The Local Math Wars Begin *Again* – Part 2

This is a continuation of the article at The Local Math Wars Begin *Again* . The San Mateo-Foster City School District (SMFCSD) recently cited a research study by Burris, Heubert and Levin in the American Educational Research Journal, Spring 2006, Vol. 43, No. 1, pp. 105–136 which supports detracting middle school mathematics. I have devoted several hours to this paper today and posted the following comments on Nextdoor. I continue to believe that we need to consider other ideas to close the achievement gap besides detracking.

I’ve been going through the paper by Burris et al. for close to three hours today. It is a very detailed and qualified study and I am not completely finished but have read enough to relate some important notes to all of you.

First, I highly doubt that most of the people that cite this study have actually taken the time to really study it.

This does not mean that it is a bad study, but it reflects the myriad complications faced by education researchers, and the text is consequently loaded with required qualifications that make a careful study very time-consuming.

Here are a few examples.

First of all, note that the study was based on a single district in a small Long Island (Nassau County) community. They tried detracking middle school students AND placing them into an accelerated math track as Gene McKenna noted earlier.

Detracking started in 1995 for sixth graders. Six years of students were followed through high school – students from the three class years before the detracking and the first three years of students who went through the detracked program. The last of these students graduated in 2002.

Note that our country has gone through many changes since 2002…

Most of the students in the school district were white with “upper middle class incomes” and the article implies that there was a single high school with an “average enrollment of 1,100 students.” African-Americans made up 8% of the students, Latinos 12% and Asians 2%. The majority of the African-American and Latino students came from lower income families and lives in subsidized or government-owned housing. This is pretty different from our local demographics.

From the paper:

“The district developed a multiyear plan to eliminate tracking in mathematics at the middle school level (Grades 6–8). In addition, it instituted changes in teaching and learning conditions that school leaders believed would help all students succeed. These changes involved the following: (a) revision of the curriculum in Grades 6–8, (b) creation of alternate-day support classes known as mathematics workshops to assist struggling students, (c) establishment of common preparation periods for mathematics teachers, (d) integration of calculators, and (e) a revised mathematics teacher schedule consisting of four accelerated classes and two mathematics workshops.

The district decided that all tracking for instruction in the middle school would end with the sixth-grade class that would enter in 1995 and that all subsequent sixth graders would study accelerated mathematics in heterogeneously grouped classes. The superintendent and the middle school leadership team believed that the combination of (a) heterogeneous grouping, (b) a high-track curriculum, and (c) mathematics workshops would enable all learners to be successful without reducing the achievement of the most proficient students.”

So note above that the district started out with the belief that this method would work and did a lot to make it so:

“Students were placed in the alternate-day mathematics workshops according to teacher recommendations or parent requests. Workshop class sizes averaged eight students, and students were allowed to enroll in or leave the class on the basis of how they were doing in their regular class and their personal desire for support. All work in these classes supported instruction in the regular mathematics classroom, and, whenever possible, students were assigned to a workshop taught by their regular mathematics teacher. Approximately 25% of all students took a workshop class at some time during the year, including a number of high-achieving students who wanted the additional instruction.”

It is clear that this small district thought this process through carefully and devoted resources to improve the odds of success.

The researchers took the data from this district and analyzed it.

To place students into low, average, and high achievement groups, the only data that the researchers had to use was a national math competency test created in Iowa (Iowa Test of Basic Skills) and administered a single time in fifth grade.

Furthermore they had to deal with the problems of dropouts and people entering/leaving the district:

“Selection effects are possible, however, even in stable populations. For example, the inclusion of transfer students whose educational histories differ from the majority could bias a study’s results. A strategy for dealing with such effects is to include only data for the cohort members who have the most similar histories (Cook & Campbell, 1979). To reduce this possible source of bias, we included student data only for cohort members (entering high school in 1995–2000) in regular education who (a) were continuously enrolled in the school district from fifth grade to their exit from high school or completion of this study, (b) entered ninth grade between 1995 and 2000, and (c) had a permanent record folder containing all data of interest.”

This creates obvious problems with interpreting the data for the low achieving group.

The Iowa test mentioned above to define achievement levels creates an issue about interpreting data for the ill-defined high achieving group.

Overall, though, the superintendant and others in that district were happy with the results which is the most important take away.

However, the researchers note in their discussion:

“Nevertheless, it is important that further research explore the essential components of this reform. The district that implemented the reform is a suburban district that has allocated generous resources in providing support to struggling students. Fifth-grade stanine scores in mathematics indicate that students in the district earn higher scores than the national average, and the proportion of low achievers in this study was proportionally lower than the number of average and high achievers. Would the reform work in a district with fewer resources and larger numbers of struggling students?”

They do not know the answer to that question.

This study illustrates common problems with education research. The study is valuable in showing that one community attained the results that it desired. Such an outcome is not guaranteed without the desire to succeed, resources, and careful planning, and no representation is made in the paper that such a reform would necessarily succeed in areas with “larger numbers of struggling students.” This does NOT mean that we should therefore do nothing to help struggling students, but it does mean that simply detracking students in itself is not a magic bullet that will guarantee success.

I may have additional comments later, but this is about all of the time that I can spend on this today. I have not had time to go through the detailed data analysis, but am concerned from a first pass that, even though there was quite an improvement in the low performing group, the results still need detailed consideration.

For example, the “Seq II” high school math class in the paper, which is geometry, went from a 46% “low achiever” pass rate by 10th grade before the middle school curriculum change to a 64% pass rate after the change. Note that passing means a grade of >= 65%.

I don’t have the comparable “low achiever” numbers for our local high schools, but I would not be surprised if they are lower, meaning that this work might be a much heavier lift for local teachers.

Author: David Kristofferson

Retired scientist, teacher, bioinformatician, IT director, software product manager, AAAS Fellow, avid cyclist (7690 miles and 724,300 feet of climbing in 2015), backpacker, you name it! Current avocation is tutoring high school students near San Mateo, CA in mathematics, physics and chemistry. Please see the Bio link in the right sidebar for my detailed background information.

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