Research Base

Math Matters is a comprehensive, long-term professional development program. The program addresses teachers’ knowledge and understanding of mathematics as well as teachers’ ability to deliver effective standards-based instruction. We work with schools and districts over time to develop their capacity to sustain systems of professional learning in mathematics. Math Matters improves teachers’ knowledge of math and their ability to transfer that knowledge so that students can master state standards. We believe that schools and districts must continuously build on their knowledge and experience to improve student achievement at every grade level and in every classroom. Schools and school districts have dramatically improved their student achievement in mathematics after making the commitment to implement the components of Math Matters.

The professional development Math Matters provides to schools is successful because it uses practices that research has shown to be effective in raising student performance. Math Matters’ theory of action, displayed in the Figure 1, is to increase students’ achievement by improving teachers’ knowledge and practice in the classroom.

During a two-week Math Matters academy and practicum, teachers and principals learn adult-level mathematics, effective classroom instructional strategies, and how to plan and develop standards-based assessments and lessons. During this time, participants also practice what they have learned in a classroom setting with their colleagues. Directly after the academy and practicum, participants continue practicing the skills at their own school site under the guidance of a math coach. The math coach models instruction for teachers, observes the teachers as they practice the skills they have learned, and help teachers to become more self-directed and reflective learners. To continue the ongoing nature of the professional development, teachers return to regularly scheduled mini-academies that further enhance their knowledge in mathematics, pedagogy and coaching.

Mathematical Knowledge
The professional development offered by Math Matters begins by teaching teachers adult level mathematical knowledge. Regardless of the topic, effective teachers know more about their subject matter than ineffective teachers (Brophy, 1991; Fennema and Franke, 1992; Darling-Hammond, 1997 and 2000). In mathematics, teachers that have a greater understanding of the subject matter can have an effect on student achievement (Monk, 1994). When teachers have a deeper understanding of mathematics, which they do not always develop at a university, they are better able to teach students conceptual as well as computational math skills (Ma, L. 1999). Teachers with a stronger understanding of the conceptual underpinnings of mathematics and why students may make mistakes are also better able to teach all students and provide students with examples in a variety of ways (National Research Council, 2000). Professional development can increase teachers’ content knowledge; however, studies have shown that not all professional development is equally effective. Professional development in mathematics has a larger impact on student achievement when it focuses on specific academic content, when teachers have substantial opportunities to learn about the academic content and how students learn the subject matter, and when it is connected to the curriculum students will use (Cohen, and Hill, 2001; Kennedy, 1999). These areas are emphasized by Math Matters in the academy and practicum as well as in follow-up sessions.

Instructional Strategies
In addition to deepening teachers’ mathematical content knowledge, Math Matters works with teachers to broaden their instructional delivery knowledge. The Math Matters training increases teachers’ repertoire of effective instructional strategies and improves their ability to plan instruction aligned with state standards. How teachers teach makes a difference in student performance (Good, 1983; Wang, Haertel, and Walberg, 1993). But more specifically, teachers’ choice of instructional strategies can have a bigger impact (Marzano, Gaddy, and Dean, 2000). Math Matters presents teachers with specific strategies in management, involvement, focus and feedback (MIFF). The management and involvement strategies help teachers increase the amount of time students are actively engaged in learning (Cotton, 1990; Evertson, and Harris, 1992). The focus and feedback strategies help teachers improve their questioning techniques and create a positive learning environment (Cotton, 1989; Marzano, 2000). In addition to effective delivery strategies, Math Matters helps teachers learn how to plan instruction effectively. Brophy and Good (1986) note that the articulation of learning goals to students, monitoring student work, and careful lesson planning are hallmarks of effective teachers. In Math Matters, teachers learn how to design a strong curriculum of well planned lessons, aligned with state standards, so that students reap the benefits (Marzano, 2000).

Skill Practice
When participating in Math Matters, teachers have multiple opportunities to practice their newly learned skills in a safe environment. Providing time for teachers to practice new skills leads to their increased use in the classroom (Joyce, and Showers, 1984). As Kutner (1992) states, “Teaching strategies must be modeled and practiced many times before they are internalized. When learning new instructional techniques or procedures, participants should first be allowed to practice them in a safe environment in simulations and role plays, with opportunities for positive and constructive feedback.” Teachers are allowed the opportunity to embed the instructional strategy and mathematical content knowledge learned during the academy and practicum as they implement them in their own classrooms with the support of a math coach.

Reflection
Math Matters provides professional development for teachers to become reflective practitioners and self-directed learners. The teachers learn by reflecting upon and examining their own practice and impact their teaching has on student outcomes. To enhance participants’ learning and refine their practice, each teacher works with a coach similar to the way outlined by Joyce and Showers (1980 and 1996). The coach regularly models instruction and provides instructional feedback to the teacher. Coaches also use the “cognitive coaching” model developed by Costa and Garmston (2002) to shape and reshape teachers thinking and to improve their problem solving capacities. Math Matters coaches help teachers to think through their teaching strategies as well as the mathematics content and determine the what strategies are critical and what mathematics is essential. By introducing the coaching model at a school site, benefits can accrue not only to the coaching recipients but to the school as a whole by improving the school climate and fostering interest in change (Showers, 1985). Teachers engaged in reflective practice can improve their sense of teaching efficacy, which often translates into increased in student performance, especially for low-performing students (Chase, Germundsen, Brownstein, and Distad, 2001).

Results
Math Matters has had a strong, positive impact on the achievement of students in a number of schools and districts. For example, in just two years, the West Contra Costa Unified School District in California saw a twenty-nine percent increase on the Stanford– 9 mathematics assessment in classroom where Math Matters training and coaching had occurred. Classroom that did not have training or coaching from Math Matters did not see any significant increase in their scores.

In Providence, Rhode Island, Math Matters has been in place at the Vartan Gregorian Elementary School teachers for five years, 1999 to 2003. In each year the percentage of students that have met or exceeded state standards has grown markedly each year compared to the district as a whole.

Percentage of Students that Met or Exceeded Math Standards
Providence School District, Rhode Island
1998 - 2003

Math Matters also has a strong impact on teachers and teacher practice. Our focus is to develop teachers who understand how to embed procedural skills with conceptual understanding and mathematical reasoning so that students truly learn mathematics. Participants who have participated in Math Matters have commented:

“I liked the examples that were given to apply management in the classroom. They are common sense, but sometimes we need that reminder to ‘let go’ and have the students do the work.”

“A lot of the information was ‘universal’ to teaching, rather than just mathematics.”

“I now believe I am capable of making the needed shift from teaching the processes of mathematics to teaching the concepts, number sense, and processes. I did not believe I could understand it and, since I was successful in math without the understanding, that it wasn't really necessary to teach my students that way (denial). I've dreaded algebra and integers in the classroom because of this. Now I am excited about the opportunity to teach them. I am looking forward to the future in-services and coaching experiences.”

Math Matters works with districts and schools that are committed to long-term professional development in mathematics for teachers and administrators. We work with teachers to improve their knowledge and practice. We also work with administrators to develop instructional leaders who know how mathematics is to be taught and how to observe teachers using instructional techniques and strategies so that all students learn. Over time, participation in Math Matters has a profound and lasting impact on student achievement.

References

Ball, Deborah Loewenberg, Implementing the Professional Standards for Teaching Mathematics: What's All This Talk about Discourse?, The Arithmetic Teacher, Nov 1991, 44-48

Brophy, J. (1991). Advances in research on teaching: Teachers' knowledge of subject matter as it relates to their teaching practice (Vol. 2). Greenwich, CT: JAI Press.

Brophy, J., & Good, T. (1986). “Teacher behavior and student achievement.” In M. Wittrock (Ed.), Handbook of research on teaching (pp. 340-370). NY: Macmillan.

Chase, B., Germundsen, R., Brownstein, J. C. & Distad, L. S. (2001). Making the connection between increased student learning and reflective practice. Educational Horizons, 79 (3), 143-147.

Cohen, D. K., & Hill, H. C. (2001). Learning Policy—When State Education Reform Works. New Haven: Yale University Press.

Costa, A. & Garmston, R. (2002). Cognitive coaching: A foundation for renaissance schools. Boston, MA: Christopher-Gordon Publishers, Inc.

Cotton, K. (1990). “Educational Time Factors.” Close-Up No. 8. Portland, OR: Northwest Regional Educational Laboratory.

Cotton, K. (1989). “Classroom Questioning.” Close-Up No. 5. Portland, OR: Northwest Regional Educational Laboratory.

Darling-Hammond, L. (1997). Doing what matters most: Investing in quality teaching. New York, NY: National Commission on Teaching & America’s Future.

Darling-Hammond, L. (2000). Solving the Dilemmas of Teacher Supply, Demand, and Standards: How We Can Ensure a Competent, Caring, and Qualified Teacher for Every Child. New York, NY: National Commission on Teaching & America’s Future.

Evertson, C.M., & Harris, A.H. (1992). “What we know about managing classrooms.” Educational Leadership, 49(7), 74

Fennema, E. & Franke, M. L. (1992). “Teachers' knowledge and its impact.” In Douglas A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). New York, NY: Macmillan Publishing Co.

Greeno, J. G., Collins, A., & Resnick, L. B. (1996). Cognition and learning. In R. Calfee & D. Berliner (Eds.), Handbook of educational psychology (pp. 15–46). New York: Macmillan Library Reference

Good, T. L. (1983). Recent classroom research: Implications for teacher education. In D. C. Smith (Ed.), Essential knowledge for beginning educators. Washington, DC: American Association of Colleges for Teacher Education.

Joyce, B. & Showers, B. (1996). “The Evolution of Peer Coaching.” Educational Leadership, v53(6), 12-16.

Joyce, B., & Showers, B. (1984). Power and staff development through research on training. Alexandria, VA: Association for Supervision and Curriculum Development.

Joyce, B. & Showers, B. (1980). “Improving inservice training: The messages of research.” Educational Leadership, 37(5), 379-385.

Kennedy, M. M. (1999, November). Form and substance in mathematics and science professional development (NISE Brief Vol. 3, No. 2). Madison, WI: University of Wisconsin–Madison, National Institute for Science Education.

Kutner, M. (1992). “Staff Development for ABE and ESL Teachers and Volunteers.” ERIC Digest. Washington, D.C.: NCLE, Center for Applied Linguistics

Liping Ma. (1999). Knowing and Teaching Elementary Mathematics, Mahwah, NJ: Lawrence Erlbaum Associates.

Marzano, R. J. (2000). A new era of school reform: Going where the research takes us. Aurora, CO: Mid-continent Research for Education and Learning.

Marzano, R. J., Gaddy, B. B., & Dean, C. (2000). What works in classroom instruction. Aurora, CO: Mid-continent Research for Education and Learning.

Monk, D.H. (1994). “Subject Matter Preparation of Secondary Mathematics and Science Teachers and Student Achievement,” Economics of Education Review, 13 (2), pp.125-145.

National Academy of Sciences/National Research Council. (2000). "Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium," Washington, DC: National Academy of Sciences/National Research Council.

Showers, B. (1985). “Teachers coaching teachers.” Educational Leadership, 42(7), 42-48.

Wang, M. C., Haertel, G. D., & Walberg, H. J. (1993). “Toward a knowledge base for
school learning.” Review of Educational Research, 63(3), pp. 249-294.