kitchen table math, the sequel: DI Math (chapter six)

Monday, February 26, 2007

DI Math (chapter six)

Chapter Six of Zig's book is now available for download.

As usual, the whole thing is pretty interesting but one of Zig's anecdotes in particular should be of interest to KTM readers. The anecdote concerns the Gunnison school in Utah. It's interesting because the school, while serving an at-risk population, had a low turnover AND a K-6 DI implementation. For math.

The Gunnison school managed to teach all six levels of Connecting Math Concepts and you know how scarce reliable math education data is. I'll let Zig explain the outcome (pp. 44 and 45).

One of the reasons Gunnison had potential to become a spectacular school was that it had a very low student-turnover rate, compared to the other schools we had worked with. We figured that possibly more than 75 percent of the students who began in K or 1 would go through the sixth grade. After the first couple of years, the fifth and sixth grades inherited children who were far above grade level, and these teachers were models of technical proficiency. Students completing the elementary-school sequence were very impressive.

I believed then and believe now that the achievement test results for Gunnison were doctored by the State so the reported scores were substantially lower than what they really were. I say this because the Gunnison sixth graders “scored” around the 58th percentile, slightly above the average of the comparison groups, but Gunnison students performed far above the reported level.

I understand that I’m making an ugly suggestion, particularly since I have no hard evidence. But there is data that may support my suspicion. For example, when the first cohort of children to go from first grade through sixth grade reached the eighth grade, it had the highest scores on the SAT [Ed: SAT-9?] ever recorded in the school. 17 of the 86 children in this class—20 percent—scored at or above the 90th percentile overall. It would be spectacular for five students from the school to achieve such outstanding results. Seventeen is amazing.

This cohort graduated from high school a couple of months before this writing. The group had the highest GPA and the highest number of college scholarships in school history.

Earlier we had engaged in some battles over the way the junior high was to interface with the elementary school. Here’s part of the letter I wrote in 1999 to Rodney Anderson, principal of the elementary school and a really good guy.

I have to meet with … the superintendent. I want the superintendent to know that he has to adjust the Junior High so that it accommodates our students. We didn't go through all the work of accelerating the students so the school district can decelerate them in Junior High. We are giving them gifted kids and precious few low performers. The ground rules are that the district is to respond accordingly.

A specific controversy had to do with math. The elementary school petitioned the junior high to put our graduates directly into algebra, which was traditionally an eighth-grade subject. Our sixth graders had completed the sixth level of our math program, had awesome fifth-grade and sixth-grade math teachers (Loraine Sorenson and Crystal Childs) and performed extremely well.

Both the superintendent and the junior high math teacher argued that seventh graders could not go into algebra. We told them to make up a test of what they needed to know and see if the students could pass it. They made up the test and the students passed it, with no difficulty.

The response from the middle school was an accusation that Crystal cheated, by giving the students the answers. After a couple of go-rounds, the junior high math teacher made up another test with different items. He sent a teacher to monitor the students as they took the test, and Crystal had to leave the classroom during the testing so she would not be able to cheat.

The students passed the test. They not only went into algebra along with the eighth graders; at the end of the term, our seventh graders placed first, second, fourth and fifth in the class.

The only thing that surprises me is that the kids finished up the math course in sixth grade -- they should have finished up in fifth. The other important point is that there is no need for any kind of pre-algebra work. Middle school/junior high math is a waste of student time.

More importantly, high performers can be finished with the CMC scope by the end of third or fourth grade and be ready to go right into algebra. There they can explore and do all the deep-thinking the school wants them to do.


Tracy said...

Amazing account, though it does puzzle me that the junior high school didn't set up the test properly in the first place (teacher not in a position to cheat, trusted person monitoring the test).

One of the puzzling things about the USA is that, according to what I read in newspapers and blogs, there's no test security for high-stakes tests.

Aa for the kids still doing the sixth grade course - it depends how sixth grade was defined. I still haven't quite figured out how DI handles the case of the fastest-learning kids running out of maths at school.

KDeRosa said...

SInce this was an at-risk school, I don't expect that there were many wile e coyotes that could have been accelerated much beyond grade level.

And in math, the lower performers really do need a lot of practice for mastery. A lot of practice. What probably happened was that the low performers got extra math time for practice and the higher performers didn't need this extra time but nor was material skipped.

Catherine Johnson said...

We didn't go through all the work of accelerating the students so the school district can decelerate them in Junior High.

One of my campaigns now is to push for value-added assessment here in IUFSD.

"Decelerate" is the perfect word. I've come to believe that the district has an unconscious desire to decelerate these kids - not just to prevent any and all acceleration, but to decelerate the kids who managed to accelerate in spite of them.

Parents here widely share the perception that the school does nothing for high achievers and is focused only on low achievers.

I now believe it's worse. First of all, I don't think for a moment that the school is focused on low achievers, unless low achievers are classified special ed. The middle school special ed folks sound like a crack team, and we've got terrific teachers for Andrew & Jimmy.

If a child isn't classified, forget it.

When it comes to kids who are working above grade level the goal of the math department has been to wash these kids out into a slower track.

Meanwhile the ELA department is assigning books fare below most of these kids' reading level.

Christopher's reading level on the ITBS is 12.6; The Outsiders is 5.1.

PaulaV said...

Meanwhile the ELA department is assigning books fare below most of these kids' reading level.

My son's reading level was a 5.4 on the ITBS. His teacher was letting him read Arthur books unti I questioned her. She said he liked them. Well, um, of course he does, they are easy!!


Anonymous said...

Deceleration is exactly the right word for what they’re doing, and it’s intentional.

You should be wary of a growing educational trend - mandated equalized outcomes. Everyone must reach a certain level of achievement, no one can exceed a certain level of achievement.

The push for equalizing outcomes has coincided with the recent release of the book, "Education, Equality and Social Cohesion" by Prof. Andy Green and Dr. Jan Germen Janmaat (though, the authors have published various incarnations of their ‘social reform through educational practice’ recommendations for about 10 years now).

A Peabody Journal of Education article (PJE is America's second longest existing publication devoted exclusively to educational research, practice, and policy, and is committed to providing information and reasoned opinion that will enhance understanding and practice among institutions and individuals, in the United States and throughout the world, concerned with human learning and development. - Peabody College of Education and Human Development, Vanderbilt University) depicted the premise (as Figure 1) as follows:

"Educational Outcomes Equality => Income Equality => Social Cohesion"

and explained as:

"Put simply, countries with education systems producing more equal outcomes in terms of skills and qualifications are likely to have more equal distribution of income, and this in turn promotes social cohesion."

The authors argue that this relationship is what should be influencing education policy if a more cohesive (less crime, more involvement in the community, social justice) society is desired.

Of course, a more cohesive society is desirable. BUT, I take significant issue with the premise that the way to achieve this is to mandate equal educational outcomes onto a population.

To truly attain a majority population of equal educational outcomes to equalize income levels, that educational outcome level would have to be slightly below average.

Where does that leave our children’s and the U.S.'s ability to thrive in an increasingly global economy?

Tracy said...

SInce this was an at-risk school, I don't expect that there were many wile e coyotes that could have been accelerated much beyond grade level.

As I understand it, IQ tends to fall into a bell curve. One sub-set of the population (eg low income kids) may have a lower average than the whole country - and perhaps a different standard deviation, but you're still going to get a bell curve. So there would still be one or two kids per grade who were capable of learning much faster than the remainder of kids in that school because they happen to be at the extreme top end of that school's IQ curve.

They may not have been capable of being extended much beyond average grade level, but would be capable of being extended much beyond grade level of that school.