Entries from ParentsTeachingKids

See also: MathInTheBlood (Part 1)

I should explain that for my son, school has never been an ordinary undertaking. As a young child, he was diagnosed with an autism spectrum disorder (Pervasive Development Disorder, which is a diagnosis that means 'looks like some kind of autism to me'). His preschool years were a nightmare of trying to treat his developmental problems with Applied Behavioral Analysis therapy, while simultaneously searching for a medical treatment that would help him. The tough thing about having a kid with this disorder is that you have to work on him hardest in the earliest years, when you're most clueless about his prognosis: it's utterly crazy-making, and I was pretty crazy.

In his elementary school years, my son has made great progress; but he still has an attention deficit, severe organizational difficulties, and problems with deep reading comprehension and social cognition. So the fact that he was flying independently with Saxon math, and hit a mountainside when we encountered Everyday Math in fourth grade, was a Big Deal.

Besides, he's a smart kid with an autism spectrum disorder. Math is his greatest strength, and a career in math, science, computers or engineering is his most likely future. In those fields, his colleagues will know how to deal with him (given the sheer numbers in which kids are getting autism-like disorders these days, they'll probably be just like him).

At the end of fourth grade, during a conference with his teachers, I floated the possibility of his doing fifth grade math on his own, with me as his tutor, using Saxon math. It's legal in this state to homeschool in one subject like that, but we all had big reservations about it. We've worked so hard to enable Ben to function in a regular classroom with the other kids that the thought of separating him from the other kids at that point, just because we didn't like the math curriculum, seemed unbearable. So I sighed, gave up, and we entered fifth grade with Ben still signed up for Everyday Math.

Somewhere early in fifth grade, Catherine and I struck up an Internet Friendship (we have never actually met in the flesh!). Among her other interests, Catherine is a noted non-fiction author who specializes in autism research and treatment... we encountered each other in the way that people do online, and I figured out who she was.

Catherine is a true Math Revolutionary. While I, with all my math degrees and our successful experiences with Saxon Math, was still dithering about whether or not to pull my son out of school and teach him myself, Catherine was actually doing her ten-year-old son's fuzzy math homework for him every night, so she could get that over with quickly, and move on to teaching him mathematics from what she regarded as a better curriculum.

Completely independently, she had chosen Saxon Math for him.

Catherine and I, in spite of our different paths in life, have a heck of a lot in common.

more to come...

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.

(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.

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.

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

BonusPreTeenPost 07 Jul 2005 - 21:21 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

---

SummerSupplementTime 07 Jul 2005 - 21:25 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

---

PrenticeHallArrives 07 Jul 2005 - 22:17 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?

---

SaxonPlacementTestsAndGuides 07 Jul 2005 - 21:42 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

---

TwentyFirstCenturySkills 17 Jul 2005 - 21:02 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

---

ILikeMath 07 Jul 2005 - 21:22 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

Number 2 Pencil

Which brings me to a blog I like called Number 2 Pencil, written by Kimberly Swygert, psychometrician.

In a post today, she writes:

Wouldn't it be fun to produce research showing that the students who learn the most in school and do the best on standardized tests are also the ones who are happiest and have the most love of learning? I'm not saying I know that's so; I'm saying it would be fun to poke at the anti-testing folks with those kinds of correlational results.

I hope someone does that study.


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

---

ILikeMathPart2 07 Jul 2005 - 20:43 CatherineJohnson


from Barry Garelick (I've added paragraphs to increase white space):

When my daughter tells me she hates math, my response is always the same. "Well, I have good news for you. You don't have to like it. You just have to know how to do it."

She's stopped telling me she hates math.

We shouldn't be so concerned with whether kids like or hate something. I hated history and English, but you either toe the line or get bad grades, and I didn't want bad grades.

In terms of math, kids hate it when they can't do it. When my daughter catches on to something, she likes doing it.

Math is not easy sometimes and it takes work, and that message should also be imparted to children. Not that it's impossible; but that it can be difficult, and that we all had to work at it.

When math isn't taught properly, then kids are not able to do it, and then they hate it. I've been talking to various adults lately who fit the description NCTM wrote about in the Jay Mathews' Post column of May 31 in which they talked about adults groaning when they heard the familiar story problem about distance, rate and speed. (A man starts out at 9 AM at 15 mph, etc etc). The adults I talked to said they hated those problems because they couldn't do them. When pressed, they admitted their teachers were not very good.

This is not a definitive sample by any means. I lucked out and had a very good algebra teacher who gave us very good instruction on how to solve story problems. As a result, I liked them. The fact that I ended up majoring in math may or may not be coincidental.


I like math
I like math, part 2
BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
SummerSupplementTimePart2
SundaySchool
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids

---

NewComments 07 Jul 2005 - 20:47 CatherineJohnson


SteveH has a new comment about Base 5 & fuzzy math in the CompareAndContrast thread.

update: More from Steve!

Thank you!

I love this, especially:

when my son was born, I told my mother that I wanted 3 things for him in life: 1. To care about other people. 2. To know the value of hard work. and 3. To be happy. Her response was that if he did numbers 1 and 2, then number 3 will take care of itself.

And this:

If Everyday Math (as an example), thinks that doing things in different ways is helpful, then why do they completely avoid the standard algorithms (the best ways)? While doing Singapore Math with my son at home, he ends up doing a number of things in different ways than his EM at school. This can be helpful, or it can be an overload of the brain.

I think SteveH is also the commenter who pointed out that ed school students are taught constructivist teaching methods via direct instruction.

I say that's not fair.

If our kids have to discover math, ed students should have to discover discovery.

Guess and check, guys!

Lots of sharp observations on math & practice, math & creativity, math & solving problems more than one way here: ILikeMath

---

TheSaxonMathOfSpelling 20 Jul 2005 - 15:35 CatherineJohnson


Boy.

Blogging (or blikki-ing) takes time.

I've got all kinds of great stuff to post on engineering & discovery & creativity, and it's still sitting around in emails & Stickies.

And now it's 7 pm.

A comment from Susan got me going on Megawords, so anyone interested in the research on how children learn to spell should click on MoreSpelling.


BeingYourChildsFrontalLobes
LiveBloggingTheSpellingBee
GreatMomentsInWorldHistory
SummerSupplementTime
SummerSupplementTimePart2
HowToSpell
HowToSpellPart2
MoreSpelling

---

AnotherWikiPossibility 19 Sep 2005 - 23:07 CatherineJohnson


Another possibility for communal Wiki pages is to do something like the thread for RussianMathPart3: pose a problem or a lesson everyone can comment on.

I'm interested in comments on the fraction lesson J. D . Fisher has posted at Math and Text.

My immediate reaction to J.D.'s post is that it would be terrific for developing teachers' conceptual understanding of mathematics, and possibly for developing teachers' pedagogical content knowledge (pdf file).

But I wouldn't be able to teach it to Christopher, even though he does know that a fraction is (also) a division problem.

(I'll pull my thoughts together on this later--time for a bike ride now.)

I'd love to get other people's reactions.


KitchenTableMathIsAWiki
WikiPagesForReadersAndCommenters
WikiHowTo
AnneDwyersSingaporeMathClass

---

FreeWorksheets 07 Jul 2005 - 21:26 CatherineJohnson


from SusanS:

Two more sites with free math worksheets (and other free stuff) are edhelpers.com and superkids.com. I do love the free stuff.

Thank you!

our favorite math supplements

We are slowly but surely pulling together the sidebar pages, so you might want to take a look from time to time.

We also need to get a reader recommendation page going.

I'm adding Susan's recommendations to the 'our favorite supplements' page so they'll be where people can find them easily.

I'll also gather together the grammar, spelling, handwriting, etc. book & curriculum recommendations into one place, with links to the original reader comments. These are invaluable, so keep them coming!

Back to online math resources, also remember Carolyn's recommendation:

... These math worksheet generators can come in very handy.... very configurable; you can set the number of columns and rows of problems, and the difficulty of the problem, and the numbers of significant digits in the solution, and so forth....

We especially found the sheets for fraction and decimal long division useful. That's a skill that just takes a lot of practice.

computer learning versus paper-and-pencil

Susan inspired me finally to track down some of my favorite online resources and get them entered on the Our Favorite Supplements page.

But first I should say that I'm leery of online math practice, for 3 reasons:

• Christopher has never learned well using a computer

• I've seen research showing a slight decline in student achievement in Israeli schools after the introduction of computers in classrooms

• Jakob Nielsen says people read 25% more slowly onscreen than on paper

Christopher didn't really get his math facts down cold until we started doing the Saxon fast fact paper-and-pencil worksheets.

He didn't make any headway that I could see using a software math facts program, and I don't think he made much progress using standard flash cards, either.

To be fair, we have problems using materials like flash cards, since I'm constantly having to hide them from Andrew, which of course makes it harder to find them when I need them, which, in turn, makes me tend to use them less than I would if they were easy to get to ...

So I don't know whether anyone should be drawing conclusions from my flashcard experience.

But when it comes to computers-versus-paper and pencil, if you've got time to print out the worksheets Carolyn & Susan have pointed you to, that's probably the better choice.

Online 'worksheets' may be to paper worksheets what fast food is to homemade.

That said, I've eaten plenty of fast food in my day, and so have my kids.

So here's one of the main online resources I've liked thus far.

Saxon Math online problems and math activities

• I've seen a number of parents around the web recommend this Saxon Math 'fast facts' generator. The page is clean, simple, and visually compelling. You decide which math-fact problems you want to do, how difficult the problems should be, and how many you want to do. You can also do timed or untimed problem sets. That's great, because kids love seeing their timing get faster.

• Saxon online math activities I love these things. Don't know why; I just do. They're fun.

• Here are the 5th grade activities.
  Apparently the site now tells you which activities to do after which lessons in the book; plus you can download the activities for use when you are not online.

• Saxon online equivalent fractions These are great. OK, I'm sold. Forget the Israeli kids; we're doing online equivalent fractions this summer.

• Saxon online rectangular area

TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4
SummerSupplementTimePart5 (resources for preventing summer regression)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

TeachYourChildToTypeThisSummer

And lots more....

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SummerSupplementTimePart5 02 Jul 2006 - 17:49 CatherineJohnson


In SummerSupplementTimePart4 I mentioned that I think I have useful advice for 3 groups of kids:

• kids who, for whatever reason, have fallen significantly behind their classmates

• kids who are right on track, doing well, and you want to keep their math skills in shape over the summer

• kids whose parents want to accelerate their math learning -- in particular, to get them in position to take and master algebra in the 8th grade

My own strategy for kids who have falllen behind (Christopher's situation last summer) is in that post.

But please! Everyone! Chime in.

These are the ideas I've come up with working with one child, and talking to a group of 4 people (Carolyn, Ed, my neighbor & friend Laura, and my friend Debbie), with as many on-the-fly advice sessions as I could get with Christopher's teachers thrown into the mix.

One of the main reasons I wanted to do a bliki with Carolyn was to find out what other people are doing!

avoiding summer regression

For kids who are doing fine, here are my thoughts.

Assuming the research I've found (pdf file) is to be trusted (it makes sense to me, for what it's worth) there are two points to bear in mind:

• summer loss equals about one month of a child's learned skills and knowledge from the previous school year

• summer vacation is more detrimental for math than for reading, and most detrimental for math computation and spelling
  

I find the math-versus-reading factoid ironic given that schools universally hand out summer reading lists, not summer math lists.

So here's my own stab at a summer maths list. (I think the British plural works for this.)

summer maths list

• 'mad minute' worksheets daily (be sure to include fractions, decimals & percents if your child has gotten that far)

• a word problem or two each day, if you feel ambitious (Carolyn is posting problems from the Singapore series)

• a Math Olympiads word problem each day, if you feel really ambitious (I'll probably post some of these)

books (worksheets)

I did a quick scan of the various 'Mad Minute' books on Amazon, and folks seem to like this one best:

• The Mad Minute: A Race to Master the Number Facts by Paul Joseph Shoecraft, Terry James Clukey

The Mad Minute covers Grades 1 through 8, and includes fractions & percents.

If any of our teachers or parents have used this book, let us know.

• Saxon Math Tests and Worksheet Booklets for each grade level. 120 'fast fact' worksheets to be completed in under 5 minutes. These are the worksheets that finally got Christopher up to speed, and we're doing them again this summer. Cost for the Tests & Worksheets book alone is around $20, probably less at the Homeschool Super Center. If you're just going to use the worksheets you don't need to buy the textbook or the solution manual.

books (story problems)

• Singapore Math Challenging Word Problems series. These are terrific books. Almost 300 story problems in each, grouped according to subject area (e.g. measurement, time, multiplication-and-division, etc.) All problems are multi-step, & all answers are in the back. $7.80 plus shipping.

caution: your child almost certainly needs to use a book 1 or 2 grades younger than the one he's in. So you might want to have your child take the placement test before ordering.

• Math Olympiad problems -- you can find Math Olympiad books all over the place. They're expensive, so try to rustle up a used copy.

• Math League Contest Books from Math League. Wayne Wickelgren strongly recommends these books for everything from building your child's math achievement to preparing for SAT's. I love them, too. Filled with the kinds of problems, including logical reasoning, children are going to need throughout their lives & much more 'sensible' than the showy problems from Math Olympiads. Each book spans 3 grades, and all answers are in back. $12.95 a book plus shipping.

worksheets

• Carolyn likes these free online worksheets from homeschoolmath.net, a favorite site of mine. (I think their e-books look good.)

• Homeschoolmath.net has fraction & decimal worksheets, too.

• Susan S likes edHelper.com and SuperKids.com.

• Brenda M likes Basic Facts Worksheet Factory from School House Technologies. (Thank you, Brenda!) They offer free worksheets as well as worksheets for purchase.

virtual worksheets & problem-solving

I've mentioned that I'm leery of online learning, but you can't beat it for convenience and speed. I like Saxon's offerings:

• Saxon Math 'fast facts' generator The page is clean, simple, and visually compelling. You decide which math-fact problems you want to do, how difficult the problems should be, and how many to do in one set. You can choose between a timed & untimed option. That's great, because kids love seeing their times get faster.

• Saxon online math activities I love these things. Don't know why; I just do. They're fun.

• Check out 5th grade activities.
  Saxon now has online exercises for each grade. They tell you which activities to do after which lessons in the book, and you can download the activities for use when you are not online.

• Saxon online equivalent fractions

• Saxon online rectangular area

• Saxon has lots, lots more, so take a look

• Batter's Up Baseball Game I can't find the 'addition facts baseball games' the kids at school love so much, so here's another one. Christopher told me just now that he loved playing online 'addition baseball' when he was in 2nd grade.

I found it!

The kids at school were crazy about Funbrain, especially math baseball.

update: reader recommendation

Also check out Singapore math's Intensive Practice books. These books cover all sorts of fun things including word problems, computation, puzzles and patterns etc... They are not joking when they call it intensive. Some problems are extremely difficult (and some are quite easy too) and we cover them orally and together with the view that exposure to these types of problems will only expand abilities!

I agree. I have two of these books, and they're terrific. [Catherine]

FreeWorksheets
TreadingWater

SummerSupplement
SummerSupplementTime
SummerSupplementTimePart2
SummerSupplementTimePart3
SummerSupplementTimePart4 (resources for kids who have fallen behind)

SaxonPlacementTestsAndGuides
SingaporeMathPlacementTest

and:

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

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WickelgrenOnIntroducingAlgebra 08 Jul 2005 - 17:19 CarolynJohnston


I've been looking again at one of Catherine's favorite books, Math Coach (by Wayne and Ingrid Wickelgren).

Wayne and Ingrid have a lot to say about what they consider the most difficult aspects of elementary math -- long division and fraction manipulation. But it's what comes after that that interests me now: their discussion of the importance of teaching algebra early. Wayne suggests that the most important thing you can show your kid, what should motivate them most to want to continue in math, is the power of algebra to solve hard problems.

Most problems in prealgebra and early algebra start out something like this:

John is 27 years old. If his age is 3 times Pete's age, how old is Pete?

If you have a kid like Christopher or Ben, you know he's going to spit out the answer on the spot and tell you not to waste his time with this stupid letter stuff.

That's why Wayne Wickelgren suggests that, when you're ready to introduce your kid to the notion of algebra, the first thing you should do is sit down with him and let him watch you do a problem like this one:

In two years, Jean will be twice as old as Chris will be. In six years, Jean will be four times as old as Chris was last year. How old is Chris now?

In short, start with a demonstration of how algebra-at-your-fingertips gives you mindblowing powers. I was reading this last night and thinking: if I tell him that this problem is what algebra is all about, Ben will be blown away. Why scare him off? Maybe start with something simpler...

But the hard thing about this sort of problem isn't going to be doing the algebra: it's going to be setting up the equations, given the word problem. And that's going to be hard no matter how I try to teach it. Doing the mindless rote stuff required to crank out the answer, once you have the equations, is the easiest part of the problem. And I know Ben: he'll think that's the cool part.

Given that, I can't see a reason to hold off introducing algebra. Once a kid is at the sixth or seventh grade level in math, the heck with guess-and-check and pan-balance problems; the heck even with bar models. The most general tool that we currently have for solving word problems, and the only one that we have that isn't stymied by some word problem or other, is algebra. He may as well be motivated to go full speed ahead with the letters and symbols. Wickelgren says that algebra is the key to the castle; it's the most effective means for solving tricky math problems that's ever been devised. As such, you want it to be the tool that kids reach for instinctively when they have a tricky math problem to solve.

Here's a quote from a great article by Ethan Akin, "In Defense of Mindless Rote":

On the other hand, mathematics is cumulative and there are a great many skills that you have be unthinkingly familiar with. Every grumpy calculus teacher will tell you that most of the problems his students have come from weaknesses in algebra. For the students who say "I really understand it but...." the but is that for them algebra is not easy background knowledge. They are trying to build on a foundation of dust. A lot of college majors need a bit of calculus or statistics which are simply walled off to students who don't have sufficient skills in algebra. These are basically not hard subjects but they appear unnecessarily terrifying to such students.

Conversely, a practiced facility with algebra can provide its own positive reinforcement. Not only is the mathematics built on the algebra, but facility in algebra gives the student confidence in the face of new mathematical challenges. As the above discussion makes clear, such confidence is entirely justified.

I am motivated now to try to introduce real algebra by the end of the summer. No more pussyfooting around!


Wickelgren on introducing algebra
Wayne Wickelgren on algebra in 7th & 8th grade
Wickelgren on math talent & when to supplement
late bloomers in math & Wickelgren on children's desire to learn math
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
Wickelgren on why math is confusing

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CalculusProfessorEmailExchangeWithParent 01 Aug 2006 - 19:53 CatherineJohnson


Number 2 Pencil links to this exchange of emails between a math professor and one of his students, who is flunking calculus.

The professor is using a pedagogy known as Process Guided-Inquiry Learning, or POGIL:

I mentioned in an earlier post that one of the more controversial -- and to me, appealing -- aspects of POGIL instruction is that the instructor is not seen as a source of knowledge but rather as a facilitator of learning. In non-eduspeak, this means that the instructor is there to observe and to guide, rather than to tell students what to do or think.

I also mentioned, and one commenter pointed out, that students HATE this (at least at first). Typically, students -- even upper-level students in the major who have been around the block -- just want to get the darn problem done, and when people like me insist on students asking the right questions rather than just forking over the answers, things can get heated.

In practical terms, POGIL means that when 'Pat' comes to his professor's office for help, the professor refuses all requests for one-on-one demonstration of the problems being taught in class:

…when Pat would ask me a question such as, "Can you tell me how to do problem 7?", I would say: Let's start by asking the right questions. What are you being asked to do in this problem? What information is given to you in the problem statement? And what do you know from the course, your reading, or your work on other exercises that will help get you to the goal? I made it a point to NEVER give Pat explicit help on content unless it was a last resort -- Pat absolutely HAD to cut the apron-strings from me an learn how to approach, analyze, and solve a problem alone, or else Pat's chances for success in a future career or even making it through college didn't look good.

This goes nowhere.

Finally 'Pat' sends an email explaining that he requires direct instruction in order to learn.

The professor tells him he is wrong.

Pat sent me an email just after midterms that said something like: I now understand why I am not doing well in your class. My learning style is such that you have to show me exactly what to do, or else I can't do it. But you always answer my questions with more questions, which isn't showing me exactly what to do. So from now on, please show me exactly what to do first, and then I should be able to do it. My response was something like: Pat, we've been doing this every day in class -- I work a few problems at the board all the way through during lecture, and then I give you exercises that are based on the stuff you've seen. So you are seeing me show you what to do, and yet you're still having difficulty solving problems on your own. So perhaps your assessment wasn't quite right, and we should be working on your problem-solving skills in office hours.

Then Pat's mother gets into the picture.

(via email): I know [Pat] tried to explain to you that when [Pat] asks questions [Pat] needs answers not another question. We had [Pat] tested at [a local university] in January through the suggestion of [an academic counselor at my college].

During this testing we found out [Pat] has a learning disability. [Pat] does better with visual explanations then being asked another question. [Pat] needs to see how to physically work a problem so he can comprehend it. [Pat] is a slow reader which also frustrates [Pat]. If it is a word problem [Pat] has problems figuring out what are the essential parts of the question to find the answer.

This infuriates the professor, and, subsequently, all of his commenters as well, who pretty much stomp mom to death in the comments thread.

Pat fails the class.

The commenters are united in their view that Pat is a lucky guy to have experienced POGIL calculus, and he had no business hosing the course.

Memo to self: the time to begin instilling core take no course from professor who blogs principle in 10-year old son is now.

POGIL

POGIL, POGIL, POGIL

This does not sound good, POGIL.

I should reserve judgment.

I should, but every one of the little-red-light thingies on my Constructivist Nightmare Detector is flashing wildly, and all the sirens are going off—

So I’m not doing a very good job of reserving judgment.

POGIL is a student-centered method of instruction that is based on recent developments in cognitive learning theory and results from classroom research that suggest [sic] most students experience improved learning when they are actively engaged, working together, and given the opportunity to construct their own understanding. POGIL emphasizes that learning is an interactive process of thinking carefully, discussing ideas, refining understanding, practicing skills, reflecting on progress, and assessing performance. In a POGIL classroom or laboratory, students work on specially designed guided-inquiry materials in small self-managed groups. The instructor serves as facilitator of learning rather than as a source of information. The objective is to develop skills as well as mastery of discipline-specific content simultaneously. (Emphasis added)

OK, that does not sound good.

homeschool mom with common sense-y

I'll get to the professor’s various posts on POGIL as soon as I can.

I do want to read them.

But in the meantime, there's one homeschooling mom on the thread (son has LD) whose comments make sense to me:

Pat says clearly that your Socratic style doesn't work for [him]. Why do you then believe that it does work? You (rightly) want [him] to learn problem solving, but just because your method of teaching ... works for others doesn't mean it works for [him]. Maybe [he] needs repetition, repetition, repetition of the underlying content before [he's] ready for process. Other students may grasp the process after going through the underlying solutions three times, or six times, but maybe [he] needs thirty times.

You model the problem solving that you want [him] to do-- Where have you seen a problem like this? What rule did we use?-- but in a sense that's no better than modeling the actual rule for Problem 13. You want [him] to intuit that [he] is supposed to be asking [himself] those questions. But what if, as seems to be the case, [he] isn't intuiting that? Then [he's] not learning anything.

The bad news here is that, clearly, constructivists are giving lots of workshops to math professors.

Even worse, math professors are attending them.

inflexible knowledge, flexible knowledge, and expertise

One of the problems with constructivism (and, apparently, with POGILism) is that it tries to teach higher-order problem solving first, instead of second.

That option probably isn't on the menu.

According to Daniel Willingham, knowledge is always inflexible before it's flexible. You can't hopscotch over the inflexible stage by teaching process, or asking students to discover addition.

Problem solving and critical thinking seem to grow out of extensive practice of surface, shallow, inflexible knowledge.

I’d like to know more about how this happens.

At a minimum I’d like to know what cognitive psychologists (psych department cognitive psychologists, I mean) understand about the process at this point.


And I hope that Robert, who writes the brightMystery blog, will join us at KTM once in awhile to think about these things.

update

WelcomeRobertTalbert

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MeasurementAdviceFromCarlL 08 Jul 2005 - 21:46 CatherineJohnson

Re: Measurement

My first year teaching high school freshman (I just finished my 3rd year at a urban neighborhood school) I was completely shocked that none, and I mean none, of the kids could measure using an inches ruler.

How can they get out of middle school, or even grade school, not knowing how to measure? I still have no clue. I doubt its the constructivists fault due to their fondess for hands-on, manipulatives, and project, which all lend themselves to measurement.

What I have observed:

• Metric OK, Inches Not -- While the kids can't (or won't) measure in inches, many (but not all) can measure using a centimeter ruler. Fractions rear their ugly head again.

• Estimation, Schmestimation -- The kids do not know when it is, or is not, appropriate to estimate. The kids have trouble estimating measurements between the lines of the ruler. But the kids are very willing to make bad estimates to avoid having to figure out what the little lines mean. 2 5/16 inevitably becomes 2 1/2.

• What is a protractor? -- The kids REALLY don't know how to use a protractor (except as a frisbee). Most don't even know that its purpose is to measure angles.

A side note related, I believe, to measurement. Each year I do a lesson where we compare the kids height in inches to their shoe size. The majority of the kids do not know how tall they are, let alone how to convert the height in inches.

So by all means get a ruler, protractor, some measuring cups and spoons, and a kitchen scale (or even better a pan balance) and start measuring everything around the house!

I intend to take this advice.


SummerProgramUpdate (measurement skills)
EarthboxDay

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EarthboxDay 21 Nov 2005 - 04:14 CatherineJohnson


Since it's my birthday, and since I get to do what I want on my birthday, more or less, and since I DON'T HAVE A CAT TO BLOG ABOUT, I am choosing to blog about EarthBoxes.

EarthBoxes are even better than Russian Math

To prove this to KTM readers, I am going to enlist Christopher in a measuring task.

No!

Not a task!

An investigation!

WE ARE GOING TO PERFORM A MEASURING INVESTIGATION!

WE ARE GOING TO COLLECT DATA!

AND WE ARE GOING TO USE A RULER TO DO IT!


OK, now we have resistance and rudeness.

'No!'

'Not today!'

'Then I'm not doing a lesson!'

Funny how the kids in the Math TRAILBLAZERS PLAYLETS never seem to react this way when a grownup suggests that they collect data in order to solve a problem.


Alright, while the moaning and groaning continues in the background, I will locate:

• a ruler

• a tape measure