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CPMP
Evaluation
Each CPMP course
is the product of a four-year research, development, and evaluation cycle.
After a year of initial development, a pilot version of a course was tested
the next school year in 19 Michigan high schools. Changes identified by
this formative evaluation were incorporated in a revised field-test version
of the course. During the third year, a national field test was conducted
in 36 high schools (and in 6 middle/junior high schools in the case of
Course 1) in Alaska, California, Colorado, Georgia, Idaho, Iowa, Kentucky,
Michigan, Ohio, South Carolina, and Texas. A broad cross-section of students
from urban, rural, and suburban communities with ethnic and cultural diversity
were represented. Further changes and refinements identified in the field
test were incorporated in the final published version of each course.
Based on evidence
from nationally standardized tests (ITED, SAT, ACT, NAEP), course-specific
tests, researcher-developed tests, college mathematics placement tests,
interviews, surveys, and other data, the CPMP curriculum has been shown
to enhance students' mathematical achievement and attitudes toward mathematics.
There is a large and growing body of rigorous research documenting the
effectiveness of the CPMP curriculum. Research findings have appeared
in articles in peer-reviewed journals,
in peer-reviewed book chapters,
in papers presented at research conferences,
in CPMP field-test reports, and
in doctoral dissertations.
Student Achievement
Quantitative
Thinking
CPMP students outperform comparison students on the mathematics subtest
of the nationally standardized Iowa Tests of Educational Development ITED-Q.
Conceptual Understanding
CPMP students demonstrate better conceptual understanding than students
in more traditional curricula.
Problem Solving
Ability
CPMP students demonstrate better problem solving ability than comparison
students.
Applications
and Mathematical Modeling
CPMP students are better able to apply mathematics than students in more
traditional curricula.
Algebra
CPMP students perform better on tasks of algebraic reasoning than comparison
students. For tasks involving algebraic manipulative skills, the field-test
research indicates mixed results. On some evaluation tests, CPMP students
do as well or better, on others they do less well than comparison students.
As part of the curriculum development process, revisions have been made
to strengthen students' algebraic skills.
Important Mathematics
in Addition to Algebra
CPMP students perform well on mathematical tasks involving geometry, probability,
statistics, and discrete mathematics.
National Assessment
of Educational Progress (NAEP)
CPMP students scored well above national norms on a test comprised of
released items from the National Assessment of Educational Progress.
Student
Perceptions and Attitudes
CPMP students have better attitudes and perceptions about mathematics
than students in more traditional curricula.
Performance
on State Assessments
The pass rate on the 2004-05 Tenth-Grade Washington Assessment
of Student Learning Mathematics test for 22 state of Washington high schools
that were in at least their second year using the Core-Plus Mathematics
curriculum was significantly higher than that of a sample of 22 schools
carefully matched on prior mathematics achievement, percent of students
from low-income families, percent of underrepresented minorities, and
student enrollment.
College Entrance
Exams - SAT and ACT
CPMP students do as well as, or better than, comparable students in more
traditional curricula on the SAT and ACT college entrance exams.
Performance
on College Math Placement Tests
On a mathematics department placement test used at a major midwestern
university, CPMP students performed as well as students in traditional
precalculus courses on basic algebra and advanced algebra subtests, and
they performed better on the calculus readiness subtest.
Performance
in College Mathematics Courses
CPMP students completing the four-year curriculum perform as well as,
or better than, comparable students in a more traditional curriculum in
college mathematics courses at the calculus level and above.
Student Beliefs and Conceptions
Data from a Student
Belief Survey indicate that CPMP students grew significantly in confidence
about their mathematical ability and in their interest both in mathematics
and in taking more mathematics. They also had a significantly more positive
attitude than the control group of students about their mathematics course.
Interviews and journal reports of students indicate that they think CPMP
is challenging, especially at first, yet useful, interesting, and enjoyable.
Some representative student comments are presented below.
Student Voices from CPMP Classrooms
| Student 1: | Wow! This year's math was really different from last year! I begun to understand difficult ideas and methods, & they didn't seem as hard! I now have a stable foundation to base next years math on & I learned a little bit about every aspect of mathematics. |
|---|---|
| Student 2: | When I really think about it, no other math class could have taught me this stuff. We learn a lot about real life problems instead of just plain boring math. It keeps you more interested and wanting to learn. Also when you discover the answer, you feel good about knowing what to do. |
| Student 3: | The material [Exponential Models] was real and you could imagine the problems as you did them. That made the problems easier for me. It was done in such a way so that I could investigate my way through a problem. This is a better way for me to learn than to be lectured at and then expected to understand. |
| Student 4: | It's a little tougher than a regular math class. Doing 100 problems of the same things doesn't really help you, but when you do the integrated problems [in CPMP], it makes you think more and I'd say it really helps you. |
| Student 5: | This course lets you prove that you are smart and that you know how to do a lot of problems which you would never think you could do. |
| Student 6: | This class is fun, exciting, creative and makes people use their mind and common sense to solve problems that you might face in real life situations. Not those boring classes where you learn how to do a problem and remember the formula. This class is also hard work, but you learn a lot as you're working. |
| Student 7: | I like being able to work together to figure things out. I like when I finally grasp the idea or figure out a question that really makes you think. |
| Student 8: | In the past, if a problem was too hard, I would simply skip it. Now, I can look at a problem, think about it, and then, pick it apart until I find a solution. |
| Student 9: | I learned how to problem solve. If I look at a problem and don't understand it at first, I can spend time on it and think about it for other angles until I solve it. |
| Student 10: | I felt I was well prepared in math because I did very well on placement tests for college. I helped friends with their math homework often. I am able to explain a process to help them understand. I can show them a different way to do a problem that may be easier for them. In my chemistry and biology classes, I can understand the math in class because of my background. I feel I was very well prepared. |
Teacher Reflections
| Teacher 1: | I know that the kids are learning more, they remember it longer, and they put all the pieces together to form the big picture (the connections are everywhere). |
|---|---|
| Teacher 2: | I have found that students will remember topics in terms of the "big problem" and then recreate the steps from memory as they encounter a similar problem a year later. |
| Teacher 3: | Focusing on big ideas such as constant rate of change has payoffs. Many of my CPMP students have a better understanding of linear functions than my precalculus students. |
| Teacher 4: | ...mathematics becomes an important tool for solving many problems in real life situations and other disciplines. The role of mathematics in solving a variety of problems has made mathematics closer to students' lives so that for many students, mathematics is more interesting and challenging. |
| Teacher 5: | The modeling of mathematical concepts is great. The wide variety of topics helps students keep going when they would otherwise become bored or quit. |
| Teacher 6: | In the traditional math class, I often found myself asking "why is this important?" ... they [the students] are beginning to understand that mathematics is not some routine, memorized, hard-to-understand area, but rather a process which makes sense and applies to the world around them. |
| Teacher 7: | For too long I "taught" concepts by "telling" students what they should know. I could see the lack of understanding in so many of their eyes, but I had no better way of helping them to learn. Now, students make sense of the concepts themselves, and many more of them are having true, deep understanding. |
| Teacher 8: | Kids can do more than we've expected in traditional classes. |
| Teacher 9: | Utilizing many ways of knowing is a strength [of CPMP]. |
| Teacher 10: | I've learned that math can be exciting and dynamic (after 23 years); that I'm not done learning; that this is math that all students can/should experience; that math classes need not be tracked; and that we need to be active in changing misconceptions about math abilities. |
| Teacher 11: | "Smart" students must learn to "THINK & EXPLAIN." All students can think and some students just need confidence to express themselves. |
The student and
teacher comments support the promise of a curriculum and instructional
model for teachers that make good mathematics, taught well, accessible
to all students. The comments also support the success of the curriculum
in engaging students in mathematical thinking.