CPM Educational Program: A Comprehensive Review
The College Preparatory Mathematics (CPM) program is a math curriculum used in many school districts, including SMFCSD and SMUHSD. CPM aims to prepare students for college-level mathematics through problem-based lessons, teacher guidance, group interaction, and spaced practice. This article examines the CPM program, its methodology, strengths, weaknesses, and the diverse opinions surrounding its effectiveness.
Introduction to CPM
CPM was created around 1990 by a group of teachers in Sacramento with the goal of revolutionizing math teaching. The CPM mathematics textbook series spans middle school to high school math, including Calculus AB and BC textbooks. CPM literature frequently mentions that in the “real world” people work in teams, and therefore CPM aims to teach and facilitate collaborative learning.
The CPM Methodology
A typical CPM lesson involves students working in groups to solve guided questions that lead them to discover new math concepts. Each textbook section begins with a series of guided questions that lead students to discover a new math concept if they answer the questions correctly and in order. Often these guided questions are quite clever and well-designed. The books do not simply explain a math idea and then provide worked examples to imitate, as do traditional math texts. Teachers are supposed to move around the class from group to group, answering questions from each group and making sure that students are on task. Lecturing is kept to a minimum. This is in agreement with the “learning by doing” philosophy. Teachers are supposed to move around the class from group to group, answering questions and ensuring students stay on task, minimizing lectures in favor of a "learning by doing" philosophy.
The first part of each textbook section consists of group problems, while the second part, titled "Review and Preview," includes practice problems and review problems from earlier sections. The “review” problems include some additional practice on the ideas just learned in the guided questions section, but also include review problems from earlier textbook sections. The spiraling concept can also come into play on CPM chapter tests, i.e., the chapter 4 test will include problems not only from chapter 4, but also from chapters 1, 2, and/or 3. This can turn a chapter test into what is basically a mid-term or final exam. The “Review and Preview” homework section may also include “thought” problems (called “preview” problems) on topics that students have not even encountered yet.
Strengths of the CPM Program
Collaborative Learning: CPM promotes teamwork, mirroring real-world scenarios where collaboration is essential. Many teachers have told me that students are more engaged with the CPM math curriculum than with any other series that they have tried. As long as the program works in this manner this is definitely a strong positive in its favor.
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Active Learning: Mathematics is definitely learned by working problems actively rather than watching a teacher do them on the board. The "learning by doing" approach encourages students to actively engage with the material. If the student groups are well-structured, the better students help those in their group who struggle with math, and everyone benefits. The good students benefit because, paradoxically, there is no better way to learn a subject than to teach it.
Teacher Support: CPM provides pre-made lessons, reducing lesson planning for teachers. CPM basically is a set of pre-made math lessons which alleviates a lot of lesson planning for teachers.
Spiraling Curriculum: The "Review and Preview" section reinforces previously learned concepts, aiding retention. On the plus side, the constant cycling back can really reinforce the material.
Potential for Deeper Understanding: The guided questions are designed to lead students to discover mathematical concepts independently, potentially fostering a deeper understanding than rote memorization.
Weaknesses of the CPM Program
Lack of Explicit Instruction: CPM's self-discovery approach may leave students without sufficient explanations and worked examples. In summary, the biggest problems with CPM are the lack of explanations, worked example problems in the textbooks, and insufficient practice problems. The first two omissions are by design because each group is supposed to discover the concepts through the guided questions. However, if a group does not “get” the topic and fails to complete the guided problems in class, they are left with nothing to explain how they should do the homework!
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Insufficient Practice Problems: Traditional texts give a far greater number of practice problems than CPM. Students may not get enough practice to solidify their understanding. This is much harder to do using the CPM series. In my experience a teacher who decides to use CPM needs to give students supplemental practice problems.
Challenges with Weaker Students: The CPM method can be problematic in classes with lower-level students who struggle with math. Putting pre-teens or teens who “hate math” into groups results in a major “classroom management” challenge for a teacher. Essentially the student has a textbook with only questions and little or no explanations. This is a significant problem in classes with weaker math students and with students who are absent from class. They have nothing to refer to at home unless the teacher puts additional material on the Web.
Reliance on Group Dynamics: The success of CPM depends heavily on group dynamics, which may not always be effective. The whole functionality of this method relies on at least one of the four students understanding the information provided and being able to share it with the group. As a student who has been in the CPM program from Precalculus to AP Calculus BC, the class environment has not worked like that idealistic model provided above. There are usually one or two groups that do not have a single student who understands the concept. I have struggled in math for the past three years and have been in groups with people that have understood the subject, but they simply cannot explain their thinking.
Potential for Tediousness: Students also aren’t big fans of the CPM’s homework problems, which reinforce ideas but, unfortunately, are also very repetitive. On the other hand, students, myself included, still blame CPM for making math more tedious than it has to be.
"Review and Preview" Drawbacks: Too often I have tutored students who are just beginning to master a new concept when the homework diverts them back to earlier topics without cementing the knowledge just learned.
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Diverse Opinions on CPM
Teachers tend to love the CPM math series, currently in use in many SMFCSD and SMUHSD classes, while parents have the opposite opinion.
Teachers' Perspective: Many teachers find CPM engaging and appreciate the ready-made lessons. Many teachers have told me that students are more engaged with the CPM math curriculum than with any other series that they have tried.
Parents' Perspective: Parents often find CPM confusing and less comprehensive. My observation is that this curriculum is more confusing and less comprehensive.
Students' Perspective: Student opinions vary. Some appreciate the collaborative learning and problem-solving focus, while others find the lack of explicit instruction and repetitive homework tedious. Many students are appalled by the idea that everything they learn is through solving problems with no example solutions.
CPM Training for Teachers
CPM offers professional development opportunities for teachers, including the Building on Instructional Practice Series. This series includes events focused on discourse, assessment, and equity.
Building on Discourse: Participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments.
Building on Assessment: Participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions.
Building on Equity: In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning.
Concerns and Criticisms
Over-Reliance on Calculators: Dr. Klein brings up that the whole program relies too much on students caring about math, aimless activities that in no way help simplify “high-order thinking projects”, and it heavily relies on calculators, which inevitably will lead to a “symbol manipulation” way of thinking.
Lack of Student Representation: This all boils down to an underrepresentation of student voices in decision making for the programs we need and don’t need. Underrepresentation is a nice way to put it, because in reality students have no representation whatsoever and aren’t taken seriously by the adults at the Board of Education.
Questionable Research: The methodology of this study is very flawed, however, because it appears to only take the results of school districts that CPM knew used their books and compare them to statewide averages. There is no controlling for differences in, e.g., demographics between districts that adopted CPM and the state as a whole.
Alternative Approaches
Teachers can supplement the CPM curriculum with additional practice problems and explanations. In my experience a teacher who decides to use CPM needs to give students supplemental practice problems. One must also strongly believe in the value of the self-discovery process.
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