From reading, attending conferences, and soliciting researchers to give presentations on their findings, the group formed another key takeaway: Students learn mathematics best when they start with a big picture that has some sort of mystery to be uncovered. Beyond being supported by research, the veracity of this principle of learning was experienced first hand by some of the original group. For example, founder Judy Kysh cites an Algebra textbook written by Johnson, Lendsey, Sleznick, and Bates (an Addison Wesley book) as having deeply influenced her thinking. Unlike most texts of the day that had problems that could not be successfully completed without first examining pre-worked examples, in this text, learners could solve new problems by reasoning about what they had done in prior problems. A lot of problems in CPM’s original text were inspired by the Johnson and colleagues textbook, pictured right. They were also inspired founder Judy Kysh’s (then Judy Salem) work on a Scott Foresman (a bygone publisher) Algebra 1 and Algebra 2 textbook series (copyright 1984) in which each chapter began with a real problem, and by the end of the chapter enough math had been developed to solve the opening problem. Following this inspiration, CPM chapters were originally named for their real-world big problems, rather than for the mathematics in them. Anecdotal evidence from student portfolios and interviews suggested students remembered the mathematics by the problem that they encountered it in, and this helped them solve similar problems in other contexts.
Research takeaway: Narrative and mathematical storylines support aesthetic responses
Over the years, building on more recent research, CPM materials have developed to not only use big problems, but even more, to develop both narrative and mathematical storylines (e.g., Dietiker, 2013, 2016, 2019). CPM’s textbooks are designed such that the mathematics storyline and the narrative storyline go hand in hand, one does not serve the other. In CPM texts, students encounter situations with an enigma— something that students will not yet know how to resolve. The mathematics in the texts was and is organized so that students experience ah-ha moments— so that students experience aesthetic dimensions of mathematics, such as feelings of curiosity and surprise as they construct mathematical connections and elegant solutions.
CPM’S FIRST TEXTBOOK
From the peer-reviewed academic research described above, CPM synthesized three design principles that have since become known as The Three Pillars of CPM: Collaborative Learning, Problem-Based Learning, and Mixed Spaced Practice. Grounding the curriculum in these three pillars, the group wrote a new set of Algebra 1 material (aka Math 1) in five weeks in the summer of 1989, with an additional smaller team editing and polishing. Then, during the 1989-90 school year, the teachers who worked on the materials piloted them and took notes on how to improve them. They met nearly every month of the year to share and create a collective record of their experiences teaching with the materials. After this pilot, the teachers revised the Algebra 1 materials and created the first Geometry text (aka Math 2) in the summer of 1990, then piloted the Algebra 1 materials for a second time and the Geometry materials for the first time in the 1990-91 school year. An Algebra 2 text (aka Math 3) was written a few years later, beginning in the summer of 1992, then undergoing two rounds of field-testing and review, and settling on the final first edition in the summer of 1994.
Back in those days, the text materials were distributed by chapter as shrink-wrapped stacks of loose leaf pages from the back of a van that founder Judy Kysh drove to a central location. Teachers drove there to get their pages, engaged in professional development together for the entire day, and then took the materials back to their schools for copying. Most teachers distributed a unit or chapter at a time.
CPM EDUCATIONAL PROGRAM: A CALIFORNIA NON-PROFIT ORGANIZATION
In 1993 when the quantity of materials began to exceed the capacity of Judy’s van (borrowed from a university), CPM incorporated as a California nonprofit corporation so that soft-bound versions of Algebra and Geometry could be printed and sold. Teachers no longer had to copy and distribute materials at their schools.