Entries from MiddleSchoolMath

A comparison of our eighth- and ninth-grade data reveals three middle grades experiences associated with students who take and succeed in higher-level courses in grade nine.

These experiences are:

• studying “something called algebra” in the middle grades;
• reading a great number of books in grade eight; and
• expecting to graduate from college.

Studying “something called algebra”

Across all schools, 62 percent of the students who said they had a course with “algebra” in its title during the middle grades were enrolled in college-preparatory mathematics in ninth-grade. Eighty-five percent of these students earned a “C” or above. High enrollment schools enrolled 82 percent of students who had algebra in the middle grades in college-preparatory mathematics courses. They had virtually the same success rates as schools with lower enrollment rates. Clearly, students who begin algebra earlier are more likely to succeed in an accelerated mathematics curriculum if high schools choose to enroll them inthis curriculum.

You can just feel how much fun it is trying to drag information out of young teenagers for the purposes of a Major Report.

Yeah, I studied something that said algebra. I think.

Hotmath.com

[Hotmath provides] explained solutions to the odd-numbered homework problems from most of the popular secondary math textbooks used in California. Thus, teachers can now assign practice problems for homework where teacher-prepared, explained solutions are instantly available, and can mix in even-numbered problems for challenges. Students who do not need to see the worked solutions needn't bother, and students who might abuse the availability of worked solutions will be tested on the even problems.

Providing students with worked out examples of math problems has been found to be more effective than simply assigning the same problems for the students to work out on their own. In one experiment (Carroll, 1994), 40 high school students were instructed in how to solve linear equations. In an “acquisition phase” the students were divided into two groups and their instruction differed in the following way: in the “conventional learning” group, students were assigned 44 unsolved problems to work out (in the classroom and at home homework), and in the “worked examples” group students were provided with the same problems, but half of the problems were accompanied by correct solutions. After completion of the assigned problems, both groups were tested on 12 related problems, 10 of which were very similar to the linear equations presented in the acquisition phase, and 2 of which were word problems, used to test whether students could transfer and extend their knowledge to a new context. No worked out examples were available during the test. The test results revealed that students in the “worked examples” group outperformed students in the “conventional learning” group on both types of the test problems. A second experiment, employed a similar methodology but focused on “low achieving” students (students with a history of failure in mathematics, and students identified as learning disabled). Here, the data revealed that students in the “worked examples” group required less acquisition time, needed less direct instruction, made fewer errors, and made fewer types of errors than students in the “conventional learning” group.

Related research (Pass & Van Merrienboer, 1994) sheds light on the cognitive underpinnings of the effects described above. In this study, 60 college-aged students were instructed in geometry concepts. As in the Carroll experiments, students were assigned un-worked problems to solve or worked out examples to review (unlike the Carroll study, the “worked examples” group was assigned no un-worked problems to solve). In this study, the researchers manipulated the nature of the problems presented to the students: within each group, some students received problems which were all similar to each other, while others received a more varied problem set. Furthermore, the researchers measured the “cognitive load” experienced by the students. This research revealed that while students in the worked examples group completed their work more quickly, they perceived the work as less demanding and displayed better transfer performance at test. The effect was most pronounced for the students given highly-variable problems. The researchers suggest that the reduced cognitive load associated with the worked examples enabled students to “take advantage of” the variability in problems by using the available cognitive resources to process the underlying similarity in the problems (i.e., the mathematical concepts being taught), and to integrate the current problem with existing knowledge (Linn, 2000).

I think it's going to be fantastic for Christopher to have an answer source that isn't His Mother.

Especially since it looks like I'm going to have to start some heavy-duty Writing Instruction this year. (That's another story.)

cognitive load

We're trying to reduce cognitive load.

update

OK, that was unkind.

Anyway, Carolyn and I have been trying to figure out WHICH Prentice-Hall middle school math textbook the state of California adopted, since we had thought we were both using the same one.

It turns out we're not. (OK, it's possible Carolyn is not obsessing about this. I, however, am losing Valuable Work Time trying to track down which text the folks at mathematically correct like, and why.....)

So far I find a positive review of Ben's text for the fall (Prentice Hall Math Course 2) at mathematically correct; then I find, on what I assume must be David Klein's web site, that Prentice Hall Pre-Algebra (Christopher's Prentice Hall book for the fall) is the one California actually adopted.

Apparently, my plan is to let this Get To Me. Who moved my cheese? And why, why, why?

(I may become calmer if Ed resolves the computer crisis that's currently unfolding upstairs in my office.....)

Here we go:

CA 2001 middle school textbook adoptions

positive review of Prentice Hall Math Course 2

severely fragmented review of Prentice Hall Pre-algebra

Prentice Hall California Mathematics
(this is probably going to be terrific for me, assuming CA is actually using Pre-Algebra, not Course 2...)

teachers' resources on Prentice Hall CA Math site

• in the STUDENT SECTION: online 'self-tests' for each of the chapters in Prentice Hall Pre-Algebra
• in the TEACHER SECTION lists of prerequisite skills for each chapter in Prentice Hall Pre-Algebra

I may be able to pick up some pedagogical content knowledge in my spare time.

prerequisites for Chapter 1: Integers and Expressions

• adding and subtracting whole numbers
• multiplying and dividing whole numbers
• comparing whole numbers
• combining whole numbers
• reading numbers on a number line
• using whole number patterns
• graphing on a number line

OK, we've got it covered.

Except maybe for the using-whole-number-patterns business.

update, update

And here is a whole big web site for middle school math that looks like fun. (Did I just say that? Have I lost my mind?)

Apparently I have become a person who SEEKS OUT Problems of the Week.

I'm going to have to get Bernie to tell me what this means.

[pause]

uh-oh

There's a whole lot of spatial stuff on the problems web site.

I have a long way to go.

They have an article about Kitchen Table Math in the latest issue! (Although so far I haven't been able to find it.....I don't think....)

Sigh.

However, I have managed to attach and display the logo they sent me!

A ktm guest left a link to an online course that is actually called Universal Algebra.

I'm going to add this link to the Favorite Math Supplements for Kids page (on the sidebar) so people can find it.

By the way, anyone who has resources to add to the list should let Carolyn or me know.

Today was Ben's first regular day at his new middle school (yesterday was officially Transition Day, for 6th-graders only). He came home pretty happy; they are helping him with his organizational stuff, he is coping with his locker, and he doesn't have any homework yet. He is enjoying feeling like a big kid. Life is pretty good.

I went to pick him up at the end of school; he wanted to give me the grand tour of his teachers and classes, but we didn't have enough time to do the whole thing. I did ask him to take me to his math teacher, so I could shake her hand and tell her that I'd chosen this middle school because I thought it had made a good choice in math curriculum (having chosen Prentice Hall's Math Courses 1 through 3), and that I'd fought like heck to get Ben into their school for just that reason, and was commuting for a half hour in the morning in order to get him there.

So Ben and I went into his math class, and I introduced myself, and stuck out my hand and smiled, and got about halfway through my spiel when I noticed that in back of her there is a stack on the floor of Connected Mathematics pamphlets. So my final sentence actually came out something like--

"... I really approve of the curricular choice you've made and -- what curriculum are you using ???"

It turns out they are using a hybrid curriculum: every unit will be taught using both Prentice-Hall and Connected Mathematics.

A little background first: Connected Mathematics is an extreme example of a constructivist mathematics curriculum that our school district has adopted (in fact, our SD was an early adopter of Connected Mathematics). I battled long and hard last year to get Ben into a middle school that used a traditional mathematics curriculum instead of Connected Math. I had tearful phone conversations and hot-tempered meetings over this issue.

Whether or not I think Connected Math is a reasonable math curriculum has not been an issue in my fight to have Ben learn math from a traditional curriculum. Ben has special needs, and won't have a lot of employment options; he will need a strong math background in order to have a trade as an adult.

In grade school, Ben did extremely well in Saxon math for the first 3 years; but for the last two, the school switched to a semi-constructivist curriculum (Everyday Math), and Ben ceased to thrive. He didn't cope well with the emphasis on verbal explanations, the games and group exercises, multiple methods for doing calculations, and constant jumping from topic to topic. He went from being completely independent in math class to requiring an aide on a daily basis (our story was mentioned in Linda Seebach's recent article on KTM in the Rocky Mountain News).

When we were discussing Ben's options for middle school, everyone agreed that he needed a traditional curriculum. I open-enrolled him into this school in order to ensure that he would get one, and battled the school district when it looked as though he would not get into it.

Now I find that the school I thought -- was in fact assured -- had a traditional math curriculum actually has a hybrid curriculum which incorporates Connected Math. Connected Math is so purely constructivist that it makes Everyday Math look tame.

Here is the Mathematically Correct review of 7th grade Connected Math (and the many reasons why it received an F).

Here are descriptions of the units in 6th grade Connected Math and 7th grade Connected Math. Read these to get a feel for what kids spend their time doing in Connected Math.

I attended a new parents session at our neighborhood middle school in which Connected Math was discussed. We were told that Connected Math was generally not well liked by parents, who found it impossible to help their kids do the problems because "the style in which it is taught is so different from the rote way in which parents have typically learned math". I have a Ph.D. in math, and taught and tutored math at the college level for ten years; this kind of prevarication doesn't impress me. I know what Connected Mathematics and similar curricula do; they leave college students weak, and utterly without math skills.

We have not yet decided what to do; fortunately we have the weekend to think this over.



worsethanyouthink

SingaporeMathPlacementExam 05 Sep 2005 - 13:33 CarolynJohnston


The last two nights, I've been giving Ben the Singapore Math 4A placement exam (all the Singapore Math placement exams can be found here). I had a look at the Singapore Math 3A and 3B tests, and decided that Ben can probably do them fairly easily; but I wasn't so sure at all about Singapore Math 4A.

I've been giving the test to him in little chunks. The first day I did it -- it was several days after school had started, and I hadn't tutored him at all, and he was having an easy time of it since all they were doing was factoring numbers into primes -- he howled as though I were slipping bamboo shoots under his fingernails. That was to be expected. We always get the worst resistance after he's had a break.

At this point, I've gone as far with him in these placement tests as I plan to go -- 4A is definitely the place for him to start. What I'm finding is that in the first part of the placement exam, where the problems are computational, he is doing fine; I've taught him well in that regard (using mostly Saxon math, with some Prentice-Hall). However, after the first ten or so problems, the placement exam starts to test a kid's problem-solving ability. In Ben's case things got ugly quickly. He fell apart emotionally in the face of these problems, of a type he'd never seen before.

The first two problems involved analyzing a figure for parallel and perpendicular lines, and determining the area of a rectangle that had had a couple of rectangular pieces removed. That last is a real-world problem, by my lights, if there ever was one.

These two problems were on the placement exam as well:

A rectangular swimming pool measures 24m by 16m. A concrete path 2m wide is paved around it. What is the area of the path?

Mary bought 1m of ribbon. She used 2/5m to tie a package, and 2/7m to make a bow. How much ribbon had she left?

Ben's reaction to the second one was especially interesting. By the time he got to that problem, he was frazzled by having had to skip a few of the earlier ones. He shouted:

"What do you expect me to do, add 2/5 and 2/7?"

"Yes," I said. "Oh," he said.

Ben's confidence crumbled fast with this placement exam. I tried to assure him that it was just a pretest, and that he should skip problems he can't do; but he's just frail these days. Perhaps all kids are.

I think the Singapore math curriculum may work for us. It's challenging, but we can do it; it's not impossible. And at least the evidence says we're on the right track with it.

And the books are cheap, to boot (check them out here).

---

MiddleSchool 08 Sep 2005 - 14:02 CatherineJohnson


Christopher started Middle School today.

I am wearing my black Govenator t-shirt in honor of the occasion.






UPDATE 11-20-06: good choice



parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

worsethanyouthink

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MiddleSchoolPart2 07 Sep 2005 - 17:55 CatherineJohnson


Ed was awakened at 6 am this morning by a violent anxiety dream that began with me shouting 'Get down!'

We all dropped to the floor and huddled below the window sill, trying not to be spotted by the TRUANT OFFICER, who was walking up to our door.

It didn't work. The officer came into our house and took Christopher away.


So this morning I ordered my copy of Not Much Just Chillin'.

Here's Kay Hymowitz:

...[middle school] classmates are like the KGB with orthodonture, surveilling the halls for unusual odors, dress, language or manners...

Then there's the inevitable How We Got Here passage:

Of course, peer pressure and sullenness have been defining traits of these school years since long before middle schools were introduced in the U.S. in the 1960s. At the time, educators hoped to shape learning around new scientific findings about the nature of pre- and early adolescent thinking.

What makes me think these new scientific findings about the nature of pre- and early adolescent thinking were hokum?

Could it be the fact that we are now in the midst of a movement to dump middle school in favor of elemiddle? (subscription may be required)

In a new review of 20 years of research on middle schools, Rand Corp., a nonprofit organizations in Santa Monica, Calif., concludes that states and school districts should "consider alternative structures that allow them to reduce multiple transitions across grades K-12" in order to capitalize on "continuity of schooling and introducing changes gradually."

A number of districts that have recently begun converting to K-8 configurations say they have already noticed fewer disciplinary problems among students, as well as an increase in test scores.

[snip]

Particularly troublesome in Philadelphia was the noticeable decline in test scores after students graduated from elementary schools, which mostly went through the fifth grade. "Sixth-grade test scores were always our lowest," Mr. Vallas says.

Now, an analysis of standardized test scores from 2000 to 2003 shows that reading and math scores are consistently higher for eighth-grade students enrolled in some of Philadelphia's new K-8 schools compared with those in traditional middle schools. The average reading score for K-8 students was 1218 in 2003 compared with 1146 for students in middle school. Also, Mr. Vallas says, K-8 schools have higher attendance rates and fewer incidents of student discipline than do their middle-school counterparts.

My own district has just spent a gazillion dollars building a brand new middle school next door to the high school. The two schools share a big, fancy Ikea-style cafeteria with a noise level roughly equivalent to that inside an airplane hangar.

Last night Christopher was lying on the floor playing with his WWE action figures; today he'll be watching teenage boys get B-Js in the bathroom.

What's the word for that?

Friends with benefits?

Is that it?

Or have I lost my mind?


OK, I'm going to Reserve Judgment.

I don't actually KNOW, for a fact, that the 6th graders will be sharing bathrooms with the high school kids.

update

I haven't lost my mind.

Friends with benefits.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

MiddleSchoolPart3 09 Sep 2005 - 02:39 CatherineJohnson


Given the fact that Middle Schools were an invention of the late 20th century, I am perfectly willing to assume they were a bad idea from the get-go.

And I've read enough about other countries' curricula to believe this observation:

"The middle school is the crux of the whole problem and really the point where we begin to lose it," says William H. Schmidt, a professor of education at Michigan State University and the U.S. research coordinator for TIMSS. "In math and science, the middle grades are an intellectual wasteland."

Still, I'm not persuaded middle schools are entirely to blame for the middle school slump, necessarily.

Everyday Math in Schaumburg, IL

(It's Schaumburg-with-a-U)

I'd been meaning to write about this for awhile now.

I met two retired teachers, a married couple, from Schaumberg, IL at the airport on my first trip to Chicago this summer.

I was working on problems from my Russian Math book, so we got to talking about school & about math, and the wife, who had been a first grade teacher, told me that Schaumberg has been using Everyday Math for 15 years.

They were one of the first districts to try it out, and their students' scores promptly went up by 3 times. So they adopted Everyday Math, and have been using it ever since.

The grade school teachers apparently love E-Math, and the parents don't seem to mind. There was a Schaumberg district mom sitting next to me, who said she couldn't help her daughter with any of her math homework because she didn't understand it. This wasn't a problem; she seemed to think it was natural not to understand anything your 4th grader is doing in math, and not to be able to help with homework. No complaints.

The middle school teachers were another story.

When I asked how the middle school kids were scoring, both grimaced & said, 'Their scores are terrible.'

Then the wife gave me the story on the middle school teachers. 'They don't want to change,' she said. 'They want to keep doing things the same way they've been doing them for 20 years.' Her husband nodded.

They were sure that if the middle school also changed curricula, those students would have high scores, too.

I started to say kids need to know fractions & long division to do algebra, but had to stop when the wife grew visibly alarmed, thrust out both her arms at me hands first, and said emphatically, 'I teach first grade. I don't know anything about that.'


Schaumberg, I learned from my brother-in-law, is the 2nd largest school district in the Chicago area, after Chicago itself.

update

We have our answer!

THE STUDENT SHOULD BE THE UNIT OF ANALYSIS!

Tomorrow I'm reading up on Cargo Cults.

update update

connecting high school scores to elementary school


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

MiddleSchoolPart4 19 Sep 2006 - 12:40 CatherineJohnson


Day 2 and we have locker trauma.

Christopher can't open his locker. He spent hours after school trying to open it until finally a teacher came by and opened it with a key.

The reason we have locker trauma, apart from the fact that lockers are apparently not easy to learn when you're 11, is that Christopher's locker was jammed on Day 1, so when they taught the kids how to open their lockers Christopher wasn't able to follow along with the moves, or practice the moves after the demonstration.

No practice, no learning.

It's a Discovery Locker.

Google has failed me

So naturally I was searching all over the web for locker opening instructions....and I came up with these, which are fine, but which apparently are not the instructions for Irvington lockers.

today's advice: before your kid goes to middle school, buy a combination lock and have him practice it 5 gazillion times.


they grow up so fast





parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

---

ExtendedResponse 08 Nov 2005 - 22:52 CatherineJohnson


My sister-in-law, a fantastic teacher in central Illinois, says the Big New thing in math is extended response. She's going to fill me in when she finds out what it is.

In the meantime, I found this page of released extended response items on the ISAT.

my extended response to extended response

OK, my initial reaction to extended response is: I'm against it.

Actually, make that mixed. My initial response is mixed.

Here's one of 2 released 2004 extended response gr5 items:

A company makes a wall calendar each year. The company sells ad space
around the calendar to local businesses. The cost of ad space is based on
the number of square units each ad contains. The company charges $40.00
for Ad Space D. Using this information:

Draw an Ad Space that costs exactly $60 in the gridded space on page 10 of
the answer document.


And here's the illustration:




I like this problem, although wiser heads here at ktm may give me reasons why I shouldn't, in which case I'll revise my opinion.

I like it because it's visual & spatial as well as 'numerical' (if that's the right word), and because I've found Christopher to be very challenged by any problem that asks him to combine numerical thinking or problem-solving with spatial 'thinking' or problem solving. And of course I love the Singapore bar models, and this problem reminds me of them.

I also like it because it has 2 steps: you have to figure out how much each square costs & then you have to figure out how many squares $60 would buy.

I like the open-endedness of this particular problem, too. A child could simply count the number of squares in Ad Space D (40) and then divide 40 dollars by 40 squares to get $1/square. Or he or she could notice that Ad Space D is a standard multiplication array, and multiply 4 by 10 to get 40. I'm sure a lot of kids would start out counting & then notice, mid-stream, that they could have arrived at their answer more efficiently by multiplying instead. Which is good. A little Math Object Lesson buried inside a story problem.

I like that!

Last but not least, I kind of like the fact that each square turns out to cost exactly one dollar. I don't know why. It reminds me of a genre of problems in Russian Math, in which you go through all kinds of elaborate, painstaking calculations only to end up with an answer of ONE. Or maybe TWO. Or, when things get really fancy, ONE HALF.

Interestingly, I'm finding, as I work my way through RUSSIAN MATH, that I'm becoming quite attached to the number one. Every time it crops up as an answer I think: I should have seen that coming. An answer of one always seems like a flag, a sign that there was an easier, more elegant way to do whatever it was I was doing.....but I missed it.

Russian Math has all kinds of 'surprise answers,' and I think a surprise answer in the middle of an ISAT could be slightly.....fun?

An answer of one is like a little joke.

What I don't like...

...is the injunction to Explain in words how you got your answer and why you took the steps you did to solve the problem.

That is a terrible, terrible idea for a test.

It's a good thing to do on homework once in awhile, or in the classroom. RUSSIAN MATH asks students to write out explanations, although it doesn't ask students to explain how they did a problem. It asks them to restate the definitions & explanations given in the lesson.

Items like these can't possible be graded well on tests. They are far too time-consuming, and graders will end up scoring on length or number of explanations given. When you have items like these teachers are going to end up devoting all kinds of class time to writing extended responses, as Susan H says is already happening. We're looking at a massive waste of teachers' and students' time.

Last but not least, I'd bet the ranch you learn nothing from the verbal explanation that you didn't already learn by looking at the student's work.

Being able to produce a fluent, intelligible verbal explanation of a mathematical solution is almost certainly important for math teachers.

It's not important for the rest of us.

I really don't like this one

The number of fifth-grade students going to the museum is greater than 30
but less than 50. Each student will have a partner on the bus. At the
museum, each tour group will have exactly 6 students.

How many students are going to the museum?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.

Unless 5th graders in Illinois are doing a lot of prime factor problems, I don't see any reason to include an item like this one on a timed assessment.

First of all, no one should have to be doing discovery ON A TEST.

And second, this problem has two answers (36 & 42, right?), but the wording implies that it has just one answer, and that one answer is findable.

I am DISCOVERING the fact that I don't think red herrings belong in math classes. Certainly not in elementary school math classes.

What is the point? You are teaching children to distrust the English language at the precise moment they're learning grammar & composition. An unreliable narrator in a work of fiction can be a terrific device.

But an unreliable questioner in an examination is just wrong.

I'm against it.

update: I forgot 48!

sigh

(thank you, Dan K)

extended response in 8th grade

Here's the 2004 released 8th grade item:

Peter sold pumpkins from his farm. He sold jumbo pumpkins for $9.00
each, and he sold regular pumpkins for $4.00 each. Peter sold 80 pumpkins
and collected $395.00.

How many jumbo pumpkins and regular pumpkins did he sell?

Show all your work. Explain in words how you got your answer and why
you took the steps you did to solve the problem.


The problem is fine, assuming these kids have actually been taught some algebra.

If they haven't, this is a discovery problem on a timed assessment, and I'm against it.

So, assuming they've learned how to set up & solve equations with unknowns, the problem is good. IMO.

The demand that the student explain each step in words is not.

Russian Math rocks

Instead of writing about Russian Math, I should be downstairs (at the kitchen table!) actually doing some Russian Math.

So I think I'll sign off.

But tomorrow I'll give some examples of what a proper extended response item should be.

A proper extended response item should be a RUSSIAN MATH EXTENDED RESPONSE ITEM.

update: scoring rubric for extended response

'Student Friendly' Mathematics Scoring Rubric

Assuming I'm reading this correctly (I feel a little distrustful), students must get all computations correct in order to earn the highest possible score of 4. They can earn a score of 3 with minor mistakes in computation, which I feel is fair, though others may disagree.

What I reject absolutely is the explanation section:

• I write what I did and why I did it.
• If I use a drawing, I can explain all of it in writing.

This is wrong. I don't believe a 4 should depend upon being able to supply an explanation in any case. But here you have a child who can explain why he or she did what she did in a drawing, which is no mean feat (and I'm in a position to know) and even that isn't enough.

Pace Anne, you'll notice that it's not OK for a child to explain what he/she has done by offering a mathematical demonstration, as the teachers in Liping Ma's book do. Anne's right about that; it struck me, too. Over and over again, when Liping Ma asks a Chinese teacher why he/she teaches an idea a certain way, the teacher responds by writing out a proof-like mathematical demonstration. That's what makes the book incredibly difficult (and incredibly valuable) to read for most of us; the teachers don't translate math into words, and neither does Ma.

For Chinese teachers, math is math.


This drops you to a 3:

• I write mostly about what I did.
• I write a little about why I did it.
• If I use a drawing, I can explain most of it in writing.

A couple of years ago the head of our school board sent out an email explaining the adoption of TRAILBLAZERS that included this line (from memory): In recent years math has become language-based.

I think that would come as a surprise to actual mathematicians.


extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

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MiddleSchoolPart5 18 May 2006 - 21:27 CatherineJohnson


From a paper posted on a (pro-)Middle School site:

Converting a school system to a K-8, 9-12 configuration also eliminates the transition from fifth to sixth grade that occurs when there are 6-8 middle schools. As every parent knows, whenever a young person transitions from one level of schooling to another, whether that is from fifth to sixth grade23, or eighth to ninth grade, or twelfth grade to post-secondary education, there is potential for difficulty. These transitions require developing new relationships with adults and peers, negotiating unfamiliar and unwritten social norms, and responding to expectations of higher levels of academic performance.

Particularly for young adolescents who are also experiencing a variety of developmental stresses, the transition from elementary to middle schools can be problematic. The experience of adolescent development is filled with variables and unknowns, and one can argue that a potential beneficial effect of eliminating the fifth to sixth grade transition is to reduce, or perhaps just delay, the problematic effects of some variables.24

One researcher concluded that the fewer school-to-school transitions children experience, the more likely it is they will have a positive academic experience. After analyzing passing rate data from 232 schools in a large Midwestern inner-city school system, she reported:

As grade span configuration increases so does achievement. The more grade levels that a school services, the better the students perform. The more transitions a student makes, the worse the student performs..The longer a student stays in a given school, the better the student performs.25

The K-8 configuration may also lead to unanticipated political benefits for the school system. Families of young adolescents are understandably concerned about losing influence and control over their children. While many families are quite involved in their children’s elementary schools, their participation declines dramatically when their children enter middle school. This is not entirely the responsibility of the parents; middle school leaders often make less effort to engage parents as full partners in the educational process.

source: Still Crazy After All These Years: Grade Configuration and the Education of Young Adolescents (pdf file)


Our middle school does not permit a parent-run after-school program or any other form of parent involvement that would allow parents to set foot inside the door.

This is taken to such an extreme that, I'm told, the school has a formal policy against sending notices home in backpacks about school clubs & teams. (Naturally I'll be checking this out on back to school night. I could be wrong, though seeing as how my source is the PTSA president, I don't think so.) The administration believes that, at age 11, children must become responsible for themselves, so it's up to them to decide which clubs and teams to join, and to handle the details.

This week a mom who has one child in college told me that, back when he was in middle school, she used to hang out in the parking lot so she could introduce herself to teachers walking out to their cars.

My sister has been told exactly the same thing about middle schools in CA.

not entirely the responsibility of the parents—I'll say.

When middle school starts, the doors slam shut.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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MiddleSchoolPart6 10 Sep 2005 - 22:51 CatherineJohnson


I think Dan K wins the award for Itinerant Schoolboy:

I know that personal anecdotes don’t generalize, but, hey it’s a blooki, right? So I will share that I attended six different schools for grades K-8. My family never moved. We just lived in a rural area outside town, so we were going to be bused wherever we went. Whenever a school on our side of town got a new addition built, we got bused there. Sure I had a number of bad first days or first weeks at school, but all the kids on my bus route went through the same thing. No one treated us as transient outsiders or kids who needed to be hazed or something to join the school. We just went to school. No big deal.

That's incredible!

(btw, I think anecdotes do generalize, which is one of the reasons I put so much time into ktm. I learn huge amount from Other People's Anecdotes. Anecdotes are just the everyday form of raw data. So while I don't personally know how Dan's multi-schooled childhood generalizes to other kids, I assume it does.)

Here's the rest:

Last school year, my wife and I were both working, so we put our younger daughter in an all-day pre-school. She was four at the beginning, so there were some transitional problems. Thereafter, she was fine. This school year, she has started at the public school. We did our best to prepare her, and…guess what?...she’s doing well. Is this unusual? Of course not. If a five-year-old can go from a private pre-school to a public school with zero classmates in common, I really think the major source of middle schooler trauma—-when all their classmates transition right along with them—-is due to everybody warning them that it’s a big deal. It’s a self-fulfilling prophecy.

I can certainly see that it’s much different for parents, especially if teachers belligerently keep parents out. Even without that, the fact that there isn’t one, clear homeroom teacher with which to interface makes it harder for parents. The upside, though, is that middle school and high school accommodate more tracking and electives. So, you’ve got to take the good with the bad.

So, to me, the question is much more about when students transition away from the homeroom-centric model to the subject-oriented class model.

The one observation I take issue with here is the notion that you get more electives & tracking with middle school.

I don't know about 7th and 8th grade yet, but there are no electives in our middle school 6th grade, and no more tracking than there was in 3rd, 4th, and 5th.

In that sense it's a case of taking the bad with the bad.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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MiddleSchoolPart7 11 Sep 2005 - 17:55 CatherineJohnson


This could be fun--

Save the date! Unmuddling the Middle—September 14, 2005 American students are achieving academic success—until they reach middle school.

The Thomas B. Fordham Institute is proud to host this timely debate on why the middle grades have become "the place where achievement goes to die." Dr. Cheri Pierson Yecke (newly appointed Chancellor of K-12 Education in Florida and author of the new Fordham report, Mayhem in the Middle) will join leading middle school researchers and practitioners to discuss the necessary steps for bringing children in this age group back on track before they reach high school. Joining (and debating) Dr. Yecke will be: Dr. James Beane (Professor in the National College of Education, National Louis University), Sondra Cooney (Consultant, Making Middle Grades Work, Southern Regional Education Board), Susan Schaeffler (Executive Director and Founding Principal, KIPP DC) and moderator Richard Whitmire (USA Today). Please RSVP no later than Monday, September 12, 2005, at 5 pm via phone at 202-223-5452 or email rsvp@edexcellence.net.

When
Wednesday, September 14, 2005
9-11 am (Continental breakfast available at 8:30 am)

Where
National Press Club
Holeman Lounge (13th Floor)
529 14th Street, NW
Washington, DC

So that gives you some idea about my idea of fun.

I wonder if Middle School actually is "the place achievement goes to die"??

Do we know for a fact that our kids are achieving in elementary school?

And that they slow down and/or stop in middle school?

I finally read Stevenson & Stigler's Learning Gap over vacation; I'll check exactly what they have to say about this & post.


parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC

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TeachingSubtractionAndIntegers 18 Sep 2005 - 02:42 CatherineJohnson


click on Printable Version to print


What is subtraction?

Subtraction is the ______________ of addition.


When you subtract, you __________ ___________ ___________________ of the number you are subtracting.


An absolute value is always _________________.


1 - 2 = _________

1 - ( - 2 ) = _________

-1 - 2 = _________

-1 + -2 = _________

1 - | 2 | = _________

-1 - | 2 | = _________

-1 - | -2 | = _________


answers
study sheet for class quiz on pages 2 - 16, Prentice Hall Mathematics: Explorations & Applications & Prentice Hall Pre -Algebra

outloud sheets: integers & absolute value
answer key
notes on outloud sheets for integers & absolute values
Carolyn on introducing absolute value
keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

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PracticeSheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:38 CatherineJohnson


I wrote up a study sheet for Christopher's test (it's in the next post) & dragged him through it kicking and screaming.

I think it worked, but we'll see.


If you hit 'Printable Version' it prints out great, exactly enough space for answers in big, round middle-school handwriting.

update

Christopher said last night he doesn't like it when I tell people he screams when we do math.

I told him, Stop screaming and I'll be happy to stop telling people.

We are at an impasse.

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StudySheetIntegersSubtractionAbsoluteValue 16 Sep 2005 - 14:45 CatherineJohnson


(study sheet is here: subtracting integers & absolute value)


Here is how Christopher does this problem:

-1 - ( - 2 )


He pencils in a vertical line across both of the minus signs in the middle, turning them into plus signs:

- 1 + ( + 2 ) =


That works for him every time, no matter what the numbers, and he isn't thrown off by the same problem written with an absolute value:

-1 - | - 2 | =


This reminds me of Carolyn's belief that you need to get math into a child's hand.


For some reason a problem like:

-1 - 2

makes sense to him. He 'sees' that he's adding two negative numbers.

Here, too, however, he does a swoop and swoop thing: he squeezes in a plus sign between the 1 and the second minus sign, like this:

-1+-2 =

Ed's explanation to Christopher that you can think of -1 - 2 as adding two debts -- first you owed 1 dollar, then you borrowed 2 more dollars and you owed 3 -- seems to have been the ticket.

I tried that explanation on a friend of mine who is severely math phobic, and she instantly got it, too. Adding debt to debt is something everyone can grasp! It's EVERYDAY MATH FOR THE MASSES!


From one of Carolyn's first posts:

That's what the standard algorithms are: they are moves that you learn how to make. Those moves get into your fingers, just like learning the piano or the violin or typing, and eventually you can do them completely mindlessly.


swoop and swoop
the craft of math
subtraction as the difference between 2 numbers
outloud study sheet: subtracting integers & absolute value
answer key
notes on integer, subtraction, & absolute value study sheet
Carolyn on introducing absolute value

keywords: integers subtraction addition absolute value opposite add study sheet outloud out loud

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ILikeMathPart3 17 Sep 2005 - 02:47 CatherineJohnson


I almost forgot!

Monday or Tuesday night, when Christopher was doing one of his first homework assignments from Prentice Hall Mathematics: Explorations & Applications, he saw an illustration on the side of the page with the caption:

The early Egypticans drew pairs of legs walking in different directions to stand for addition and subtraction.

He looked up at me and said happily, "I like math. I just don't like math when you make me do it."


BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
ATeachersStory ("I like the idea of math")
BonusPreTeenPost
fun with Saxon Math in the summer
SundaySchool
I like math
I like math, part 2
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids
Christopher on his 39
I like math, part 3

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GlencoePreAlgebra 18 Sep 2005 - 00:05 CatherineJohnson


Glencoe Pre-Algebra is supposed to be one of the two decent not-completely-fuzzy Pre-Algebra texts out there....but I just found this review, by an Amazon reader calling himself wiredweird that I thought was so funny I'm posting it here. (No idea whether he's right or wrong, though I'd bet money he's right about the page splatter):

It is hard to imagine a worse math book, except maybe the earlier editions of this title. This book demonstrates just about every bad teaching and typographic practice I know. Every page is splattered with colored text in a menagerie of fonts. Most pages feature irrelevant or misleading photos, perhaps several. There are dozens of distracting sidebars, many full of errors in fact. Just looking at a typical page, I feel my attention batted about in a pinball trajectory. Holding a thought for the length of a Glencoe page is quite a challenge.

Math skills are cumulative; each new technique is founded on the earlier one. I can't think of a case where this book seems to sustain an idea for more than a few pages. Some students, through chance or a teacher's skill, may manage to glean some mathematical fact from this book. It will do them little good, though. The book's complete lack of continuity gives no reward for that success, measured in skills used later in the course.

Students who can't squeeze understanding from this book - the ones it calls "alternative assessment" students - are very nearly abandoned, as far as any real education goes. Instead of being offered meaningful help, they are invited to draw pictures and write essays about their feelings. Such students are not only left in the dust, they are patronized and insulted in the process.

I have examined earlier editions of this book, back to 1997. The only thing I can say in favor of it is that, in preparing the 2001 edition, some of the worst errors and blatant commercialism were removed. It improved, but its basic flaws remain.

Do yourself and your math student a favor: find a different title. A little web searching will point you to sites that review and recommend better books, as well as more detailed analyses of this one. Or just pick another title at random - this is so bad that almost anything would be an improvement.

(based on the 2001 edition)

I've just given wiredweird an honorary entry on Wit and Wisdom of Kitchen Table Math.

He's also written a review of an interesting-looking book called Four Colors Suffice: How the Map Problem Was Solved by Robin Wilson.

update

I had no idea there even was a Four Color Map Problem. Lucky for me there've been mathematicians around for lo these many years figuring this stuff out.

page splatter

I'm going to be using that one again.


Glencoe page splatter
Doug Sundseth on ransom note typography
Tom Friedman piles on
distance tutors & mathematicallycorrect review Glencoe
page splatter and the frontal lobes
page splatter redux
pagesplatter

---

GlencoePreAlgebraPart2 21 Sep 2005 - 11:03 CatherineJohnson



Susan has Googled up the Mathematically Correct review of Glencoe Pre-Algebra. (Thank you, Susan)

I had remembered it as being good, but didn't have the patience to go find it again for the gazillionth time.

They give Glencoe an A.

Pretty amazing.

I found it

While I was on vacation, USA Today ran a fabulous photo of a Distance Tutor chained to his terminal in India. There was a copy of Glencoe Pre-Algebra in the foreground that was so huge it was bigger than the tutor.





I love it.

That photo alone should be worth another billion or two in sales.


source: Overseas tutors help U.S. students online By Greg Toppo

hmm

OK, here is a picture of Glencoe Pre-Algebra.

This textbook cover & the Distance Tutor textbook cover are two different things.

mystery solved

This is the one, right?





Glencoe Pre-Algebra on Amazon.


Glencoe page splatter
Doug Sundseth on ransom note typography
Tom Friedman piles on
distance tutors & mathematicallycorrect review Glencoe
page splatter and the frontal lobes
page splatter redux
pagesplatter

---

DecisionMadeIThink 20 Sep 2005 - 01:45 CarolynJohnston


I've finally decided what to do about Ben's middle school math situation, which started out with a nasty shock and has been declining ever since.

We can't go on like this. I've been struggling with constructivist math in vain for three years, because I wanted to try to keep Ben in the mainstream math classes. I think, though, that something I wrote in this post has really taken root in my mind over the last few days; Ben may need to work on his social skills, but I don't want him doing it during math class.

And so it hardly seems worth keeping him in the regular class. What's the point? He can work on social skills in English, Social Studies, and Science, where the knowledge base isn't as relentlessly cumulative.

So now, at least, I know what I want to ask for. They've got an aide following Ben around a good part of the day anyway, so she might as well just take Ben out of the class and sit with him while he does a Saxon section a day. If she can't help him learn the day's lesson, that doesn't matter; I can do that. I just want him getting the bulk of it done during regular math time.

If he works through Saxon 8/7 successfully, he'll be way ahead of the other kids in his class. While I'd rather he did Singapore Math, I believe Saxon will be easier to do for everyone; Ben, me, the teacher, the aide. Plus, my major rule of thumb regarding Saxon -- that it's the curriculum of choice if a kid has lost confidence -- applies to Ben at this point. He needs to get his confidence back; he's had two-going-on-three difficult, confusing years. I can, and will, supplement from Singapore.

I agree with the commenters here that it's too bad that every kid can't have an IEP, and that (looking at it from a slightly different perspective) it's a shame that, in spite of IEPs, parents still have to take their school districts to court to get what they need for their kids. I am hoping that my request is simple enough that it just goes through, without my having to generate a big fuss; but if I have to, I will. The meeting is later this week.

Stay tuned though -- after I go to bat on math, I get to go ask sharp questions about why Ben, in his intensive reading and writing clinic, is doing less reading and writing than he did in elementary school.

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KumonMathInDetroit 17 Nov 2005 - 13:28 CatherineJohnson



fyi:
KUMON math program
KUMON reading program


I've had an amazing email from an engineering professor who learned of Kitchen Table Math while she was in China (!)

(Apparently, not being listed on Google isn't a problem in China.)

She also sent me a copy of her paper on Kumon supplementation in Detroit schools (the results were incredible), and I'm waiting to see whether it's OK to post. In the meantime, she says it's fine to post her email:

I'm sure you must have come across Kumon mathematics? I'm a professor of engineering at Oakland University, and so mathematics is obviously very important to me. As a consequence, to make up for the problems with the American school system I've had my own daughters in the Kumon program for about ten years each--between the ages of three and thirteen. Their math skills are far better as a result. I was so impressed with the ideas behind Kumon (it is an outstanding supplement that provides the additional practice missing from K-12 math), that I started a program using the Kumon method in a local inner urban school district, Pontiac. The results are described in the attached paper.

Kumon provides the easiest, smartest way I've ever seen for a Mom to help her kids with math. I couldn't recommend it more highly.

One last thought. I've taught in China as well as the US. The US is definitely way ahead on the "creativity" side. But we are so far behind in math that it is ridiculous--and it is potentially crippling for our source of engineers and other professionals. There are many aspects involved in good engineering, for example, where a good math background is critical. Most of the engineering professors where I work now (Oakland University), are foreign born. Although I greatly respect my foreign-born colleagues, it's really an indictment of the American system that we can so rarely grow our own any more.

Thanks for your blooki, which I have bookmarked and will be following!

Kumon for children with severe disabilities, too?

And, in a follow-up:

Actually, the woman who ran one of the Kumon centers I brought my children to originally got into Kumon because she saw how much it was helping a profoundly mentally disabled child who she was working with. So I suspect it may be surprisingly beneficial for Andrew. I couldn't have done the outreach in my local inner-urban outreach without the incredible help I got from Doreen Lawrence, the Vice President of Research for Kumon, North America. Her phone number is 248-755-2587, and her email is