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Evaluation
Evidence
For more information
on evaluation evidence, see the Evaluation
page and the annotated list of Research Publications.


Q  What do evaluation studies say about the effectiveness of the CorePlus Mathematics Project curriculum? 

A 
There is a large and growing body of rigorous research documenting the effectiveness of the CPMP curriculum. Based on evidence from nationally standardized tests (ITED, SAT, ACT, NAEP), coursespecific tests, researcherdeveloped tests, interviews, and surveys, the CPMP curriculum has been shown to enhance students' mathematical achievement and attitudes toward mathematics. Quantitative
Thinking Conceptual
Understanding Problem
Solving Ability Applications
and Mathematical Modeling Algebraic
Reasoning Algebraic
Procedural Skills Important
Mathematics in Addition to Algebra and Geometry National
Assessment of Educational Progress (NAEP) Student
Perceptions and Attitudes Performance
on State Assessments College
Entrance Exams  SAT and ACT Performance
on College Math Placement Tests Performance
in College Mathematics Courses The above
results are drawn from several sources, including two
research papers presented at the 1998 Annual Meeting of the
American Educational Research Association:
two fieldtest progress reports:
and a paper appearing in the Journal for Research in Mathematics Education, "Effects of Standardsbased Mathematics Education: A Study of the CorePlus Mathematics Project Algebra/Functions Strand," Vol. 31, No. 3 (2000). 
Q  How well do CorePlus students perform on standardized tests like the Iowa Tests of Educational Development?  

A 
On the quantitative section of the Iowa Tests of Educational Development (ITEDQ), CorePlus students significantly outperformed both the nationally representative norm group and comparison students in the same school who had a traditional mathematics curriculum. The Ability to Do Quantitative Thinking (ITEDQ or ATDQT) is the mathematical subtest of the Iowa Test of Educational Development, a nationally standardized battery of high school tests. The ITEDQ is a 40item multiplechoice test with the primary objective of measuring students' ability to employ appropriate mathematical reasoning in situations requiring the interpretation of numerical data and charts or graphs that represent information related to business, social and political issues, medicine, and science. The ITEDQ administered in CPMP national field test schools at the beginning of Course 1 served as the pretest for all courses, so the pretestposttest analyses for Courses 1, 2, and 3 are for one, two, and three years of mathematics instruction, respectively. For the first and second years, there was a comparison group of ninth or tenthgrade students in traditional mathematics courses in some fieldtest schools with both curricula. Results for the following three cohort groups of CPMP students were analyzed: (1) all students who completed both the Course 1 Pretest and the Course 1 Posttest, (2) all students who completed both the Course 1 Pretest and the Course 2 Posttest, and (3) all students who completed both the Course 1 Pretest and the Course 3 Posttest. Table 1 below gives median (middle) ITEDQ percentiles of the CPMP and comparison distributions.
The results given in Table 1 are illustrated in the following graph. Pretest to posttest growth in percentiles indicates growth by CPMP students beyond that of the national norm group. Such increases appear consistently across the CPMP distribution for each year. For example, the median CPMP Course 1 student increased the equivalent of nearly two years in just one year's time. Allowing for pretest differences, CPMP posttest means in schools with comparison groups are significantly greater than those of the comparison students. 
Q  How well do CorePlus students perform on the SAT?  

A 
On the SATI Mathematics test, students completing CorePlus mathematics fieldtest courses performed at least as well as students in traditional mathematics curricula. SAT data for 1997 from 13 CPMP schools were separated into groups according to the secondary mathematics courses the students had completed. SAT Mathematics scores of students who had completed Courses 1, 2 and 3 were compared to students who completed traditional algebra, geometry and advanced algebra. In Table 1, these groups are labeled "CPMP 3" and "Advanced Algebra," respectively. The CPMP 3 average (mean) is greater than that of the Advanced Algebra students, but the difference is not significant at the 0.05 level.
In one fieldtest school at the beginning of the CPMP field test (Fall 1994), all ninthgrade students who qualified for prealgebra or algebra were randomly assigned by computer to CPMP Course 1 or to a traditional course. Many of these students completed Advanced Algebra or CPMP Course 3 in their junior year and took the SAT either in spring or summer of their junior year or in fall of their senior year. As shown in Table 2, the average Grade 8 ITBS Mathematics scores are nearly identical for the CPMP students and those in the traditional curriculum. Thus, these two groups were wellmatched on mathematical achievement prior to high school. They learned mathematics in the same school and sometimes from some of the same teachers. The only apparent systematic difference between the groups is the curriculum. The average SAT Math score for the CPMP group is greater than that of the traditional group, but the difference is not statistically significant at the 0.05 level.
The results in Tables 1 and 2 are illustrated in the following graph. 
Q  How well do CorePlus students perform on the ACT?  

A 
On the ACT Mathematics test, students completing CorePlus mathematics fieldtest courses performed as well as students in traditional mathematics curricula. The 2,944 CPMP and 527 traditional students in the original CPMP fieldtest sample had nearly identical average scores on the ITEDQ pretest administered at the beginning of Grade 9. ACT scores were available from a reasonably large subset of these students, and their average ACT Mathematics and ACT Composite scores are given in Table 1. There is no significant difference (0.05 level) between the CPMP and traditional averages (means) for either the Mathematics or Composite score.
In one school district at the beginning of the CPMP field test (Fall 1994), all ninthgrade students in the two CPMP fieldtest schools who qualified for remedial mathematics through algebra were randomly assigned by computer to CPMP Course 1 or to the appropriate traditional course. Many of these students completed Advanced Algebra or CPMP Course 3 in their junior year and took the ACT either in spring or summer of their junior year or in fall of their senior year. The average sixthgrade CAT Mathematics percentiles for the CPMP students and those in the traditional curriculum are similar as shown in Table 2, so these two groups were wellmatched on mathematical achievement prior to high school. They learned mathematics in the same schools and sometimes from some of the same teachers. The only apparent systematic difference was the curriculum. For this set of students, the average ACT Math scores for the CPMP group is almost identical to that of the traditional group. The average ACT Composite score for the CPMP group is greater than that of the traditional group, but the difference is not statistically significant at the 0.05 level.
The results in Tables 1 and 2 are illustrated in the following graph. 
Q  How well do CorePlus students perform on mathematics placement tests at the college level? 

A 
On a Mathematics Department Placement Test from a large Midwestern university, students completing fieldtest versions of CorePlus Mathematics Courses 13 plus the precalculus path of Course 4 performed as well as students in traditional precalculus on basic algebra and advanced algebra subtests and better on the calculus readiness subtest. The Mathematics Placement Test, compiled from a bank of items developed by the Mathematical Association of America, that is presently used at a major university was administered in several fieldtest schools in May 1999 at the end of CPMP Course 4 and traditional Precalculus courses. This test contains three subtests  Basic Algebra (15 items), Advanced Algebra (15 items) and Calculus Readiness (20 items). The first two subtests consist almost entirely of algebraic symbol manipulation, and the third subtest measures some of the important concepts that underlie calculus. A graphing calculator (with no symbol manipulation capability) is allowed on this test. The CPMP Course 4 students included in the comparison below are all those in the 199899 Course 4 field test who completed the 6unit "preparation for calculus" path as the last course in their sequence of CPMP Courses 14 (N = 164). The Precalculus students, also from fieldtest schools, completed a traditional precalculus course following a sequence of Algebra, Geometry and Advanced Algebra (N = 177). The two groups were further restricted to those students who indicated on a written survey their intention to attend a fouryear college or university in the next school year. Eighthgrade mathematics standardized test scores for both groups were, on average, at about the 85th national percentile. Means by group and subtest are plotted in Figure 1. The CPMP Course 4 mean was significantly (p < 0.05) greater than the Precalculus mean on the Calculus Readiness subtest, while the group means did not differ significantly on the Basic Algebra or Advanced Algebra subtests. Figure 1: The Mathematics Department at the university that provided this placement test combines the subtest scores by a formula to recommend enrollment for each student in one of four college mathematics courses  Calculus I, Precalculus, Intermediate Algebra, and Beginning Algebra. Using that formula, the percent of CPMP Course 4 and Precalculus students who would be recommended for each course is illustrated in Figure 2. A much higher percentage of CPMP Course 4 students (50.6%) than traditional Precalculus students (39.0%) would be recommended for Calculus I suggesting that the CPMP curriculum with this sequence of Course 4 units better prepares students for this examination and presumably for college calculus. Figure 2: 
Q  How well do CorePlus students perform in college mathematics courses?  

A 
CPMP Course 4 was field tested nationally during the 199899 school year and some preliminary evidence on how CPMP graduates perform in collegiate mathematics courses is beginning to appear. A study completed at the University of Michigan examined the performance of students from two Michigan high schools in the same district, Andover High School and Lahser High School. In 1995 and 1996, a traditional mathematics curriculum was in place at both schools, and Lahser continued to use their traditional curriculum through 199899. In 1997, all Andover students who had not previously been accelerated had studied the CPMP curriculum, and by 1998 all Andover students were in the CPMP program. Computer files provided by the University of Michigan registrar were used to generate the achievement data summarized in the following table. The table includes the number of matriculants from the school under the year, the mathematics courses taken in the first year of study at the University of Michigan together with the grade point averages, and numbers of elections and the course averages in each year. The mathematics courses are 105/110 (precalculus), 115 (calculus I), 116 (calculus II), 215 (calculus III), 216 (introduction to differential equations), and honors (all honors math courses open to freshmen). The grade point averages were calculated using the University of Michigan system as follows: A+ (4.3), A (4), A (3.7), B+ (3.3), B (3), ..., D (1), D (0.7), E+ 0.3), and E (0).
The Andover achievement for the years 1997 and 1998 when CPMP was in place is stronger than both preCPMP Andover (i.e., 1995 and 1996) and 1997 and 1998 Lahser achievement. Similarly, the number of Andover matriculants at the University of Michigan for the last two years is greater than that for the previous two years. These achievement and admissions data clearly support the view that in collegiate mathematics courses at the University of Michigan, graduates of the CPMP program perform as well as, or better than, graduates of a traditional mathematics curriculum. Graduates of the CPMP program at Andover have, themselves, commented on their preparedness for collegiate mathematics and mathematicsrelated fields. The following comments are from three students who studied the pilot version of CPMP Course 4. The first two students enrolled at the University of Michigan.
Comments such as the above are not unique to students at the University of Michigan. The following is a quote from an Andover graduate from the same class who enrolled at Stanford University.

Q  What are students' perceptions and attitudes about the CorePlus Mathematics Project curriculum? 

A 
A written, Likerttype survey of students' perceptions and attitudes about various aspects of their mathematics course experience was administered at the end of each school year during the field test. In four fieldtest schools, both CPMP Course 2 students (n = 221) and traditional geometry students (n = 134) completed this survey at the end of their respective courses. (Course 2 results are presented since the newness effect of the CPMP approach is likely to have disappeared by then). Each of the following findings was consistent across levels of pretest student achievement.
