kitchen table math, the sequel: 1/21/07 - 1/28/07

Saturday, January 27, 2007

new age education

I found these nice circles with writing in them that are representative of educationist thinking about what's needed in education. It's hard to compete with the lofty rhetoric, especially when compared to the caricature of the alternative. It's also surprising to learn what is supposedly actually being taught, when I see constructivist stuff everywhere.

Tests are intended to ensure students have minimal foundational knowledge, unless they are watered down as is so often the case. Foundational knowledge is needed to achieve these ambitious goals. So railing against tests doesn't help the cause. If schools didn't waste so much time with discovery, there would be less of a need for cramming.

Linda Moran's progress report

Linda Moran reports on her kids' progress in Singapore math.

Very worth reading.

Of course, my favorite passage is this one:

With all three kids, we've slowed to a crawl. It's going smoothly without disrupting our lives. It's downright relaxing! We wonder, "What's the catch?" Then we remember, "Oh yes, we're the taxpayers, our kids go to public school, and we're teaching our kids arithmetic."

But that's because I'm a smart alec.

Friday, January 26, 2007

eyes on you

cross posted at the Bridgewater-Raritan Parents Math Forum

I've been trying to figure out how grass-roots politics work when they do work, and I remembered this article from the TIMES Magazine:

The Eyes of Honesty
Published: December 10, 2006

In the psychology department at Newcastle University, there is a coffee station where people can help themselves, so long as they leave money in the tray — 50 pence (about $1) for a coffee and 30 for tea. It operates on an honor system.

Alas, not everyone is honorable. “The woman running the station was a little disappointed at the level of contributions,” says Gilbert Roberts, a professor in the department. Psychologists have long been aware of this dismal aspect of human behavior: people are more honest if they know they’re being observed — so when nobody’s watching, they feel they can get away with murder, or at least with a free cup of coffee.

This problem gave Roberts and two colleagues an idea for an experiment. For 10 weeks this spring, they alternately taped two posters over the coffee station. During one week, it was a picture of flowers; during the other, it was a pair of staring eyes. Then they sat back to watch what would happen.

A remarkable pattern emerged. During the weeks when the eyes poster stared down at the coffee station, coffee and tea drinkers contributed 2.76 times as much money as in the weeks when flowers graced the wall. Apparently, the mere feeling of being watched — even by eyes that were patently not real — was enough to encourage people to behave honestly. Roberts says he was stunned: “We kind of thought there might be a subtle effect. We weren’t expecting such a large impact.”

The paper prompted a British police department in Birmingham to slap posters of eyes around the city as part of a campaign called “We’ve Got Our Eyes on Criminals.” The researchers are studying the campaign to see if the posters have an effect on things like car crime and vandalism.

I'm thinking we should all chip in and post a huge billboard right outside Central Administration in our respective districts.

Or maybe hire one of those skywriting airplanes.

Of course, the problem in my district isn't, strictly speaking, honesty.

Everyone honestly believes students should take ownership of their learning.

Speaking of political actions, BARRY I HAVE TO GO TO A SPELLING BEE!

(I have to actually appear in a spelling bee. What was I thinking?)


on improving traditional teaching

Here's a question I've been struggling with for some time now:

Under the traditional curriculum why didn't mastery learning become the norm?

With the exception of the haphazard presentation of material is some of today's constructivist texts, traditional texts typically present a lesson, provide some practice, and then move on to the next topic in the sequence. Many students learned the material using this approach, but there was no effort to get the student to master the material and firmly place the material into the student's long term memory where it is somewhat protected against the ravages of forgetfulness. The inevitable result is that the student partially or fully forgets much of the material once the class moves on, unless the skills taught are used in subsequent lessons (like in elementary math). It was rare that we ever got a cumulative exam at the end of the year which was probably intentional because most of the students had forgotten the material taught in the first half of the year. This practice was mitigated to an extent by the fact that much of the material was retaught year after year--a precursor to today's spiral curriculum.

Nonetheless, this seems to be a horribly inefficient way of teaching to me. Yet it seems the have developed as the dominant form of (pre-constructivist) instruction by the latter half of the 20th century.

The question is why did it develop this way? Why not mastery learning?

Before you answer take a look at this blurb from Engelman's new book (pp. 30-31):

Mastery is essential for lower performers. Unless the practice children receive occurs over several lessons, lower performers will not retain information the way children from affluent backgrounds do. Prevailing misconceptions were (and are) that children benefit from instruction that exposes them to ideas without assuring that children actually learn what is being taught. If you present something new to advantaged children and they respond correctly on about 80 percent of the tasks or questions you present, their performance will almost always be above 80 percent at the beginning of the next session. In contrast, if you bring lower performers to an 80 percent level of mastery, they will almost always perform lower than 80 percent at the beginning of the next session.

The reason for this difference is that higher performers are able to remember what you told them and showed them. The material is less familiar to the lower performers, which means they can’t retain the details with the fidelity needed to successfully rehearse it. After at-risk children have had a lot of practice with the learning game, they become far more facile at remembering the details of what you showed them. When they reach this stage, they no longer need to be brought to such a rigid criterion of mastery. At first, however, their learning will be greatly retarded if they are not taught to a high level of mastery.

This trend was obvious in the teaching of formal operations. At first, the low- and high-performing groups were close in learning rate. Later, there were huge differences. Group 2 was able to learn at a much higher rate, largely because it was not necessary to bring them to a high level of mastery. On several occasions, I purposely taught the children in Group 2 to a low level of mastery (around 60 percent). I closed the work on the topic with one model of doing it the right way, and I assured the children that this was very difficult material. At the beginning of the next lesson, almost all of them had perfect mastery.

So, I think the answer to my question as to why mastery learning didn't become the norm is simply that it wasn't needed. Why go through all the effort of mastery learning when the higher-performers really didn't need it to learn? If the teacher is basing their performance on the feedback they are receiving from the successful students (only 60% mastery is needed), it's easy to see how one could reach the false conclusion that that's all the teaching a student needs to learn. And human nature being what it is, why teach more when less will do.

Nonetheless, I think we now know enough about how the brain works to know that retention of learned material is greatly enhanced when the learner engages in distributed practice after the initial mass practice. All students would benefit from distributed practice. So why haven't traditional educators changed their ways to offer more distributed practice?

I understand there is a philosophical objection to distributed practice (i.e., drill and kill)at the elementary school level. But what about at the secondary and post-secondary level where traditional education is still the norm? At this level, distributed practice just means giving a a couple of additional independent work problems that keeps previously taught material alive for the student until the material is better retained in long term memory. So why are classes at these levels still taught like the need for distributed practice doesn't exist?

Moreover, if the goal is to eradicate the worst practices of constructivist teaching, wouldn't it be beneficial to improve traditional teaching methods to incorporate techniques that will improve student performance? One of the reasons why constructivism has gained the foothold it has is due to the underperformance of the traditional curriculum, especially among lower-performers.


Math Panel -- College Readiness

On Nov 5, the National Math Panel devoted an entire session to American Student Readiness for College-Level Mathematics. Arthur VanderVeen, Exec. Director for College Readiness at the College Board presented studies and recommendations from research they have been collecting. (The College Board is the organization that administers the SAT exams and AP courses.) A Transcript for Nov 5 in .pdf is now available at the U.S Dept of Ed website. He refers repeatedly to what must be a powerpoint presentation, but that isn't available, so I have to guess at some of the references.

VanderVeen recounts the dismal state of college readiness -- unacceptable levels of students needing remediation and the low college completion stats for students that need remedial math (only 27% will earn a bachelor's degree). In 2003, the CB began an effort to define pre-collegiate standards and frameworks that could help coordinate or align middle and high schools with college expectations.

Second, the CB felt they needed "a framework to increase the number and diversity of students who were prepared and ready with the skills they would need to succeed in AP." The CB put together an advisory committee made up of teachers, ed school people, college math teachers, research mathematicians, curriculum specialists, etc.

Here's where things get a little sticky. The CB committee put together a sequence of standards from middle school through pre-calculus. The committe "permuted" those expectations to "offer an alternative framework of six integrated courses to support those states and districts that are using an integrated approach to math education."

Hmm. This has me worried -- is the CB going integrated on us? Worse, VanderVeen goes on to highlight the inclusion of statistics and data analysis in the courses. The purpose is to increase courses outside of a math major -- business, science, health science, and finance. The are looking for a decrease in repetition that is seen in traditional sequences. They have developed very specific standards, although these are not available to us through the website.

Specific standards sounds good. Especially if it defines algebraic skills. But part of what CB is doing is "to align to national and state content standards as well as the NSF integrated curriculum." VanderVeen switches gears at this point to discuss extensive surveys of what is taught at the best high schools, where things don't mesh between high school and college. While much of this is interesting, there are no real surprises. High school -- college alignment is pretty poor across the country.

But it's the statistics/data inclusion that raised the most heated exchanges between the panel and VanderVeen. Dr. Loveless starts the questioning and really probes the statistics issue. VanderVeen states that 15% of the math instructional calendar in HS should be devoted to statistics and data analysis.


Loveless points out that the curriculum is already a mile wide and inch deep. Doesn't this exacerbate the problem. Wu says there aren't 15 days available to add another topic. We don't do the basic stuff well enough as it is. This is "fatal" to math achievement. Vern Williams jumps in:
Maybe one reason why students need more advanced courses to become successful in college is because so many things have been taken out of the basic courses because of the addition of topics like data analysis. I can't understand why data analysis would be a part of a geometry couse. American students are extremely weak in geometry. In many cases, that is the only proof-based course, or at least it used to be a proof-based course, that students get. So, of all places, why sould data analysis be included in geometry?
The day ends with this basic dispute hanging.

I've left out a lot of information. The ACT was also there. That could be another post.

But I'm stunned by this. If the CB backs off their high standards in the SAT and AP, where will that leave us? Is the SAT and AP a bellwether for the future of math education? Is this the right direction for US math education and what can we do about it?

Thursday, January 25, 2007

Everyday Math's smoking gun

I want to bring this up front.

LynnG said... Steve, it is always worse than you think.

Here's what EM's Teacher's Reference Manual (Grades 4 - 6) has to say about fraction division.

"Indeed, few adults ever need to divide fractions once they leave school.
Therefore, the main goal of division of fractions in Everyday Math is not to
give students practical skills . . ."

This is an exact quote?

This is an incredibly damning statement to make. I've heard this argument before from regular people, but never so blatently from a math program. I would consider this to be a smoking gun statement. There is no other interpretation.

The simple question is how on earth can they decide on this in K-6! This philosophy guarantees that kids will never need to divide fractions as adults.

Dividing rational expressions like

1/(x-5) divided by y^3/(X+5)

is a required and common skill, even for any high school college math track.

Invert and multiply. What's the big deal? Just think about all of the complicated tasks in life that most kids master. This doesn't rank very high, but oh no! Math is different. It's complicated! It's scary! You have to "understand" it.

It's not about understanding. It's about LOW EXPECTATIONS!

When I talk to other parents about our public schools, they might not know about the problems in math, but they sure know about low expectations.

Everyday Math is based on low expectations. According to Andy Isaacs, it's not for the "elite", and now we know what that means. It means that if you want your child to get into a college math track in high school, you need lots of outside help.

math insurgency

A few days ago I had posted on a group called "Wheres The Math? " that was responsible for the now infamous Math Education: An Inconvenient Truth video.

The groups purpose was to force reform of Washington State's math standards and to advocate against "fuzzy math".

It appears they have had at least a small victory:

Seattle Times: Bergeson OKs independent math review

Superintendent of Public Instruction Terry Bergeson has agreed to an independent review of state math standards that critics have called at least partly responsible for Washington students' poor math achievement.
Mukilteo parent Hugh Taylor, a member of the state "Where's the Math?" group, called U.S. math instruction "uniquely unsuccessful." He said that since the state developed the original math standards, allowing the Office of the Superintendent of Public Instruction to conduct the standards review "would be like the fox guarding the henhouse."

He said he welcomed an independent review, "as long as it's conducted by a mathematician."
As Catherine alluded to earlier, a parent revolution is difficult to pull off, but with a little persistence it seems it is possible to make headway.

Now changing math standards will not by itself eliminate weak math curricula, but by raising the standards it will at least add little pressure.

I suspect that it's a lot easier for well connected middle class parents to force changes than the parents of disadvantaged kids. This is unfortunate because its middle class parents who are more likely to supplement the less that satisfactory math programs in school. Their kids are more likely to pass, despite the weakness' of schools, and cover up the inherent problems.

It's very unlikely there will ever be a mass national uprising, but hopefully all the disjointed successes that happen here and there in the country, inspire other small groups of concerned parents to take on the schools.

I think that the term "Math Wars" might not be appropriate. Instead to borrow a phrase from the Iraq War, as loaded as it is. What we have is a "Math Insurgency".

Wednesday, January 24, 2007

i want snow

ok, i see freezing cold temps coming up

i don't see snow

if we're going to have freezing cold temps, i want snow

i need a snow day

from Drudge

black and white

We are having some issues with my son Sean. He is in 3rd grade and a very bright kid. He is in the talented and gifted program and made the A-B honor roll last semester, but lately he is presenting us with some difficulties.

On Monday night we discovered that he turned in a blank reading log for the previous week. This despite him assuring us several times that he had filled it out. We go through stages where we physically check it, but last week was one where we assumed he did. We know he read (he has to read for 15 minutes a night and record what he read) and filling out the log only takes a few minutes, but he totally ignored it (and us).

Tuesday evening he forgot his science book even though he had to do some science homework, and it was listed in his agenda. By nature he is a bit scatter brained (like his dad), but we have repeatedly had this problem and counseled him to check that he has all his books before he leaves the class. In the past, we were usually able to let him borrow his step-sister Christina's books since she is also in 3rd grade, but she didn't have it this time. We wrote a note to the teacher, telling her that we would have him do it tonight, along with any other "extra" homework she saw fit to give.

We also found out on Tuesday, that he had gotten behind in his TAG class. He is meant to make flash cards for a few prefix's and suffix's every month and learn them, but he was a month behind. It didn't take long to make them up, and I am reasonably sure he could memorize the years worth of words in two or three days if he applied himself. He has a good memory and has no problem learning his spelling words. I do have to admit that I hate his TAG program, because it's all enrichment and ran by a kooky art major, but I still expect him to do well in it.

Tonight he remembered his science book so he was able to do the missed assignment plus an extra assignment his teacher assigned, but there was a note in his agenda to work on a social studies composition. When we asked him about it, he told us that he had no idea what she was talking about.

Additionally, he often acts like... well a big dummy. Tonight he was answering questions and we had to make him reread it several times for him to get the answer. At one point, my girl friend got frustrated and told him that the answer was right there in "black and white".

He replied, "I see the black words, but where is the white?"

Later when Shannon had him read the sentence with the answer to the question, he replied "That sentence doesn't have the word 'why' in it."

He is not a bad kid at all. He is very sweet and pretty well behaved, but its like he has no common sense sometimes, either that or its laziness.

It's hard not to pile on punishment after punishment. We think we give appropriate positive feedback to encourage him. Our main problem is that because of the number of kids we have, it's very difficult to micromanage his homework and still teach give our other kids the time they need.

I would tear my hair out if it wasn't the fact that I have none.

another one

as in one of those worksheet questions (and no, I'm not leaving anything out):

If you have 40% of the cookies, what percentage does Mary have?
About which Ricky asked:
Are Mary and I the only ones with cookies?
Bravo, son! Bravo!


full-sized photo

Seth Roberts on IQ

Charles Murray vs. Charles Murray
The Bell Curve (1994) by Richard Herrnstein and Charles Murray, which argued that IQ is destiny, was the most IQ-glorifying book since . . . well, ever. Now Mr. Murray has taken a big step away from his position in that book, yet he continues to glorify IQ.

In today’s Wall Street Journal, Mr. Murray wrote an op-ed piece (“What’s wrong with vocational school?”) with which I mostly agree. His main point is that for most students, college is a waste of time. As a college teacher (at Berkeley), I have seen that all too clearly. Mr. Murray has an unfortunate way of stating his position. “A four-year college education teaches advanced analytic skills and information at a level that exceeds the intellectual capacity of most people.” I’d put it differently: A four-year college education teaches analytic skills and information at a level that exceeds the interest of most people. I am sure that if my students or anyone’s students were more interested in the material, they would learn it better. That most college students are not interested in the same things as most college professors is a good thing, economically speaking. A healthy economy is a diverse economy; a diverse economy requires a wide range of skills and knowledge, much wider than the narrow skills and knowledge possessed and taught by college teachers. But it is a bad thing for the students and teachers, who are trapped. They have to be there. I feel worse for the students, of course — they are paying to be there.

It isn’t complicated: IQ tests were designed to predict school performance. They do. People with higher IQs do better in school. To believe in the value of IQ is to believe in the school system it reflects. To glorify one is to glorify the other. Now Mr. Murray has taken a step away from one (the school system) but not the other (IQ). Well, nobody’s perfect.


In The Nature of Economies, Jane Jacobs pointed to the stultifying effects of discrimination. “Macho cultures typically have pitiful, weak economies,” she wrote. “Half their population, doing economically important types of work, such as cooking and food processing . . . are excluded from taking initiatives to develop all that work [e.g., open a restaurant] — and nobody else does it, either.” IQ discrimination is also stultifying. If our society did a better job of helping students who are not good at college — helping them find jobs where their abilities shine, instead of wasting four precious years of their lives — the entire economy would benefit.

This has become an issue for me. In my own district, as in everyone else's, kids who are "receiving services" are simply assumed to be defective.

No effort - none - is made to find out what they shine in, or what they could shine in if someone took them seriously and taught them to mastery.

I've seen at least two boys who have obvious talent for math who aren't going anywhere in math because they are receiving services, etc. They "struggle in school," so "struggle in school" is their entire identity.

The only way out of this dilemma is athletics. Everyone believes you can "struggle" in school but be good at sports. That was one of the main arguments in favor of the fields bond; the fields should be built to give something to the kids who "struggle in school."

Of course I'm sympathetic to that argument, but it makes me furious that we have so many kids struggling in school that we have to build $5.5 million dollar fields to save them. Why are so many of our very bright, hard-working kids struggling in school??

(This isn't an argument against building fields, btw. Schools should have athletic fields and facilities. Fields or no-fields isn't my point. My point is: if we're spending $19,000 per student kids shouldn't be struggling.)

The notion that you could struggle in school but be, or become, terrific in a particular subject simply does not exist.

Seth on Factor X

from an exchange with Steve Sailer:

The Flynn Effect implies that there are one or more powerful environmental effects on IQ. They can raise or lower IQ on the order of 20 points. For simplicity, let’s say there’s just one factor, Factor X. If you are high on Factor X, your IQ will be 20 points higher than if you are low on Factor X. Herrnstein and Murray speculated on the possible genetic cause of Black/White differences and other group differences without knowing (a) what Factor X is and (b) where Whites, Blacks, and other groups fall on this factor. Once those two pieces of info were known, there might be nothing left to explain. Differences in Factor X might entirely account for the observed group differences.

good schools raise IQ, bad schools lower IQ, part 1

good schools raise IQ, bad schools lower IQ, part 2
good schools raise IQ, bad schools lower IQ, part 3
Seth Roberts on IQ

fuzzy math makes you smarter
IQ quiz
school raises IQ
intelligence is verbal, perceptual, and image rotation
math isn't English

measurement in EM

My first grader has been learning about measurement in 1st grade. In principle, this is a worthwhile topic. I understand that on most international comparisons, U.S. students tend to do quite badly on measurement. There is an interesting compilation of international studies by the National Center for Education Statistics. According to NCES, US 4th graders did their worst on measurement; it was the only content area where 4th graders couldn't even meet the international average.

So, what are we doing about it in the schools? My first grader spent a couple weeks now on measurement. First, their only homework for the week and the bulk of their classtime was spent on making up their own measurements. For example, she might measure a book to see how many forks long it was. She was to find common objects and use them to measure other objects. After a week or so of this, she segued into standard measures. It's hard for me to gauge the amount of class time devoted to this, but it does seem that she spent at least 1/2 her time on made up measurements. This might aid her conceptual understanding of the topic, but I'm not sure that it is the best use of her time.

Judging from my 5th grader, there is little effort spent between 1st and 5th grade on the tedious task of learning to carefully line up your ruler, or protractor, to get an accurate measurement.

In the end, conceptual understanding is topping careful accuracy. Based on what I am seeing of Everyday Math in the elementary schools, I doubt we'll see much improvement in this content area on the next international assessment.

at NYC HOLD: Decline in Student Performance in Math by JHU math professor Steve Wilson

Stephen Wilson, a math professor at Johns Hopkins, has written a paper on the decline of students in their math abilities based on a statistical analysis that he conducted. He gave a group of students in his Calculus I class in fall of 06 the same final exam that he gave for the same course in 1989. He then compared the SAT Math scores for each of the classes and found that while the SATM scores were the same on average, the average final exam scores were lower by a statistically significant amount for the 06 class. Among his astute conclusions are the following:

Nineteen eighty-nine is, in mathematics education, indelibly tied to the National Council of Teachers of Mathematics’ publication, Curriculum and Evaluation Standards for School Mathematics (1989), which downplayed pencil and paper computations and strongly suggested that calculators play an important role in K-12 mathematics education. My 2006 students would have been about two years old at the time of this very influential publication, and it could easily have affected the mathematical education many of them received. Certainly, one possibility is that mathematics preparation is down across the country, thus limiting the pool of well prepared college applicants.
There is nothing that universities can do to correct the lack of preparation of their applicants. However, it is difficult to believe that there are not enough students to fill our classes with 1989 quality students. One of the major gate-keepers, the SATM test, is oblivious to this significant shift in preparation. Universities can certainly demand a more effective SATM test.

To misquote Bob Dylan's Ballad of a Thin Man: "Something is happening, but you don't know what it is; do you, Mr. Fennell?"

shangri la la la

from Andrew Gelman's blog Statistical Modeling, Causal Inference, and Social Science and Seth Robert's blog at his website on the Shangri-La Diet.

Shangri-la, the collected works:

September 11, 2005
the Shangri-La diet

July 10, 2006
Shangri-La part 2

July 14, 2006
early adopter

July 17, 2006
the price of food in Shangri-La

July 17, 2006
Marginal Revolution on Shangri-La

July 23, 2006
your own lying eyes

July 23, 2006
the Daily Plate

July 24, 2006
Shangri La part 3

July 26, 2006
mind hacking food & Java

July 27, 2006
Larry Summers fallout

August 6, 2006
my life and welcome to it

September 12, 2006
Shangri-La 9-12-2006

September 17, 2006
Shangri La La La

October 24, 2006
real world math problem

Octboer 27, 2006
seeing is believing

(click on links for full-size photo)

June 21, 2007
Christopher & Christian

August 12, 2007
Johnson & Johnston

January 1, 2007

Xmas photo


social justice conference coming right up

In today’s NY Sun, an article on teaching social justice in math.

It’s a useful piece, but as is customary the article is structured around dueling experts. No parents are interviewed, cited, or even so much as alluded to.

Do parents want their children taught ed-school social justice in math class?

We don't know!

January 24, 2007 Edition > Section: New York
Do Social Issues Belong in Math Class?

BY GARY SHAPIRO - Staff Reporter of the Sun
January 24, 2007

Can social and economic justice issues be integrated into mathematics curricula?

Radical Math, Long Island University, and Math for America, a nonprofit founded by a Wall Street titan, James Simons, who is president of Renaissance Technologies, are sponsoring such a conference in April to explore such issues called "Creating Balance in an Unjust World."

The conference will feature both a Harvard-trained civil rights leader named Bob Moses and a former Weather Underground member turned educator, Cathlyn Wilkerson, whose father owned the West 11th Street townhouse where she and Kathy Boudin survived a 1970 explosion of a bomb intended for others.

A research professor of education at New York University, Diane Ravitch, believes combining math and social justice is ill-advised. She said students may learn the political opinions without learning the math. Ms. Ravitch said too much of combining social justice and mathematics was propagandizing and introducing politically partisan positions into the teaching of mathematics. "It doesn't belong in the math classroom. Leave that for social studies," she said.

A professor of education at the University of Illinois at Chicago, Eric Gutstein replied, "Where is the presumption that exposing youth to real questions of social justice in their world is either ideological or propagandistic?"

The communications director for one of the sponsors, Math for America, Lee Umphrey, said the group had contributed a small amount of money to the conference more in support of one of their fellows than of the content of the conference. He said Math for America supports the idea that everybody should have access to quality math.

That organization, whose board includes a former director of the Institute of Advanced Study at Princeton and a former managing director of Salomon Brothers, has a mission of improving math education in public schools.

A professor at the Courant Institute at New York University, Sylvain Cappell, cautioned that combining social justice and math elided a reasonable concern with a potentially very damaging one. He said there was legitimate concern about society providing disadvantaged children with a full opportunity to get high-quality mathematics training. But he said the substitution of teaching of concrete mathematical skills with ideology threatens those very children.

Mr. Gutstein has found that youth in Chicago public school were often disengaged and did not learn mathematics — "high-quality or otherwise." A high school teacher and co-organizer of the conference, Jonathan Osler, said studying issues relevant to students' lives is one way of engaging them in the mathematics material.

An advocate for mathematics education, Elizabeth Carson, said student engagement is only the beginning of the process of effectively teaching, not the end or goal.

Mr. Gutstein said the purpose of schooling was to create opportunities for young people to simultaneously develop academic competencies and to understand real issues in their world.

Mr. Cappell said that in combining social justice and mathematics, the math might get short shrift. Mr. Gutstein turned the question around by saying that when a social studies teacher puts a graph on the board and takes the time to explain the mathematics involved, few would say the teacher was giving short shrift to social studies.

Ms. Ravitch, said one of the things children learn in mathematics is how to review evidence and come at questions with a nonpartisan, dispassionate perspective.

Ms. Ravitch said it was better if children were free to reach their own opinions and politics. Mr. Gutstein again responded, "Where is the presumption that we are substituting students views with our own?" He said students in his classroom consider multiple perspectives and make up their own minds and have to back up their opinions with mathematical evidence.

Messrs. Osler and Gutstein acknowledged that it would take much work balance math and social justice in an effective way.

Ms. Ravitch was less sanguine. "What they really need is to work on is teaching mathematics and equipping students for careers in the 21st century — that would be the most radical thing of all."

January 24, 2007 Edition > Section: New York

cross posted to Irvington Parents Forum

Tuesday, January 23, 2007

brain freeze and Ziggys book

I am on 12 hour shifts this week because of an exercise (Yes I am in the Air Force). Since I couldn't think of anything worthy to post today, I decided to pass on some stats.

According to Google Analytics, Kitchen Table Math gets about 105 unique visits a day, with over 700 page views a day.

Not bad for a bunch of amateurs.

Now, everyone get on over to D-EdReckoning and read about Engelmann's new book that he is publishing excepts from online.

Read Engelmann. He's not a naive observer of education. Once you understand what Engelmann is talking about, you have the antidote to all the education nonsense you'll encounter on a daily basis. If chapter one is any inducation, this book will be an easily accessible introduction for the layman.
You will have to click over to get the link to the book, but I recommend you read D-EdReckonings observations.

I have already read the 1st chapter and can't wait to read the rest.

essay on NCTM Focal Points on NYC HOLD

Stanley Ocken, a mathematics professor at the City University of New York has written an essay on NCTM's "Focal Points."

He states that:

"The NCTM Focal points are issued at a time when many parents are appalled by the lack of quality and content in their children's math programs. The Focal Points in grades 6 to 8 seem reasonable. But in earlier grades, they fail to disqualify very weak programs, still in use, that derive inspiration from and are consistent with the 1989 Standards.

"In Grades 1 to 5, the Focal Points fail to explain that sustained experience with nontrivial multi-digit arithmetic problems is critical to success in algebra and higher mathematics. They omit all reference to memorization. They do not admit the interpretation that skills can be developed first and understanding filled in later. Some content material is vague or weak. Indeed, the description of whole number division activities with multi-digit dividends suggests that the hardest problem that students need to handle is 99 divided by 9, while the description of place value fails to name numbers above 1000. That is unacceptable. The NCTM authors should have incorporated existing documents, most notably the State of California's Mathematics Content Standards, which provide a crystal clear grade by grade delineation of computational and symbolic skills appropriate to a content-rich elementary math program."

Check out the whole thing.

math night

Trailblazers Math Night happened last night.

Apparently there were some walk-outs. Parents had been told they would be able to ask questions; instead they were treated to the standard "Math Night" dog and pony show that appears to be the main fuzzy math marketing tool. No questions were taken, though parents who wished to do so could write a question on a Post-It and attach it to board that had been set up outside the auditorium.

cross-posted at the Irvington Parents Forum:

Hi all---

Some background on “Math Nights” ---

Math Nights appear to be a constructivist innovation. Traditional math curricula don’t urge schools to host math nights for parents; nor do innovative curricula such as Primary Mathematics & Saxon Math.

The stated purpose of math nights is to head off parent complaints. Publishers know large numbers of parents will be unhappy with these programs, so they create marketing materials and events for districts to purchase along with the curricula itself.

The main Trailblazers document advising schools on how to manage parents can be found here, here (pdf file), and here.

My favorite passage:

Be pro-active with parents. Don’t wait until complaints hit. People have done a lot of things to involve parents, from math nights to big math carnivals, where the kids teach the activities to the parents. There are letters in the program that go home to parents. In one district, the coordinator ran a six-week course for parents and taught them mathematics, essentially. It depends on what will work with your audience. Teachers need to communicate with parents, making sure that the parents see the math facts practice and that the arithmetic they value is visible.

Don’t wait until complaints hit!

I love it!

I propose that the Board adopt as a matter of policy a rule barring the district from purchasing curricula whose supporting documents say things like “Don’t wait until complaints hit.”

Another favorite:

The math nights have helped [with parent complaints] a lot. I took one of my math nights and just addressed Trailblazers. I actually took them through the steps of how they teach addition and subtraction, using all the base-ten blocks and the manipulatives and how it flowed into the algorithm. After that, I did not have another negative letter. There are still a lot of parents who are worried that, at the end of 3rd grade, kids haven’t memorized all of their multiplication facts. The focus of the math night that I just had was on games that parents and children could play at home to work on math facts, just using decks of cards and things. These are things they can work on with their kids that are fun and easy to do. I don’t want to spend a half hour in class memorizing multiplication. We have far greater things, bigger things to think about.

We have far greater things, bigger things to think about!

If you were wondering why it’s up to parents to discover how to help their children commit math facts to memory (not easy to do), this is it.

Last but not least, here’s a report from Barbara Martin, principal of the Holmes Elementary School in Chicago (“The Holmes school has 772 students in grades pre-K through 5; the student body is 100% African-American, and about 95% of the students live in poverty.”)

We invite parents to an orientation where we talk about all our programs early on in the year. Our math coordinator speaks to the group about math lessons. Math Trailblazers has parent letters that go home all the time telling about what’s going on in the math program. We do also have a math day, and on that math day, we invite parents to be in the room. The kids do math all day. In order to get the parents in the room, I offer them a little stipend.

I offer them a little stipend.

I looked up Ms. Martin’s test scores:

Third grade: 32.5% of the kids meet state standards
Fifth grade: 19.7% meet standards
Eighth grade: 15.7% meet standards

Look at their reading scores:
3rd grade: 18.5% meet standards
5th grade: 16% meet standards
8th grade: they're up to 43.5% meeting state standards

Reading scores are harder to raise than math scores, and yet this school is raising children’s reading comprehension while at the same time math scores fall.

Kendall Hunt doesn’t mention Holmes’ scores.

Instead, Ms. Martin is quoted:

Wherever students go into in the middle grades, if they’ve had a sound foundation in the primary grades, they will be prepared..... For some of my children, our feeder schools are saying, “Please, please send us more like these.”

Catherine J

letter from the superintendent

January 6, 2007

Dear K-5 Parents,

As you know, the mathematics Trailblazers program was adopted by the Board of Education in 2004 and is in its final phase of implementation this year in Grade 5. The District has provided strong support to teachers to ensure excellent initial training and ongoing professional development, and the results to date, are very positive. As with any new initiative, however, it is imperative that we continue to monitor children’s progress and to provide ongoing opportunities to keep parents informed as well as to continually evaluate the program’s effectiveness.

As part of our commitment, there will be a Math Information night for K-5 parents on January 22, 2007 at 7:00 PM in the Dows Lane Library hosted by staff from Dows Lane and Main Street Schools. Teachers will present information about the Trailblazers program, and parents will be able to ask questions to which they will receive responses that evening or soon after the session. As the date draws near, a separate flyer will be sent home by building principals requesting confirmation of your attendance.

In addition, since students in the current elementary program are not tracked and those in the current Middle School program are in leveled classes, the staff recognizes that the transition to 6th grade is a valid concern on the part of parents and one that will soon be addressed. Therefore, parents of current fifth graders will have an opportunity to attend a meeting in February 2007 to discuss this topic. Once again, information will be sent home later this month.

I hope that you will make every effort to attend these important parent meetings.

As always, we value the input of parents [ed.: no more input] and look forward to these opportunities to hear from you and to be able to respond and work collaboratively with you as we move forward.

Thank you for your ongoing support and cooperation and best wishes to you and your families for a healthy and Happy New Year.


Superintendent of Schools

The polite term for that is chutzpah.*

I wonder how much longer things can go on this way.


* defines chutzpah a bit differently.

math night part 2

failing school reforms

I just finished reading Katherine Boo's article, "Expectations" from the Jan. 15, 2007 issue of The New Yorker." It's worth reading the entire article. The main theme of the article is an attempt to follow the path of a failing Denver school, Manual High School. It follow two main threads -- the new Superintendent of the Denver Schools, Michael Bennet, and two of the students -- Julissa and Norberto. You get a sense from the article the enormous task of trying to improve the education kids get in the inner city.

Near the beginning, we get this telling passage,
"Last year, Manual High was one of the worst schools in Colorado. Nine out of ten students failed the state writing test; ninety-seven of a hundred failed the math test; one in five freshmen graduated. This wretched showing belied the fact that, for a decade, Manual High had been the object of aggressive and thoughtful reforms. The most recent was a million-dollar intervention by the Bill & Melinda Gates Foundation, begun in 2001, which turned each of Manual's three floors into an intimate mini-school, with its own principal. In these environments, some students had a sense, for the first time, that their teachers knew and cared for them. But in many classrooms the mutual affection came at the expense of academic rigor. Discipline was weak, gang ties intensified, and in five years a student body of eleven hundred shrank by nearly half. The academic performance of the vestigial students --"the dregs," as one counsellor put it -- barely changed."

So far so good. Next we learn about the newest in the long line of reformers, Michael Bennet. A middle-aged white guy with no education experience -- a former lawyer and corporate turnaround expert. Bennet is made superintendent when a friend becomes Denver's mayor. He takes over in July 2005 knowing next to nothing about public education or underprivileged students. Probably for the best or he might not have taken the job.

There are 150 schools in Denver. The first thing Bennet does is raise graduation standards. Teachers and principals object - they fear higher standards will cause even more kids to drop out. Bennet visits Manual High and concludes the place is a disaster. Within a couple months, he announces that Manual High will be closed at the end of the school year.

Protests erupt. You might wonder why students would want to continue to attend this lousy school. But they do. Enter Julissa and Norberto. Norberto has spent a couple months in jail for dealing drugs. When his gang doesn't visit, he decides to quit the gang. But now he's balancing school with drywalling with his father. Julissa has no father, her older pregnant sister is the valedictorian at Manual. Julissa writes poetry to Bennet, "You might as well put us in jail because your plan sets us all up to fail."

Norberto is good at math, it seems, especially the kind of math needed for dealing drugs,
"how you divide and price the ounce, given your profit-over-cost calculations" (real world applications, anyone?), but he's pretty much failing everything else.

Bennet goes into the community to advocate for his changes,
"Think about it," he said. "What other public institution would we let sink to this level? If the Mayor says, 'I'm going to pave one hundred and fifty alleys,' then comes back the next year and says, 'Well, I spent all the money and only got to two, I'll get to it next year,' we'd go crazy. But when we spend three quarters of a million dollars in a school ostensibly teaching a subject, and only two kids in that school learn anything, we think that's normal. And I think that's because we've allowed ourselves to confuse the sytem's lack of quality with the kind of kids who are in our district."
Bennet appears to be trying to do everything at once, feed the kids, keep class size down, hire good teachers, improve the curriculum, keep the kids in the school . . . . He pushes for teacher merit pay; he adopts KIPP type policies; and performance begins to creep up.

But our friends at Manual need to find a new school. Bennet regrets his hasty decision that alienates the community and learns to work with parents. Still, there is a huge looming disaster -- what if a big chunk of Manual students drop out? People are accusing Bennet of being racist. He decides that Manual will be redesigned and reopened a year in the future, with community input, but that isn't going to help the current class. Bennet "grasps" some contradictions, "one way to avoid charges of racism was to continue to neglect bad schools for minority children."

The Superintendent, with his aides (and Julissa, who has been hired over the summer as a student leader) go door-to-door, like a political canvas, to try to get kids to stay in school.
"Out of panic, and of motivations that involved personal vanity as well as social justice, a safety net was being strung under a school system's hardest cases -- one involving parents, mentors, fast-food restaurant managers, United Airlines executives and city-council members who knocked on doors, an engrossed media, nonprofit organizations, and student leaders like Julissa."
OK, this has gone on long enough. You get the idea. The article lays out a plan that looks like it might work in some of the worst schools in the country.

Bennet is painted as putting in a superhuman effort. I can't see Hartford's superintendent slogging through the streets in a door to door canvas of the worst students in the worst school. If that's what it takes, I'm depressed, because we haven't got that kind of commitment around here. I mean, its encouraging what's going on in Denver, but . . .


teaching is good for the teacher, part 2

Tex left this comment:

I was pleased to read your positive comments on how tutoring benefits the teacher because of my teenage son’s current paid job tutoring a classmate.

When he first proposed this tutoring job I had mixed emotions about it. For some of the reasons AndyJoy listed in his comments on Rory’s post on peer tutoring.

This week the high school kids are taking mid-term tests. My son, as usual, seems to be spending very little time “hitting the books”. However, he has been tutoring every day.

He keeps telling me that tutoring helps him with his tests. He loves it because he feels he’s being paid to study!

After reading your post, I have come to believe a big benefit is he’s “developing and refining his schema”. This is especially relevant because he is often viewed as a walking encyclopedia.

(Also, it doesn’t hurt that his tutee is a very cute female. This leads my husband to conclude that there is a whole other set of benefits to this arrangement. lol!)

I was fascinated to see a teenager being self-reflective enough to perceive the benefits of teaching to the teacher.

It'll be interesting living with a typical teen. (Typical as opposed to atypical for people new to the blog. Jimmy, who has autism, is 20.)

I'm starting to look forward to it.

Monday, January 22, 2007

Trailblazers URLs

cross-posted from Irvington Parents Forum:

An A-Maze-ing Approach to Math by Barry Garelick
history of constructivist math

An Open Letter to United States Secretary of Education, Richard Riley
(anti-NSF funded curricula, signed by 3 Nobel prizewinning physicists & 200 colleagues)

CA Department of Education Content Review Panel review of Math Trailblazers

Math TRAILBLAZERS “backpack letters”

Math TRAILBLAZERS “backpack letters” and “backgrounds”

National Research Council - On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations (2004)
"These 19 curricular projects essentially have been experiments."

VIDEO: “Math Education: An Inconvenient Truth”
M.J. McDermott critiques TERC & Everyday Math; recommends parents "afterschool" using Singapore

book: Political Networks

This book, from John Hoven's wish list, looks interesting: Political Networks (Structural Analysis in the Social Sciences) by David Knoke.

Because power is inherently situational, it is potentially unstable. Force, violence, and coercion aside, voluntary compliance may fluctuate markedly over time, even reversing itself dramatically among the same set of actors.

My question: what happens in a school district when voluntary compliance on the part of parents and voters goes into flux?

Of course, we're not precisely talking about "compliance," are we?

Given the parking, privacy, and school visitation restrictions schools routinely impose on parents, there's no need for anyone to comply with much of anything.


After checking the index I'm not sure this book has a lot to say about citizens attempting to reform public schools. I find only 3 references to secrecy, transparency, and information management.

Andrew Googles YouTube

Speaking of IQ & teaching, last night Ed came upstairs and said, "Andrew* found some kid videos on YouTube."

Me: "He's watching YouTube?"

Ed: "Yeah. He found some kid videos. He must have Googled them."

Me: "Andrew Googled YouTube?"

Ed: "That must be how he found them."

Me: "Andrew can Google?"

Ed: "He's been Googling for a long time."

This child scares me.


* nonverbal, God only knows what his official IQ is

teaching is good for the teacher (on peer tutoring)

re: Rory's post

I wouldn't impose a peer-tutoring practice on a class of kids for all the reasons Rory and everyone else has mentioned.

I do want to point out, though, that teaching, tutoring, and writing, when freely undertaken, are good for the teacher, tutor, and writer.

Most teachers & writers will tell you that you always learn more about your subject when you teach it or write about it. There's no question this is true for me.

It's so true that learning-through-writing is a big part of the reason I write Kitchen Table Math.

It's through reading and writing about education that I learn about education.

teaching and gaps

The literature on background knowledge and expertise has given me a couple of ideas about why teaching is good for the teacher, not just the student.

For one, teaching or writing about a subject reveals knowledge gaps you didn’t know you had.

I had a vivid experience of this while working with John Ratey on Shadow Syndromes. John was keen on Richard Davidson’s work on left brain/right brain and depression, so I was writing a passage summarizing one of the main studies.

I couldn’t do it.

The study seemed obvious and simple: left brain happy, right brain sad.

But as I tried to explain this idea everything kept coming unglued. I wrote and rewrote and rewrote again; I couldn't get it down. The whole thing just kept collapsing in a heap.

I called John. He couldn't help me, though; the study seemed clear enough to him.

It seemed clear enough to me, too.

Why couldn’t I just write it down?

Eventually I diagnosed the problem. I seemed to be dealing with a contradiction inside the study itself.

caveat: I don’t remember the details well enough to be confident I’ll describe it correctly, so take this with a grain of salt.

While the study's "Big Idea" was left brain happy/right brain sad, at one point Richardson and his colleagues described people who were depressed as showing increased left brain activity.

That was what was tripping me up.

I re-read several times, trying to see whether I was just not understanding the prose.

In the end I had to call up Davidson and say: “Is there a contradiction in your study?”

There was!

His answer was matter of fact, something along the lines of, “Yeah, we were puzzled by that, too.”

I think he said (not fact-checked) his team was wondering whether maybe you see a temporary spike in left-brain activity as a person is becoming depressed. Maybe the left brain "burns itself out" trying to offset the gathering depression. If that were true, higher right-brain activity might be the end result of a depressive process.

This was speculation. In fact Davidson didn't know why they had a finding of a temporary increase in left-brain activity. The overall finding of left-brain happy/right-brain sad was correct, but the finding that at some point along the line depressed people showed increased activity in the left-brain was also correct.

My point: John and I had a gap in our knowledge of Davidson’s research that we didn’t recognize until I tried and failed to explain Davidson’s study to readers.


I’ve come to think there’s another reason why teaching, tutoring, and writing increase the teacher’s knowledge.

Knowledge consists of (at least) two things:
  • Discrete or semi-discrete facts, skills, procedures, concepts
  • The structure, organization, or schema into which the facts, skills, procedures, and concepts fit
I think teaching forces you to develop and refine your schema. Writing nonfiction certainly does. When people pay me to write nonfiction, they’re paying me largely for the schema I can produce.

You have to develop or refine your schema, because it's largely the schema that makes your work understandable to a novice.

If discrete facts & concepts were all you need to master a subject, we could learn everything we need to know from encyclopedias. But in fact an encyclopedia makes a lousy textbook. That's what’s wrong with a lot of U.S. textbooks; they’re too much like encyclopedias, not enough like books.

As I say, I wouldn’t impose a peer-tutoring program on kids during school hours.

But I would encourage my own kids to do some tutoring outside class if the opportunity arose. I've always wished my own school would set up a volunteer tutor program in which students, parents, and community residents could tutor kids who need it.


Buddha on the Brain (Davidson & the Dalai Lama)

help desk

I haven't managed to locate worksheets online in which students determine the measures of complementary, supplementary, and vertical angles by writing equations with variables on both sides.

So I'm writing some now.

I'd like to post them somewhere on the web so other parents can print them out.

Where should I do this?

I gather there are lots of free sites that allow you to post material - any recommendations?

peer tutoring

Over at Laura's blog, she has a post up about a tutoring program that she implemented. He recruited the top half of her class to adopt a member of the bottom half of the class to help mentor/tutor them.

When she reviewed the grade sheets, she didn't find much of a benefit, except on tests immediately after she implemented the program.

I left a comment suggesting that she should teach her class instead of having her students do it, but perhaps I am wrong. A quick google showed several studies that has positive effects on student tutors and tutoree's.

Having said that though, I am not convinced. Here are my reservations.

1. If done, are the tutors being specifically trained on how to be effective tutors?

2. Even though the studies I found show increases in the tutors scores, could their scores be improved even more if they were given more instruction.

3. Is tutoring a subconscious effort by teachers to teach to the average?

4. Is it fair to ask other students to be semi-responsible for other students grades?

5. If students were taught to mastery the first time, would peer tutoring even be needed?

6. At what point does peer tutoring become peer teaching?

Having been one of the kids who was asked to provide tutoring during my childhood, I admit I might be prejudiced against the idea. I always resented having to spend time helping kids who didn't put in the effort at home. Yes, some of the kids did put in effort, but just didn't get it. On these kids, sometimes I was able to help, but other times I felt like I was banging my head into a brick wall.

So, what are your thoughts? Do I owe Laura an apology and a cup of coffee?

today's spit take*

Reform math -- guidelines for which were introduced by the National Council of Teachers of Mathematics in 1989 -- is research-based, and teaches students to be problem solvers, said Sheryl Stump, associate professor of mathematics education at Ball State University.

The Star Press

*spit take

Sunday, January 21, 2007

college is bad for your brain

well this is depressing

...the more you know the more you have to lose. The rate from test-year to test-year at which the more educated participants lost their word-recall ability was proportionately faster, with both groups finishing with nearly identical word-recall capabilities at the study’s end.


“Even though we find in this research that those with higher education do better on mental-status tests that look for dementia-like symptoms, education does not protect better against more normal, age-related declines, like those seen on memory tests,” said Dawn Alley of the University of Pennsylvania, a co-author of the study

This fits nicely with the research I read somewhere this weekend showing that kids, especially high-stress kids like, say, TWO AUTISTIC KIDS, shorten your life.

Chronic stress appears to hasten the shriveling of the tips of the bundles of genes inside cells, which shortens their life span and speeds the body's deterioration, according to a small, first-of-its-kind study involving mothers caring for chronically ill children.

Of course, that could work.

I can be dead before my memory goes.


isn't this Sunday?

I thought I had a rule against writing morbid posts on Sunday.


I did

I guess I FORGOT

kitchen table math, the book

Carolyn and I always said we'd write a book.

I give up

Now these take-home worksheets are making me feel like an idiot. Here it is:

x2 + 2y = 10

What do you notice about the expression?

Uh, and she's looking for ... what, exactly?

to do

"If students need distributed practice, parents can find worksheets online."
Irvington math chair - 12/13/2006
$19,000 per pupil spending
$22,000 per pupil spending [update: 9-1-07]

$25,000 per pupil spending [update: 5-13-2008]
$26,718 per pupil spending [update: 4-5-2009]
$27,722.32 per pupil spending school year 2009-2010 [update: 6-1-2009]
$28,300 per pupil spending school year 2009-2010 [update: fall 2009]

keyword: todo