# MCP Teaching Approach

We talk about the MCP instructional approach being curriculum independent because the approach allows the pedagogy to focus on the critical features of instruction (Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Oliver, A., & Human, P., 1997). Regardless of the curriculum, the MCP teachers are expected to include in their pedagogy the following activities:

- posing a problem or frame an activity;
- allowing students to work freely, circulating to monitor, encourage, and strategically guide students;
- questioning students to probe thinking and to evoke deeper understanding;
- encouraging students to develop multiple representations and identify mathematical connections;
- encouraging students to communicate reasoning and justification for their work;
- facilitating discussions about student solutions and problem-solving strategies;
- documenting the on-going assessment throughout the lesson; and
- >grounding instructional strategies for the next lesson on assessment.

**MCP In the Classroom**

In the classroom MCP teachers provide opportunities for students to think mathematically and develop flexibility, fluency and connections among mathematical topics. Mathematical topics are comprised of concepts and procedures, and according to Baroody (2007) deep understanding of mathematical knowledge results from richly connected conceptual and procedural knowledge. The expectation is that teachers will utilize existing curriculum materials to provide these learning opportunities, designing instruction, and enhancing and adjusting curriculum materials as necessary.

Teachers determine the necessity of adjustments to curriculum by analysis of MCP student pretests, results of on-going classroom evaluations, review of student classroom work, and results of classroom tests and quizzes. The teacher learns about analysis and use of these assessments in planning and debriefing sessions with the coach. These sessions include discussions on student data, mathematics content and instructional strategies. Once the teacher understands the students’ learning, the MCP teacher can base curriculum adjustments and instructional decisions on that student learning.

Curriculum adjustments may include: 1) making a problem a better problem; 2) adding a problem or activity where there is a gap in the curriculum; 3) incorporating the NCTM Process Standards and 4) adding a problem or activity to the curriculum when there are gaps in student learning, to re-teach or deepen understanding before moving to the next curriculum topic. Although adding material to the curriculum may need no explanation, we believe the concept of making a problem a better problem does warrant a brief explanation. Making a problem a better problem may mean making the problem more open-ended, not easily solved algorithmically, or involving more rigorous content. It might also mean designing the problem to encourage multiple solution strategies or to differentiate for different levels of learners.

**MCP Research Base**

The teaching approach supported by the MCP program and its coaches and teachers is grounded in a rich history of mathematics education research that includes but is not limited to work around

- Cognitively Guided Instruction (Fennema, Carpenter, & Franke, 1991; Fennema, Carpenter, Franke, & Carey, 1992);
- teaching and learning mathematics with understanding (Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human. 1997);
- constructivist teaching dependent on deep knowledge of mathematics for teaching (Ball, Hill & Bass, 2005);
- student centered instruction (Cornelius, 2007);
- a pedagogy driven by the mathematical processes (NCTM, 200);
- an integration of procedure and concept (Baroody, 2007; Star, 2007);
- problem posing (Freire, 1973/1989); and
- a teacher commitment to social justice through mathematics instruction (Frankenstein, Marilyn, 1987; Gutstein & Peterson, 2005; Pace & Hemmings, 2007).

**MCP References**

Ball, D. L., Hill, H. C. & Bass, H. (2005). Knowing mathematics for teaching. * American Educator.* 14-22; 43-46.

Baroody, Arthur J. (2007). An alternative reconceptualization of procedural and conceptual knowledge.* Journal for Research in Mathematics Education, 38* (2), 115-131.

Cornelius-White, Jeffrey (2007). Learner-centered teacher-student relationships are effective: A meta analysis.* Review of Educational Research, 77*(1), 113-143.

Fennema, Elizabeth, Carpenter, Thomas P., & Franke, Megan L. (1991) . *Cognitively Guided Instruction* . Wisconsin Center for Education Research.

Fennema, Elizabeth, Carpenter, Thomas P., Franke, Megan L., & Carey, Deborah A. (1992) . Learning to use children’s mathematics thinking: A case study. In R. Davis & C. Maher (Eds.), *Schools, mathematics and the world of reality* (pp. 93-117). Needham Heights, MA: Allyn and Bacon.

Frankenstein, Marilyn (1987). Critical mathematics education: An application of Paulo Freire’s Epistemology. In I. Shor (Ed.) *Freire for the classroom: A sourcebook for liberatory teaching*. Portsmouth: Heineman.

Freire, Paolo (1973/1989). *Pedagogy of the oppressed.* New York: Continuum.

Gutstein, Eric & Peterson, Bob. (2005). *Rethinking Schools: Teaching Social Justice by the numbers*. Milwaukee, WI: Rethinking Schools, Ltd.

Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Oliver, A., & Human, P. (1997). *Making sense: Teaching and learning mathematics with understanding.* Portsmouth, NH: Heinemann.

Pace, Judith L. & Hemmings, Annette. (2007). Understanding authority in classrooms: A review of theory, ideology, and research.* Review of Educational Research, 77*(1), 4-27.

Star, Jon R. (2007). Research commentary: A rejoinder foregrounding procedural knowledge.* Journal for Research in Mathematics Education, 38* (2), 132-135.