Need for Support
CMP is a coherent set of materials designed to guide teachers and students in the development of mathematical knowledge that includes deep understanding, proficiency in skills, and the ability to make connections within mathematics and connections to other disciplines. In CMP this is accomplished by embedding the mathematics in problem situations.
Introducing a mathematical idea through a contextual problem that embodies the concept helps students develop meaning and use the knowledge they need to solve the problem. Students also draw upon the contexts of the problems to help them recall the mathematics associated with those contexts. In addition, these real-life situations provide a transition into the world of symbols, helping students to make sense of the symbols even in abstract situations. Solving such problems requires using many kinds of mathematical skills, so students are constantly practicing important skills as well as developing understanding and advancing their reasoning.
For the CMP curriculum materials to help students reach their full potential, teachers must develop the knowledge and skills to use the materials to engage students in appropriate ways. Hence, the focus of professional development for teachers enacting CMP is to enable them to learn mathematics content and the pedagogy they need to plan their instruction around an inquiry-based curriculum. A problem-centered curriculum is a radical departure from the traditional classroom in which most of us have learned or taught. Teachers need time and assistance to become familiar with the mathematical concepts and skills that are embedded in the problems. They also need to develop instructional strategies for helping students bring these ideas and skills to fruition. See helping teachers.
CMP uses an inquiry-based instructional model, which promotes a different form of classroom interaction than has historically been used within mathematics instruction. Investigations encourage students to explore, to conjecture, to validate, and to communicate their ideas.
To guide classroom discussion, teachers need a deep and broad understanding of mathematics as well as knowledge of a variety of pedagogical strategies. Teachers also need a variety of assessment tools that can capture the richness and depth of students' understanding and reasoning and can inform instructional decisions.
Because CMP may be quite different from the mathematics curricula experienced by teachers, administrators, and parents and guardians in the community, a shift to CMP is likely to generate excitement as well as cause some discomfort and uncertainty. Some concerns are shared by all members of the community. For example, in the early stages of the adoption process, members of the community will want to know what data research already exists that describes the effectiveness of CMP. As the implementation proceeds, members of the community will be interested in the results of a well-planned, ongoing evaluation of student learning in their school district. Some issues are of greater concern to administrators and teachers than to parents and guardians. For example, administrators will need to plan for multi-faceted professional development to support teachers through different stages of the curriculum implementation, from novice first-year teachers to confident, successful teachers. Teacher concerns include the need for ongoing support, not just in the initial implementation stage, but also later in the development of a continuing, thriving culture of professionals working together to make decisions about how to improve the teaching and learning of mathematics in the building. For more details about long-term professional development for teachers see helping teachers.
Parent and guardian concerns are likely to focus on two issues: how to help their students be successful in a curriculum that may look unfamiliar to them, and how CMP students will perform on high-stakes assessments. Below are some suggestions for informing, engaging, and preparing all members of the community as they tackle the necessary work-from early evidence gathering and planning to well-supported, successful implementation of CMP.
Curriculum by itself is not enough, but an engaging curriculum in the hands of a good teacher, with support of the administration, the local community, and long-term professional development can provide the kinds of mathematical experiences that support higher levels of performance for all students.
CMP is standards-based and problem-centered. Adopting and implementing a standards-based mathematics curriculum can be a major step for school districts.
Standards-based mathematics curricula focus attention on a core agenda of important and broadly useful mathematical ideas. Instead of traditional instruction that asks students to watch passively and imitate teacher demonstrations of routine computational techniques, these curricula engage students in challenging mathematical Investigations that help them construct a solid understanding of key ideas and a confident ability to solve tough mathematical problems. (James Fey, Montgomery Gazette, Montgomery County, September 10, 1999.)
Parents and teachers may be more accustomed to textbooks that have examples followed by pages of skill exercises. Some teachers may be accustomed to instruction characterized by working a few examples for the whole class and then assigning a set of practice problems to be done independently by the students. Although many teachers supplement this pattern by occasionally having students solve non-routine problems, such activity is not at the core of their curriculum or central to their teaching practices.
CMP asks teachers, students, and parents to play different roles. In the traditional curriculum, teachers demonstrate solutions, students observe, somewhat passively, parents and guardians support and supervise practice, and the textbook provides examples. In CMP classrooms, students actively investigate Problems and develop solutions, and teachers question, challenge, and orchestrate classroom discussions and summaries of the mathematics being learned. Parents and guardians will benefit from information about the rationale for the organization and sequencing of the Problems, the role of ACE exercises and Looking Back activities, and the way that student notebooks are designed to capture a student's evolving understanding of a topic. Problem-based curricula like CMP make different demands on all members of the community.
The mathematics in CMP is developed through a sequence of connected Problems in an inquiry-based classroom. This is a shift away from a focus on developing skills and procedures to a focus on developing a set of mathematical relationships, a specialized symbolic language, concepts, and ways of thinking, in addition to skills and procedures. School districts can make the implementation of CMP smoother by following guidelines for orchestrating this shift. Bay et al. (1999) list ten important factors related to successful selection and implementation of standards-based mathematics curricula. These include: administrative support; opportunities to study and pilot the curricula; time for daily planning and interaction with colleagues; knowledge of appropriate assessment techniques and tools; ongoing communication with parents; and articulation with colleagues at the elementary and secondary level.