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Algebra Project High School Students Succeed on State Tests and on Assessments of Deep Understanding

Two Algebra Project high school teachers have studied the impact of the project on their students’ performance on state tests.  Project members agree, however, that these tests do not necessarily indicate whether students have a deep understanding of a given concept. To meet that need, mathematician/math educator Ed Dubinsky led a team of researchers to study AP students in three high school sites using methods developed by cognitive scientists to assess student understanding.

State Tests of Mathematics

Math teacher Marcus Hung, at Thurgood Marshall Academic High School (TMAHS), San Francisco, used the district’s data reporting system to study his students’ success on both the California Standards Test (given at the end of each year) and the California High School Exit Exam.  The system allows teachers to follow their own students from year to year.  TMAHS has a very diverse enrollment including African American, Latino/a, Pacific Islander/Philipino and Asian students. About 65% of students receive free or reduced price lunch.

Before implementing the Algebra Project materials, Mr. Hung was using the College Preparatory Mathematics (CPM) text.  He compared his students who used the CPM materials with his students who used the Algebra Project’s materials for Grade 9 (Algebra I) and compared their Geometry performance in Grade 10.  He also compared students he taught for one year versus two years on each curriculum.

On the high school exit exam taken for the first time in Grade 10, the Algebra Project students fared better than the CPM students, especially after two years in Mr. Hung’s class.  Those who had been in the Algebra Project for only one year, 47% passed, compared to 35%.  Of those who had been in the Algebra Project group for two years, 90% passed, compared to 46%.

Similar differences were found on the California Standards test in mathematics (see graph below).

Snapshot of 3 Years

Among students in each curriculum for two years, the Algebra Project students achieved higher levels of proficiency.  About 15-20% of students scored at the Proficient level, while none did with CPM.  The percentage of students scoring at the lowest level (Far Below Basic) decreased over time to 5%, but actually increased to 27% for CPM.

In Petersburg, VA, a small city where nearly all students are African American from low-income families, three math teachers from Petersburg High School attended an Algebra Project institute at Cornell University in 2007.  The entire district was performing at a low level.  Teachers Keil Dawson, Andrew Wynn, and Zorica Skoro were in fact the only high school math teachers re-hired that year.

The Algebra Project was assisting the district’s middle and elementary schools through professional development, community and site development through the Southern Initiative Algebra Project, with a grant from the Cameron Foundation.  (Please contact SIAP Director David Dennis, ddennissr@aol.com for more details on those results).  Concurrently, the high school work was supported by a National Science Foundation (NSF) grant 0628132 for Instructional Materials Development

Department head Dawson, with Wynn and Skoro, implemented the Algebra Project materials for Algebra I in a three semester sequence.  Some of the original students were lost due to reassignment of overage students to the GED track, and transfers out of the district.  However, the remaining students and others on the three semester program who did not use project materials, were tested on the Virginia Standards of Learning test in January 2009.  Read the rest of this article on our website: http://www.algebra.org/news/

Andrew Wynn analyzed the results in a thesis for the Masters degree in Mathematics Education at Virginia State University, with the approval and cooperation of the school district.  He compared the Algebra Project students performance with the other students who had taken Algebra I over three semesters using the standard text, both that year and the previous year.  Algebra Project students performed better on the total scaled score, although the results was not quite statistically significant.  On the Functions and Relations substrand, however, statistically significant differences were found favoring the Algebra Project students.

This study, like that in San Francisco, necessarily involves small numbers of students. The project’s high school work is still in development, and various possible factors could have influenced the results.  But the two studies in very different sites these suggest great promise for the Algebra Project’s high school program.

Students’ Understanding of the Concept of Function

A team of early career mathematicians and researchers worked with Ed Dubinsky in three cohort sites, administering a written instrument followed by clinical interviews about students’ thinking processes. They assessed students’ understanding of: what is and what is not a function; the level of their conception; the relation of the student’s conception to the particular representation used for a function; the ability of students to understand the definition of a function; the concepts of “one-to-one” and “onto”; and the ability of a student to solve a class of fairly difficult problems about the composition of two functions.

Preliminary results of a study of 25 AP students in two pilot sites (Petersburg, VA and Summerton, SC) and 15 at Edison High School in “little Haiti” Miami, indicate that, after working with AP 9th grade material, students develop understandings and problem-solving abilities related to basic function concepts — such as composition, domain, range, one-to-one and onto — on a level that compares favorably with understandings of incoming college students, as reported in many studies such as Breidenbach, Dubinsky, Hawks, and Nichols, D. (1992).  Their knowledge of functions is even on a par with that of pre-service secondary teachers as reported in studies such as Even (1993).

Next Steps

These results, added to the earlier success of the first Algebra Project cohort who graduated in 2006 from Lanier High School in Jackson, MS, are building a body of evidence on the potential of cohort sites to meet the goal of college readiness.  Four more cohorts are now being tested under an NSF grant from the Discovery Research program for education (DRK12 grant 0822175).

However, as these grants do not fully fund project implementation and core support, we continue to depend on your generous contributions to best leverage these opportunities.


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