Conference Material

An emerging profile of the mathematical achievement of students in the Core-Plus mathematics project

The CPMP field test included schools from a broad range of community environments and with diverse student bodies. Students in CPMP courses after one year, two years, and three years illustrated better understanding of, and ability to reason in, quantitative situations (as measured by ATDQT) than did students in more traditional mathematics courses and in the nationally representative norm group. Course 1 and Course 2 students were also better able to reason with, and apply, the concepts and methods of algebra and geometry that were measured by the CPMP Posttests. At the end of Course 1, comparison students scored higher on a subtest of algebraic procedures, but by the end of Course 2 this difference had disappeared. At the end of Course 3, CPMP students performed particularly well on NAEP-based measures of data analysis, probability and statistics and on measures of conceptual understanding. Their performance was somewhat lower in some other content areas and on items assessing procedural outcomes, but still considerably higher than a nationally representative sample of twelfth-grade students.

CPMP students achieved well whether they were in rural, urban or suburban schools. They also achieved well in a variety of grouping arrangements including all students, wide range but none of the very top, wide range but not the very top or very bottom, college-intending only, and work-prep only. Both female and male students showed good achievement in CPMP. In CPMP, students whose first language was not English achieved at least as well as other students. Students in several minority groups (African American, Asian American, Hispanic, and Native/Alaskan American) varied in their pretest scores, but their pretest to posttest growth was solid and in line with that of white, non-Hispanic students. Hispanic students' growth was particularly strong. There is also evidence from a Mathematics and Science Center that the CPMP curriculum can work well with students of very high ability.

To re-emphasize an important point made at the beginning of this paper, the profile of achievement presented is an emerging one in the sense that CPMP's evaluation is ongoing and will continue for several more years. ACT and SAT data from the Course 3 field test are still being processed and analyzed. The Course 4 field-test students will complete several achievement measures. These students, the class of 1999, will be the first group to graduate from high school having completed four years of the field-test versions of the CPMP curriculum. Data concerning what happens to these students after high school especially with respect to their mathematical preparedness will eventually be a part of the envisioned profile.

The findings reported in this study are likely the result of CPMP students engaging frequently in class, homework, and assessment activities that provide them ample opportunity to reason about problems presented in realistic contexts, about mathematical models for those problems, and about connections among and patterns in various representations of those models. Class observation and teacher perception data, while still being analyzed, provide further evidence in support of the above explanation for the positive CPMP student achievement outcomes. Furthermore, analysis of students' perceptions of their experience in CPMP classes revealed two themes that were consistently rated very positively: (1) solving realistic and challenging problems is difficult, especially at first, but later students gain from the experience and find it interesting; and (2) problem solving in groups, with the accompanying discussing and writing of mathematical ideas, is an important aid to learning (Schoen & Ziebarth, 1997). Related to these themes, many teachers and students have also expressed the belief that mathematical sense-making in contextual settings is an aid to memory.

A conjecture in need of more research is suggested by the fairly dramatic improvement of urban students and of African American students in Courses 2 and 3 after slow starts in Course 1. The students in these groups who remained in the CPMP curriculum and continued to work at doing mathematics, improved in their performance, and were successful. It appears that, for them, tenacity and hard work paid off. The importance of effort, so highly valued in mathematically high-achieving countries, seems to be an important determiner of achievement in a core mathematics curriculum. While this and other important researchable issues remain in need of investigation, the emerging profile of achievement at its present stage suggests that good implementation of the CPMP curriculum results in solid outcomes on various˙achievement measures and for a wide range of secondary school students in a wide variety of schools.

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