineJohnson

If you follow the math wars, you're probably aware that the National Council of Teachers of Mathematics states that it does not endorse, and has not endorsed, textbooks.

Education reporters seem invariably to take this statement at face value.

Barry Garelick has just posted a link to the 'Key Messages' of the National Council of Teachers of Mathematics on the NY Math Forum list, among which we find:

Students who are taught with curricula modeled after Principles and Standards for School Mathematics will learn more mathematics, be better problem solvers, and be better prepared for the future.


When people talk about 'NCTM textbooks,' they're not talking about Saxon Math.

They're talking about textbooks 'modeled after Principles and Standards for School Mathematics.'

Whether or the NCTM posts lists of approved textbooks on its web site is irrelevant.

comments...

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FavoriteBarModel 08 Oct 2006 - 23:42 CatherineJohnson

I just found one of my all-time favorite BarModels, from a book called Problem Solving the Systematic Way:




UPDATE 10-8-2006 heck; it's gone now & I'm not sure what the problem was. I think it was 3 boys with 3 different weights all expressed in multiples of the first boy's weight.

I was good at the algebra they taught me in high school. I liked all the little x's and y's; I liked setting up linear equations in two or even three variables; I liked solving them.

But I didn't have a clue how they worked, apart from understanding the basic concept of doing-the-same-thing-to-both-sides.

Algebra, to me, was a little like magic.

That wasn't a problem. I like magic; I'd like to have lots more of it. I'm always mystified by the idea that it's upsetting or discouraging to be able to do something but not know how you did it, which is pretty much the whole deal when you're using procedural knowledge.

The Singapore bar models have demystified a huge amount of beginning algebra for me. This particular problem is one I could easily have solved after 9th grade, and could still solve a year ago, after not having done any formal algebra in 30 years.

But when I looked at the problem represented this way, suddenly I saw why the equations worked.

It's not always that way. I've done upwards of 300 bar models now, and I'm still confused about more difficult problems.

But I've gotten to like that about math.

comments...

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CompareAndContrastPart4 29 Sep 2005 - 15:29 CatherineJohnson





thank you: Elizabeth Carson, Co-Founder NYC HOLD


update: I forgot to mention that this chart comes from an article circulated on the NY Math Forum list, The Curricular Smorgasbord by Williamson M. Evers & Paul Clopton. (pdf file)


CompareAndContrast
CompareAndContrastPart2
CompareAndContrastPart3
CompareAndContrastPart5
CompareAndContrastPart6
CompareAndContrastPart7
MathInSalinaKansas

keywords: the f word the f-word bibliography greatest hits

comments...

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WorksheetsForSummer 16 Jun 2005 - 17:52 CatherineJohnson

Googling around the web for a copy of the WALL STREET JOURNAL article on Singapore Math, I stumbled onto a parent site called Summer School Math.

I've only looked at it for a couple of minutes, but I was intrigued by their math facts worksheets.

They offer more than just worksheets (including worksheets on adding and subtracting fractions, which I think are essential).

They've put together a systematic schedule for which facts a child works on first, second, and third, and when. (They've posted samples in pdf files, so you can take a look.)

For a child whose school is not teaching math facts, this might be the place to go.

Another resource, and this one I definitely recommend since I've used it myself (though not for teaching math facts . . . ): Math Coach: A Parent's Guide to Helping Children Succeed in Math by Wayne A. Wickelgren and Ingrid Wickelgren. Wickelgren tells you how to compress the teaching of math facts into fewer separate items to remember.

Parker and Baldridge are also fantastic on this (have to get kids to school--Parker & Baldridge are on the MathRefs page).

I'll post a couple of other resources shortly.


DontRelyOnStateTests
PenfieldParents
NewYorkStateMathCurricula
CompareAndContrastPart3
FriendlyFractions
PaperFractions
ADifficultChild
ADifficultChildPart2
WorksheetsForSummer
AssessYourChildForFree
AssessYourChildForFreePart2
BonusOnlineAssessmentQuestions

comments...

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EdSchoolDangers 10 Jun 2005 - 13:38 CatherineJohnson

David Klein:

The field of math education is more or less at the level of medieval medicine.  In those days you might be better off not seeing a physician, because he might bleed you to death trying to cure you from a bad cold.  So it is with today's colleges of education.  






(you can click on this guy)

comments...

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FromOurReaders 10 Jun 2005 - 19:43 CatherineJohnson

We have some hilarious & dead-on comments from readers.

Here's one:


"Yesterday's basics are no longer enough; we're expanding the basics to match the needs of tomorrow."

Of course, this is incredibly stupid and can mean whatever they want. They say they want to ADD more basics to meet the needs of tomorrow. Did they discover a new branch of mathematics or engineering? College professors better consult with NCTM to find out what these new basics are.

This is just the usual edu-tripe used as cover for their own ideological and pedagogical agenda. The best approach is to show parents the two different math workbooks side-by-side.


+ + +


Here's another:

NCTM says that "yesterday's basics are no longer enough..." Well, yesterday's basics got us to the moon. And every student knew how to get the answer because he was taught by direct instruction rather than being left on his own to "figure out" a method that will get the right answer (whatever that is). Then he's told that the right answer isn't really important, it's the method that's really important. Does anybody think we got to the moon or to Saturn with a wrong answer, using a proper method?

+ + +


As to that, Carolyn and I have begun a Thought Experiment on the question of Guess And Check Things We Don't Want To See In Real Life.

I say No to Guess And Check buildings, roads, and overpasses; Carolyn, a more moderate soul than I (maybe), says Guess And Check flea treatments and flower beds might be OK.

We both agree that Guess And Check ferris wheels are a very bad idea. (I think Guess And Check ferris wheels are such a bad idea I'm contemplating putting Say No To Guess And Check Ferris Wheels on a bumper sticker. Or, ummmmm, a t-shirt. Hey! That could be our very first KTM t-shirt! Just say No to Guess And Check ferris wheels!)

If you would like to contribute your own Guess And Check Thing You Would Prefer Not To See In Real Life, go here and scroll down to Comments.

comments...

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BarModelingVsGraphing 10 Jun 2005 - 14:01 CatherineJohnson

Go check out interesting comments on bar modeling versus graphing by a Ktm Guest here. (Scroll down to the Comments section.)

I'd love to hear what others think.

My curiosity about the history of the Singapore curriculum is now so intense I realize I'm going to have to see if someone there will do an interview . . .

comments...

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TakingABreakPart5 12 Sep 2005 - 21:01 CatherineJohnson

comments...

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BarryGarelickOnGeometry 11 Jun 2005 - 00:49 CatherineJohnson

Just got back from lunch and the Rosedale Nursery to find a comment from Barry Garelick, which I'm pulling it up front:


"From NCTM's PSSM, here's what NCTM has to say about their geometry standard: "Geometry. Geometry has long been regarded as the place in high school where students learn to prove geometric theorems. The Geometry Standard takes a broader view of the power of geometry by calling on students to analyze characteristics of geometric shapes and make mathematical arguments about the geometric relationship, as well as to use visualization, spatial reasoning, and geometric modeling to solve problems. Geometry is a natural area of mathematics for the development of students’ reasoning and justification skills."

Translation: High school geometry used to emphasize proofs. Now it just emphasizes shapes and formulae, with an occasional proof and in general is not much more advanced than the geometry presented in 7th grade, except for the fact that not much geometry is presented in 7th grade." -- Barry Garelick


Barry's article on the history of New Math and New New Math is probably the single most helpful piece I've seen on this subject. It's an excellent article to give to principals, school board members, teachers, and other parents.

comments...

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FromOurReadersPart2 01 Nov 2005 - 19:48 CatherineJohnson

I love this (from a reader):


I thought the guess and check symbol was a great joke, until I saw that it wasn't. Guess and check is the foundation of constructivist math where you can't possibly stunt the mathematical growth of a child by teaching them real mathematical problem solving techniques. You end up with the list below.

I noticed that none of the techniques involved defining unknowns and governing equations.

Joe starts in city A at noon and travels west at 60mph. how long will it take him to drive 745 miles?

Act Out or Use Objects - I will borrow my father's car (even though I am not old enough) and drive west at 60 mph on the highway. I will remember to reset the trip odometer.

Use or Make a Table, an Organized List, or a Graph - Where's my TI graphing calculator. Let me see. If the Y-axis is distance traveled and the X-axis is miles, then...?

Guess and Check - 3 hours? 4 hours? Am I getting hot? 6 hours?

Use or Look for a Pattern - 60, 745, ... 1430?

Use Logical Reasoning - What does "city A" have to do with the problem? Why noon? Why couldn't it be city B? What city is 745 miles west of city A? Why couldn't Joe drive south? This is a stupid problem.

Make It Simpler - OK, I will change the distance traveled from 745 miles to 60 miles. The answer is 1 hour.

Work Backwards - OK, Let's say I start with 745 and go backwards to 60. The answer is 685. This is easy because I get to use my calculator. What do you mean; "Look at the units?"

Make a Picture or Diagram - Ok, I will draw a picture of New York City and call it city A. West, will be along route 80 through Pensylvania. It's not directly west, but it is close enough. I like drawing perspective pictures of roads since the road gets narrower as it gets further away. I should get some partial credit for knowing what perspective is, shouldn't I? Where was I? Oh, I really like art because I get it in all of my classes.


International Red Cross symbol for Guess And Check

comments...

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FromOurReadersPart3 31 Oct 2005 - 14:48 CatherineJohnson

I've mentioned that NCTM officials say that they do not endorse textbooks.

Thus, the NCTM cannot be held accountable for any problems a school, child, or parent might be having with a textbook.

Here's a typical NCTM disclaimer:

NCTM does not endorse any product, any program. That's longstanding policy of the council. So the comments that you hear made that NCTM has this type of program or has that type of program is actually categorically not true. NCTM does not endorse any type of program.

This statement was made by Lee Stiff, of the NCTM, at a panel on the subject of constructivist mathemathics.

Fortunately David Klein came prepared:

DR. KLEIN: Perhaps it depends on the time of day or the phase of the moon or something, but the NCTM did endorse MathLand, and let me read you the quote from their letter, which they posed on their website: "The Board of Directors of the National Council of Teachers of Mathematics wishes to inform you of their unconditional support...for the appropriateness of their final recommendations." The final recommendations refers to MathLand and nine other programs.

I can't say that I have a grasp of the politics here. It's obvious I need to get hold of an old copy of . . . say . . . Games People Play, or maybe I should just finally sit down and read my ageing edition of The Prince.

Because I know there are names for the strategies I see NCTM officials using.

So far I've seen two:

• refuse credit for things that aren't working
• take credit for things that are
  

As to the last, at one point in the transcript we find Dr. Stiff making the remarkable claim that the CA standards--rated an 'A' by the Fordham Foundation--are based on the NCTM standards. Fortunately, Klein was prepared here as well:

But regarding the comment that California's standards are a tweaking of the NCTM standards, I suppose that you could argue that black is like white because they're both similar to gray. There's some truth to that, but if you look at what the NCTM has actually said about the California standards, if you look at the handout for my talk, go to the last two pages, you'll see the cover story of the NCTM news bulletin of February 1998, and I'll just read you the first paragraph of what the NCTM says under those circumstances about the California standards, which, by the way, are rated first in the nation by a number of independent agencies.

They say, "Mathematics education in California suffered a serious blow in December"--I'm talking '97--"over protests from business, community, and education leaders. California's State Board of Education unanimously approved curriculum standards that emphasize basic skills and de-emphasize creative problem solving, procedural skills, and critical thinking."

Well, I guess one could argue that you couldn't expect four professors of mathematics from Stanford University to understand what critical thinking is, those professors who wrote the California standards, compared to the Ed.D.s in education.

I think it's fair to conclude at this point that the NCTM, along with the developers and publishers of the NCTM standards-based textbooks, have given substantial thought to winning the war for hearts and minds. In fact, I would go so far as to say that in this, as in All Things, they are following the Master Plan.

In short, they are slippery customers.

I have no idea how to handle a slippery customer, other than to walk around with photocopies of incriminating NCTM statements in my purse (and it may come to that).

So, for the moment, I'll just say that the notion that the NCTM 'does not endorse' textbooks is a distinction without a difference.

One of our readers went to the trouble of looking up the following information. I'm keeping it in a safe place.

update: this is interesting. Lee Stiff, the NCTM official quoted above, is himself the author of a non-NCTM-endorsed constructivist math text.

These guys have chops, as Carolyn would say.


From our reader:

Authors of (drum roll please) McDougal-Littell’s Passport to Mathematics, Book 1:

(I’m going to copy all of their “credits” from the front of the book. Italics are not mine.)

Ron Larson is professor of mathematics at the Behrend College of Pennsylvania State University at Erie. He is the author of many well-known high school and college mathematics textbooks, including Heath: Algebra I, Geometry, Algebra 2, Precalculus, Precalculus with Limits, and Calculus. He is a pioneer in the development of interactive textbooks, and his calculus textbook is published on CD-ROM. Dr. Larson is a member of NCTM and frequently speaks at NCTM and other professional conferences.

Laurie Boswel is a mathematics teacher at Profile Junior-Senior High School in Bethlehem, New Hampshire. She is active in NCTM and local mathematics organizations. A recipient of the 1986 Presidential Award for Excellence in Mathematics Teaching, she is also the 1992 Tandy Technology Scholar and the 1991 recipient of the Richard Balomenos Mathematics Education Service Award presented by the New Hampshire Association of Teachers of Mathematics. She is an author of Heath Geometry and Houghton Mifflin Math Central.

Timothy D. Kanold is Director of Mathematics and Science and a teacher of Adlai Stevenson High School in Lincolnshire, Illinois. A 1986 recipient of the Presidential Award for Excellence in Mathematics Teaching, he is also the 1993 recipient of the Illinois Council of Teacher of Mathematics Outstanding Leadership Award. A member of NCTM, he served on NCTM’s Professional Standards for Teaching Mathematics Commisson. He is an author of Heath: Algebra I and Algebra 2.

Lee Stiff is an associate professor of mathematics education in the College of Education and Psychology of North Carolina State University at Raleigh and has taught mathematics at the high school and middle school levels. A member of NCTM, he served on the Board of Directors. He is also the 1992 recipient of the W.W. Rankin Award for Excellence in Mathematics Education presented by the North Carolina Council of Teachers of Mathematics. He is an author of Heath: Algebra I, Geometry, Algebra 2, and Houghton-Mifflin Math Central.

comments...

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PanBalanceProblems 11 Jun 2005 - 17:02 CarolynJohnston

In BarModelingVsGraphing, a guest mentioned that variables and equations could be introduced using pan balance problems, in simple cases.

Catherine and I were talking about pan balances this past spring, in exactly this context. She asked how I would introduce equations to an absolute newbie; I said that with Ben, I had had luck using the analogy of a pan balance. It's a rather neat analogy, in the initial stages of learning about equations. Emphasis on initial.

Not a week later, by coincidence, Everyday Math introduced a whole unit on pan balance problems. These were problems of the following sort:

Given the diagram below, tell how many squares are equivalent to a circle.

Very neat idea, I thought; it addresses, in an intuitive way, the preservation of equality under both the addition-subtraction and multiplication-division operations. I liked it.

The pan-balance problems kept coming home. Pretty soon we had moved on to double pan-balance problems:

Given the diagrams below, tell how many squares are equivalent to a triangle.

That, I thought, was getting to be a bit over the top -- I was starting to have to coach Ben on how to approach the pan-balance problems that were supposed to be helping him to approach the problem of equation-solving.

Then we started seeing pan-balance problems that looked like this:

We were getting so close to actually doing real equations, I could feel it.. and the kids were developing such great intuition; they were so ready for the next step, the step to real equations --

and then the unit ended. Fifth grade Everyday Math ended without the kids ever having really been introduced to manipulating equations.

But they are good with pan-balances, at least virtual ones.

I guess this is a sort of a cautionary tale about the dangers of falling in love with your cool teaching tools.

comments...

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PrenticeHallArrives 11 Jun 2005 - 05:47 CarolynJohnston

See: SummerSupplement

Ben's new 6th-grade math text, Prentice-Hall Mathematics Course 1, arrived in the mail yesterday. I ordered it so that we could work in it over the summer. I've seen some good things about it, and I liked the table of contents; also, it's the text series that Ben's junior high school will use, so I thought I'd get him accustomed to working in it over the summer.

Catherine, though, who has seen a lot of the math texts that are out there, has been telling me that she hates the look of it, and I can certainly understand why. Even in a world of busy textbooks, this one stands out. It's got text in a thousand colors and fonts, it has multicolored inset boxes everywhere with brightly colored graphs and tables, and photos of jumping happy children or athletes on almost every page. Just looking at it puts me back in touch with my inner ADD child.

I think the intention of designing a book this way is to keep the kids awake and stimulated, but I think it backfires. This book overstimulates me, never mind Ben; I'd have to stick index cards all over the inset boxes and jumping kids just in order to focus on the text (I do have a touch of ADD, so normal types might not be so rattled). The contents do look pretty good, when you strip away the excess.

What do you suppose is the ideal balance to strike between monotony and overstimulation in a math text? You don't want to blow the kids away with dry monocolor text and equations (at least not until they get into grad school!), but you don't want to overwhelm them with trimming either. The principles of good graphic design surely apply here as much as they do elsewhere. Is there a related principle of good textbook design waiting to be discovered?

comments...

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SaxonPlacementTestsAndGuides 23 Sep 2005 - 15:38 CatherineJohnson

Saxon placement tests

(pdf files):
Math K-3 Placement Inventory
middle grades math placement test
Placement Test for Algebra 1
Saxon Placement Test for Algebra 2
upper grades math placement test

Terrifically helpful: short, easy to use, easy to interpret.

Christopher and I had gotten through 10 or so lessons in Saxon 7/6, normally a 6th grade book, when Carolyn sent me this link. I'd been feeling that 7/6 was too easy, but didn't trust my judgment.

The test confirmed my feeling, and Christopher and I are now using Saxon 8/7 'with prealgebra.'

A wonderful resource if you're considering supplementing -- or homeschooling -- using Saxon Math.


ATeachersStory
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)

FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

comments...

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TakingABreakPart6 11 Jun 2005 - 16:10 CatherineJohnson

(you can click on this guy)

comments...

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FromOurReadersPart4 11 Jun 2005 - 19:26 CatherineJohnson

There are a bunch of good comments from KTM readers . . . JD Fisher on FromOurReadersPart3, Interested Teacher has the Andover links at NctmEndorsements, and Anne Dwyer has a tutoring story, plus a book recommendation, at GirlVsCalculator.

I think that covers it--



comments...

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SummerSupplementTimePart2 09 Mar 2006 - 20:17 CatherineJohnson

I've more or less firmed up (more or less firm?) Christopher's summer math program.

• Saxon Math homeschool edition 8/7 with prealgebra: everything in the book, including the Fast Facts sheets we skipped during the school year
  
• Singapore Math Primary Mathematics Book 3A, all bar model problems in text & workbook; proceeding to Book 3B if we finish
  

And, possibly, if we can swing it:

• every Singapore Math lesson on geometry we can get to, especially the chapter on nets
  
• something extra on fractions . . . possibly just extra 'fast facts' fraction sheets from Saxon
  

We are also going to try to get through Megawords Book 5 before the fall. I keep saying, my goal in life is to be doing the 6th grade book in the 6th grade, as opposed to years and years after the 6th grade is over.

update 2

Fun sites if you want to look at nets.

This one's especially over the top.

update

I just counted the Pages Left To Do in Megawords: 59, plus 6 test days, which is 65.

Not bad.

June 30, 2005 update

We are having such fun cruising through Saxon; it's like spending time with an old friend. Just a few 'I hate you's!' on Day One, and now we're sailing. This morning Christopher nagged me to get started on his math 'because I want to get it over with.'

Here's what we're doing:

• Saxon Math homeschool edition 8/7: 1 complete lesson a day, including the 'fast facts' sheets

• Primary Mathematics 3A textbook & workbook: all bar model problems, 2 each day, probably moving up to 3 or 4. (It's amazing how many of these problems he gets wrong, which makes me feel even more strongly that he needs to be able to do them. He's not 'seeing' the logic of, for instance, subtracting one abstract quantity from another abstract quantity, and I'm certain he needs to see this! I could be wrong.)

• Tomorrow we'll begin doing one Math Olympiad problem a day.

• One of our commenters likes the Primary Mathematics Intensive Practice book, so I'm going to see whether we should be doing some work from that--especially anything to do with measurement, the one section Christopher blew on his TONYSS test. (My neighbor told me today that apparently kids all over the state do poorly on measurement. yikes. I feel less incompetent as a teacher, though, knowing that.)

FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

and see:
LiveBloggingTheSpellingBee
HowToSpell
HowToSpellPart2
MoreSpelling
TheSaxonMathOfSpelling

BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
SundaySchool
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids

CoolProblemsToMakeYourKidDo
SummerProgramUpdate

comments...

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SchoolsInMexico 16 Jun 2005 - 10:50 CatherineJohnson

Just heard from a friend on a business trip in Mexico.

You will love this.

Two days ago I was driven around Chihuahua by a guy from the hotel. Anyway, we get to talking and the conversation drifts to the schools in Mexico, specifically the public schools.

He says the public schools are a disaster. The whole thing is politicized. They just spend the day trying to indocrinate the kids, or being politically active themselves when they should be teaching. Not like when he was a kid. Everyone who can, puts their kids in private or religious schools, since [the public schools] are so awful. He wishes he had the money. "Las escuelas publicas de hoy dia solo hacen lo minimo. Creo que asi les conviene." [Skookumchuk translates this as, "The public schools of today only do the minimum. I think it suits them that way."]

So I then launch into a discussion of NCLB and charter schools and vouchers and the like.

"Pues pronto tendremos que hacer lo mismo aqui en Mexico tambien." [roughly: "Well, soon we'll have to do the same thing in Mexico, too."]

Skookumchuk


posts on school troubles in France

FrenchCalculatorForKids
SpeakingOfTheFrench
SpeakingOfTheFrenchPart2
StillSpeakingOfTheFrench
FrenchPrincipalSaysWakeUp

comments...

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WordProblemDuJour1 14 Jun 2005 - 01:37 CarolynJohnston

In SummerMathChallenge, we promised to offer up a word problem for summer vacation practice every day or two. I've been giving Ben one a night, starting off very easily and hopefully moving up to something more challenging.

Here was tonight's word problem, from Grade 3 Challenging Word Problems. This one is not really all that challenging.

Every boy has 4 balloons, and every girl has 5 balloons. If there are 12 boys and 9 girls, how many balloons do they have altogether?

Ben was quite relieved to get that one tonight. We've also been working on some long division problems, of the sort that I've identified in a previous post as being a good challenge for a kid on the verge of mastering long division. We're working on problems with quotients that have zeroes in their decimal expansions, and that's where our effort is going right now.

This next word problem, also from Grade 3 Challenging Word Problems, gave Ben the slip last night. You have to be a pretty careful reader to get this right on the first try. This tricky sort of problem puts paid to the claim that traditional math doesn't exercise the linguistic centers of the brain.

Tom and Hannah have 1253 stamps altogether. If Tom has 856 stamps, how many more stamps does Tom have than Hannah?


AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

comments...

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SundaySchool 29 Jun 2005 - 02:44 CatherineJohnson

Christopher's attendance at Sunday School has been spotty this spring, but we made it today.

Now we're doing math -- big news on that front! Christopher just said to me:

I hate to admit it, but I like bar modeling.

tomorrow

Lots of good stuff stacked up for Monday, and see Carolyn's post just below, plus reader comments here and there----

Have a nice Sunday.









BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
SummerSupplementTimePart2
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids

comments...

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ThirteenQuartersInTerc 04 Jul 2005 - 00:37 CatherineJohnson

Breaking the Sunday blogging ban--

I just found this passage on a TERC thread at Math Forum:

A 5th grader in the gifted/talented program at her school came to a carnival. "How much money did you bring?" "Thirteen quarters," she said. "Well, how much money is that?" A blank look, followed by, "I don't know - I didn't bring a calculator." Surprised, I asked her equally bright friend if she knew how much it was. "We haven't had long division yet," she responded. The girls in the troop who use a traditional math program knew instantly that the amount was $3.25. Same ages, same grades, different kind of instruction, different results.

I just asked Christopher what 13 quarters is.

It took him maybe . . . 5 seconds (he skip-counted up by 4s rather than dividing 13 by 4 -- don't know what to think about that), then he said $3.25.


AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

comments...

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NoCommentPart2 26 May 2006 - 21:27 CatherineJohnson








Getting Your Message Out to Parents
(newsletter excerpt)




HowToGetParentBuyIn
EverydayMathDoesItToo
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
AnotherGemFromMathForum

comments...

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TwentyFirstCenturySkills 17 Jul 2005 - 21:01 CatherineJohnson

update

I shouldn't be flip about this lesson.

In fact, teaching young children to build the next set of math facts on the math facts they already know is a good idea.

I'm pretty sure Parker & Baldridge recommend this approach (I'll check).



for more on 21st century skills, see MoreSingaporeMath

comments...

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CarolynFisksBook 22 Jun 2005 - 14:21 CarolynJohnston

See also: NoCommentPart2.

Actually, what I'm about to fisk is an Amazon review of "Getting your math message out to parents", by Nancy Litton.

Litton’s premise for writing this book is that since good math teaching today looks much different than what parents know and did in school, parent education is vital as part of one’s teaching practice.

Since parents all think that what they learned was actually math, what's really needed is a reeducation camp, but I suppose newsletters will have to do.

The book gives ideas and examples of several strategies that can be used to communicate with parents.

1. Smoke signals
2. Math pep rallies
3. Mass hypnotism
4. Throwing them fresh red meat occasionally

The first section is about newsletters. Examples are given from throughout the school year in order to get a sense of how the information in a newsletter might change over the course of a year as parents become more familiar with what good math teaching looks like...

"We wish the 3/4s of the class that have been pulled out of Mrs. Nymph's fifth grade for homeschooling well, and want them to know that they'll be sorely missed."

The next chapter deals with back-to-school nights. Giving demonstrations of manipulative usage and sharing examples of previous years’ lessons that develop big concepts and ideas are two ideas mentioned.

Have the bastards put together a big paper cube made of 1000 cubes on a side. That should shut them up.

Litton has also had students write letters to their parents explaining what they do in math class.

"Dear Mom, today in math class we're writing you this letter about what we're doing in math class. Are you ready? Here it is: we're writing you a letter about what we're doing in math class."

Litton also realistically discusses how to deal with parents who still have concerns after attending a back-to-school night. She suggests scheduling a private appointment with them and finding out all their concerns prior to the meeting in order to be ready to address all their concerns.

She suggests a reconnaissance mission so you'll have all the ammo you need to grind them down when all the other parents are there.

The section on parent conferences includes many, many examples of student work that could be shared with parents.

And precise instructions about what the parents should never be allowed to see.

During the conference she recommends the following schedule. First she begins on a positive note about the student and then finds out what parent information and concerns need to be dealt with. She then shares samples of student work that may highlight issues the teacher has with the student.

"Mr. and Mrs. Fudd, instead of doing his pan-balance problems, Johnny has been doing equations on his homework and turning it in. He's just not a team player."

Finally, if she has done an individual assessment with the student, she will share that with the parents.

"Mr. and Mrs. Fudd, I conclude that Johnny has somehow been exposed to traditional math. Maybe he's picking it up from his friends."

Another interesting conferencing strategy she shares is to encourage student-parent conferences, which do not necessarily have to occur at school.

Otherwise known as Encouraging the Family Dinner. But wouldn't it be kind of fun to have Family Dinners at school?


HowToGetParentBuyIn
EverydayMathDoesItToo
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
AnotherGemFromMathForum

comments...

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SummerSupplementTimePart3 27 Jun 2005 - 17:28 CatherineJohnson

(Posted for Carolyn, by Catherine)

When I get back from my business trip, summer supplementation will start in earnest. Right now Ben is getting a bit of a free ride (especially with me being out of town).

Since school ended last week, I've been hand-writing a sheet of 5 problems for Ben to do every night. We're working hard right now on acing long division, and I want Ben to have long division problems to do that precisely target the areas that he still needs to work on. The sheets are generally a mix of long division problems, some other sorts of problems (tonight it was multidigit decimal multiplication), and a word problem. I keep the total number of problems down, and I design them so that I have a reasonable expectation that he will be successful on most of them.

[Success is really the carrot that keeps a kid moving through a program. You generally don't have to struggle to get them to work, if they feel they are succeeding. Keeping the kids working at their true level, and letting them experience gobs of success, should be (I feel) the main goal of summer supplementation.]

Next week, we'll begin working from Prentice-Hall Mathematics Course 1. I confess that I am dreading sitting down with Ben and cracking that book open. It's very busy and overstimulating; our eyes will be spinning like cartoon characters' for a while. We'll have to live with the series for two or three years, though, so it will be good to work on finding ways to cope with its horrid format over the summer.

I did some preliminary reconnaissance on the book last night. I was pleased to see that Ben already knows a lot of the material; so well, in some cases, that I feel we can skip certain chapters outright. The first section we'll work on will be Section 1.3, on sequencing of decimals.

Math won't be our only area of work this summer, though. Because Ben doesn't pick up vocabulary from context very well, he is a bit behind his peers in reading vocabulary; but this past year we discovered that he learns vocabulary very easily if he acquires it through direct instruction. The best vocabulary program for him is one in which he looks it up, sees it used in context, selects the correct usage for it, and then finally generates his own usage. The Sadlier-Oxford Vocabulary Workshop series seems to be exactly what he needs.

I have one more goal for Ben this summer: I want him to learn to touch-type, or at least to get him started. As a girl, I never learned how to touch-type; in fact, I dropped out of touch-typing class in high school (back then, though, being an expert touch-typist marked you as the secretarial sort, rather than as the thoroughly modern computer-savvy sort). As a result, I hunted and pecked until I forced myself to start touch-typing a few years ago (I still don't do it correctly).

Bernie, my husband, had no such secretarial hangups, took touch-typing in high school, and has touch-typed ever since. It's a great skill to have, and I want Ben to acquire it early.

We're an unusual household, computer-wise (and probably in many other ways, but never mind that). For one thing, we have computers for pretty much every member of the family, and a bunch more dinosaur computers and parts moldering in the basement that we can't bear to part with. Furthermore, they are all running Linux, and not even the same distribution twice; we like variety around here. This generally means that we can't run Windows software, so buying Mavis Beacon Teaches Typing for Ben is not really an option.

Happily, there is a free and open-source alternative: Tux Type (Tux is actually the name of that little penguin on the Linux logo. Every movement has its mascot). We have Tux Type on one of the kids' computers, and I tried it out the other day; it's not as much fun as Need For Speed, of course, but it's not bad; I even found it a bit addictive. I think it's more fun than Mavis. I should be able to get Ben playing it without too much fuss.

Especially if I bribe him.


FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart4 (resources for kids who have fallen behind)
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

comments...

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UsabilityFeedback 13 Jun 2005 - 15:24 CatherineJohnson

I've been reading Jakob Nielsen's book Designing Web Usability: The Practice of Simplicity.

It's great.

We're getting changes made that folks have suggested so far, and would appreciate hearing any other suggestions or advice KTM readers have -- thanks!

comments...

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TakingABreakPart7 15 Jun 2005 - 10:53 CatherineJohnson

Well, not a break, exactly. I'm going to finally collect my Dossier of Evidence to send to our new Assistant Superintendent (who's been great, so far), then go to the dentist.

While I'm doing that I'll be figuring out how to atone for this morning's bout of bad mothering with Andrew, who I blamed for something he may not have done.

Sigh.

We have got to get this kid talking. Or at least typing.

comments...

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ArePrivateSchoolsBetter 13 Jun 2005 - 18:58 CatherineJohnson

Back from the dentist to find a terrific comment:

Choice is better than no choice (for all, not just the affluent). However, you have to be careful about your choices. We felt that the public schools set such low expectations and used such a poor curriculum, that we had no choice but to look at private schools. The question was whether we could make up the difference at home. We saw the gap by sixth grade as being so great that the answer was no. He would be doing very little learning at school in spite of their claims of "differentiated learning". We felt that only with a great effort (in the evening, taking time away from other areas of interest) could we make up the difference. However, now that our son is in private school, with its own plusses and minuses, we see more details and are reevaluating our decision.

Charter schools - In our state, you have to have a pretty different charter idea to get it past the state education authorities. (More than a little conflict of interest here!) Some of these schools are fuzzier than the public schools and some incorporate "un-schooling" ideas. Not for my son, thank you. If you want to start a charter school that sets high standards and requires mastery of content and skills year-by-year, forget it. Some charter schools are technical schools that try to inspire kids with a more real-world curriculum. This is fine, but you have to be careful that the end result of this path is a job as an engineer rather than a technician.

Tutoring - This is better than nothing, but you have to be careful about not wasting your child's time and making things worse. It's expensive, but then again, look at the cost of private schools.

Private schools - When we looked at private schools (K-8 private schools are booming), we found that it was hard to get details. I asked about the math program at one very elite school, and they said that they used Everyday Math. Maybe I raised my eyebrows a little bit and she quickly added that it was supplemented. I really wanted to ask her why they didn't pick out a math program that didn't need supplementing. (How do you question the curriculum of a school that thinks quite highly of itself?) The school is known for giving out a lot of homework and I imagined that it could end up being a lot of busywork. I didn't want my son to become a homework robot. I just want a good, basic education.

I have also noticed that no school, public or private, goes out of their way to tell you exactly what they are teaching - books, workbooks, methods, homework, and tests. Having taught college math and computer science (long ago), I would like to see a yearly syllabus for each course. They usually just provide some vague description of philosophy and courses that sound so wonderful, but then you see the stuff that the kids bring home. For younger kids, it's very difficult to get a straight answer. "You did what(!) today?" Another movie? Boy, I would love to be a fly on the wall.

The biggest downsides to private school are the huge cost and the fact that I don't think some of them are much better than the public school I went to long ago. (Speaking of math, what is the future value of 8 years of private school payments at a presumed 10 percent in an S&P 500 fund when the child turns 60. I figured this out and you really don't want to know.) The biggest downsides to public school are the low expectations and the parental help or tutoring that must be added.

Another downside of private school was mentioned to me by my son's private (sorry, independent) school teacher. She said: "Once an independent school kid, always an independent school kid." This private school ends at eighth grade and at graduation (which I just went to - all kids go to the eighth grade graduation) they make a big deal about which school each child will be attending for high school. Only one was going back to a public high school. If your high school has a good honors or AP track, then I can make a pretty good argument that the difference between public and private high school is very minimal. If you are using private school to properly prepare your child to get to this track, then the implication is that it's extremely difficult to go back. Perhaps, until you look at the $20,000 - $30,000 price tag.

I can see why home schooling is now so popular. Does anyone know about small group home schooling where several parents and their kids combine their efforts and talents? One parent might handle math, one might handle music, and so forth. There would also be a larger social group than just the family.

comments...

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ArePrivateSchoolsBetterPart2 13 Jun 2005 - 17:58 CatherineJohnson

I think this may be from the same reader (the KTMGuest registration may need some tinkering--):

He gets Everyday Math in his private school - supplemented, they say, which is another issue. Most schools seem to supplement the bad math curricula rather than admit their mistake and go to a program like Singapore Math. I think that it's easier to supplement a NCTM-type math program (badly) that to replace it with something that would be hard to get past the NCTM-influenced faculty. You can't get away from it in private schools. Most of the teachers are trained in ed schools and have been indoctrinated.

He is in a private school because our public schools still use MathLand?(!) in a full-inclusion, child-centered, spiraling (circling in some cases) setting. They don't care about the above average kids because they have no influence on getting the "high performing" rating on the trivial state tests. That is why 25 percent of the kids in our town go to other schools and that is why our IEP percentage is at about 22 percent. Sometimes my wife and I can't believe that we are spending lots of money to get Everyday Math (I don't know of any school in our area that uses Singapore or Saxon Math) - and that we have to supplement! If we put him back into public school, then we would have to make up so much more.

This jibes with my experience.

I have now asked at least 4 different parents, all of whom have pulled their kids from the public school here, what the math curriculum is at the private school.

Not one of them knew.

One of them told me that the director of the private school had said, 'Your daughter is in 5th grade, not you.'

My feeling was, 'And you sat down and wrote out a check for $26,000 for that?'

($26,000 is the total sum per year to send a child to one of the private schools close to my house.)

ed school grads

The other issue raised by this reader -- that anyone who has graduated from an ed school is a closet constructivist -- is something else I've been wondering about.

An ed school student has been posting about his experiences, and his view is that the teachers all teach constructivism even when they don't realize that's what they're talking about.

In ed schools, constructivism is no long an 'ism' the way it is to us.

It's just the way it is.

comments...

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OutOfTheFryingPan 13 Jun 2005 - 18:02 CatherineJohnson

into the fire

(see the 3rd paragraph)

comments...

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WhoSaysLongDivisionIsHard 14 Jun 2005 - 01:51 CatherineJohnson

(you can click on this guy)




AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

comments...

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RegistrationChoices 13 Jun 2005 - 19:02 CarolynJohnston

I want to let everyone know that registering under a pseudonym is an option!

Any name is fine -- it just needs to be one of these mixed-case WikiWords (I have also seen these called BumpyWords and CamelCase).

I'd like to encourage pseudonym registration for those who don't want to use their names, so that we can tell all the KtmGuests apart...

to register, click here.

comments...

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CooperativeHomeschoolingClasses 13 Jun 2005 - 19:09 CatherineJohnson

Another great comment:

here in Michigan, cooperative homeschooling is thriving. I am not a homeschooler, but I looked into it because I was not happy with what they were offering my son in the first grade. Our local homeschooling groups meets in an area library. They offer each other classes, scouting, 4H and sports. They were really good people, but in the end, I put him back in the public school. Something else that seems to be happening now is parents pulling their children out for part of the day to homeschool them in a particular subject. What we really need everywhere until the public schools come to their senses is inexpensive, small group classes given by parents with expertise. There are a ton of us out here. I am giving a math class for 2nd graders this summer. My daughter just finished 2nd grade. She needs reinforcement on basic skills. So along with her Singapore math this summer, I rounded up some of her friends and we are going to have some fun doing math. I made all of the games myself. There will be some pencil and paper stuff ( our school used to do mad minute, which I love). I think the kids will really enjoy it.

What a great idea.

I would love to do a little summer school class, but so far I have no takers. (People are going to be at their summer houses, or they haven't finished researching math ed, etc.)

Keep us posted.

I agree absolutely that we need inexpensive small group classes until the public schools come to their senses. Around here we have zillions of parents with very high levels of expertise; I'd love to see this shared with kids.

I keep thinking about trying to organize a parent-child math class, but haven't gotten to it.

I've come to feel it's a good idea for parents to learn (or re-learn) math right along with their kids -- if only for the 'social modeling' aspect of it, i.e. your child sees you doing math, too. Math isn't just something school children do in school.

People always tell you to make sure your kids see you reading books.

I think the same principle applies to math!

comments...

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ILikeMath 24 Mar 2006 - 01:34 CatherineJohnson

Yesterday, after Christopher's 'I like bar models' confession, I decided I needed to hear more about this.

So I asked him, 'Why'd you start liking bar models?'

'I don't know. I got good at them.'^*

'Yeah?'

'Yeah . . . when you can do something, then you like it. Like math, I used to hate math. Well at school now I like it.'

'You like math?'

'Yeah.'

'In school?'

'Yeah.'

'Do you like math at home?'

'No.'

EOC [end of conversation]


When I started teaching math at home, I wasn't remotely thinking about creating a kid who would like math. Christopher hated math.

'Math is for nerds.' 'Math is for geeks.' 'I'm not from Singapore.'

The best I was hoping for was to have the math-is-for-nerds language go away, which it did.

Apart from that, my entire focus was on catching him up to the rest of his class, then catching him up to his peers in other countries.

We have had screaming, we have had yelling, we have had hysterical sobbing and crying. Kids really don't like their moms teaching them extra math after school.

But we kept at it.

We've had good moments, too. One night, just before bed, Christopher said, 'I love you, Mommy. I love you because you teach me math, and L.'s mom doesn't help him with his math.'

Then he got all embarrassed.

I can tell Christopher is happy I'm teaching him math; I've even heard him boast to his friends about how hard the math I 'make' him do is.

But it hadn't occurred to me that I might be creating a kid who actually likes math.

Not a bad year's work.<sup>**


*</sup> I'd say this is a classic example of the high confidence levels you see in American school children in TIMSS surveys. I wouldn't have said that Christopher is 'good at bar models,' and I was surprised to hear him say so. It's true, though, that just in the past couple of days he's moved from absolute novice to . . . advanced beginner.

^** Christopher had two terrific math teachers this year: Amy Panitz (of whom Christopher once remarked, "Mrs. Panitz is a better teacher than you") and Nancy Woeckner.

ILikeMathPart2
TeacherAppreciationWeek