**General Information**

Table of Contents

Correlations

**Student/Parents (English)**

eTools/Videos

Homework Help

Resource Pages

**Teachers**

Teacher Resources

CPM Educational Program, a California non-profit corporation, has provided problem-based instructional materials and professional development for teachers since its inception in 1989. “College Preparatory Mathematics (CPM)” was originally an Eisenhower-funded grant program. CPM teaching strategies focus on how students best learn and retain mathematics. Teaching strategies rely on the recommendations of the National Council of Teachers of Mathematics, and are based solidly on the methodological research in teaching mathematics. The research-based principles that guide the course are:

- Students should engage in problem-based lessons structured around a core idea.
- Guided by a knowledgeable teacher, students should interact in groups to foster mathematical discourse.
- Practice with concepts and procedures should be spaced over time; that is, mastery comes over time. Read More...

On a daily basis, students using CPM *Calculus* employ problem solving strategies, question, investigate, analyze critically, gather and construct evidence, and communicate rigorous arguments to justify their thinking. With the CPM instructional materials, students can tackle mathematical ideas set in everyday contexts to help them make sense of otherwise abstract principles. Students are taught how to gather and organize information about problems, break problems into smaller parts, and look for patterns that lead to solutions. Students often learn in collaboration with others, sharing information, expertise, and ideas.

Consistent with the requests we frequently hear from leaders of business and industry, CPM routinely has students solve non-routine problems. That is, students develop their skills of synthesis and analysis so that they can confidently make connections between varied mathematical concepts and deal with problems they have never seen before. Students will build problem-solving strategies that apply to most academic disciplines, the workplace, and daily life.

While students are solving complex mathematical problems, they are communicating their thinking and understanding, both formally and informally, whether they are writing or speaking out loud. Communication helps to clarify students’ thinking, and prepares them for sharing their ideas in professional settings. Communication lets teachers and peers assess students’ thinking and depth of understanding, and provide formal or informal feedback that allows for revision. In turn, all students get the chance to improve the quality of their work.

The CPM curriculum is the product of classroom teachers who created lessons that work with the diverse student population. The teaching strategies outlined in the CPM instructional materials were initially informed by theory and scholarly research into how children learn and how teaching should occur in the ideal classroom. Care was taken to pilot and field-test the lessons during the development of the first edition with thousands of students to ensure the effectiveness of the lessons. But ultimately, the development was informed in practice by the 10,000 teachers and over 5 million students that use CPM, the specific suggestions over the last 20 years from hundreds of teachers, and even comments and suggestions by students and parents.

More than two dozen studies have examined the results of both high- and low-performing students on statewide standardized tests, the SAT, and the ACT. All of these studies, as well as detailed investigations of individual schools, show that CPM students learn the basic mathematical skills and procedures that appear on standardized tests at least as well as students who use other programs. Most of the studies show that CPM students do better. Studies that measure the other elements of a complete curriculum—conceptual understanding, problem solving ability, the mathematical practices—show that they do considerably better in these areas. These studies are available at cpm.org, along with the research base of the CPM program.

Read Less...The entire CPM curriculum was designed and written based on these assumptions about student learning:

- Mathematics is a coherent intellectual system, not a collection of disjointed facts, and needs to be taught in a way that makes this coherence clear. The courses emphasize the connected nature of mathematics. Each consistently weaves the topic strands together so that the connections emerge naturally and facilitate deeper understanding. Read More...

- A curriculum should succeed with all students, including “traditionally struggling” students and “accelerated” students. Therefore, each course is designed to be challenging and engaging for all students from the very beginning. This approach not only builds stronger study teams (because mathematical discourse among the students requires something to talk about), but also helps to reduce status issues from the start (e.g., “Jimmy can do these problems quickly on his own, so he must be smart, and I am not.”). Challenging problems push accelerated students to learn more and save them from boredom. They also engage “traditionally struggling” students in the work of developing solution plans and executing them so that they become an integral part of the study team.
- Students learn more when they solve problems and discuss their thinking with others. The curriculum incorporates this research-based principle by having students collaborate in class in study teams. The teacher structures and supports learning while guiding students toward the mathematical objectives of the lessons.
- Teams work more effectively when the work actually requires a team and there is something to talk about. The classwork challenges all students so that they must problem-solve together. Each student has a defined role in the solution process. The specific responsibilities of each position eliminate the damaging team behavior of having one student solve the problems and then “tell” the other students how to complete them.
- Closure is a vital part of the lesson, so lesson concludes with a specific closure activity. Sometimes the closure activity consists of reflective writing, while at other times it involves a whole-class discussion prompted by questions the teacher may find in the Teacher Edition.
- A student’s learning is more meaningful and is better retained when the level of understanding necessary to explain and justify thinking is attained. The courses emphasize asking students to justify their mathematical thinking and problem-solving approaches to foster long-term retention of what they learn.
- A mathematical text should have usable reference elements. The text design allows teachers, parents, and students to access information through indices and glossaries and to find problems and lessons with an easy-to-use method to reference problems. The Math Notes boxes consolidate all major concepts and include definitions of key mathematical terms, as well as examples of the solving process for certain types of problems. Every lesson has a similar structure (introduction, problems/investigations, closure, a Math Notes box when appropriate, and homework) so that students know where to look for what they need.
- Rigorous and meaningful mathematical study can strengthen literacy. The curriculum supports students’ growth in reading and writing. The student text is written in an even voice with consistent language usage to help students who are challenged with reading. The text gives students regular opportunities to develop and practice their writing skills through reflections and explanations of their understanding. The bulk of the reading is done during class time when students have the support of their team members and the teacher. Homework assignments require much less reading.
- The structure of the lessons and layout of the textbook help students focus on mathematics and eliminate distractions. The consistent structure of each lesson, homework set (“Review and Preview”), and chapter closure section help to make students comfortable and confident with the lessons. The use of black-and-white printing with illustrations, that are either course icons or specific to the problems, avoids the distraction of random pictures, multiple color splashes, and layers of highlighting. The “color” in the book is the students’ excitement and engagement with mathematics.

At the same time, to support students with learning gaps and weaker skills, these courses build the conceptual foundation slowly, with an emphasis on using manipulatives and technology tools and looking at problems in multiple ways. The “mastery over time” approach accommodates different learning styles.

The homework in the “Review & Preview” section of each lesson includes mixed, spaced practice, and prepares students for new topics. The homework problems give students the opportunity to apply previously-learned concepts to new contexts. By solving the same types of problems in different ways, students deepen their understanding. CPM offers open access homework support at homework.cpm.org.

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Chapters are organized in sections. The section numbers are sequential for each chapter and are designated by the chapter number followed by the section number. For example, Section 10.2 is the second section of Chapter 10. Lesson numbers use a *chapter.section.lesson* format. Thus, Lesson 3.2.1 is the first lesson of the second section in Chapter 3. Read More...

Each section contains several lessons that develop a mathematical topic, and is designated by a section number and a signpost icon. A signpost icon, which appears at the beginning of each lesson in a, is representative of the mathematical concepts contained in that section of the text. Signposts that point to the left represent “AB” lessons, while signposts that point to the right represent “BC” lessons. Each chapter is framed with Chapter Goals and a Chapter Outline.

The basic structure of every lesson in the text includes the core mathematical content followed by a Review and Preview homework section. Lessons may include some additional elements, such as Calculator or No Calculator Problems or Math Notes boxes. A description of each element follows.

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