**1.*** Doing** mathematics** is about making sense of and thinking deeply about fundamental concepts.*

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Sorto, M. A., McCabe, T., Warshauer, M., & Warshauer, H. (2009). Understanding the value of a question: An analysis of a lesson. *Journal of Mathematical Sciences & Mathematics Education, 4*(1), 50-60.

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White, A., and Van Dyke, F., (2004). “Making Graphs Count*,”* *Mathematics Teaching,* 42 – 45.

**2. ****Persistence** is critical to success in problem-solving and doing mathematics.

Ames, C. (1992). Classrooms: Goals, structures, and student motivation. *Journal of Educational Psychology, 84*, 261-271.

Ames, C., & Archer, J. (1988). Achievement goals in the classroom: Students’ learning strategies and motivation processess. *Journal of Educational Psychology, 79*, 409-414.

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Dweck, C. S. (2000). *Self theories: Their role in motivation, personality, and development*. Philadelphia: Psychology Press.

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Stevenson, H. W., & Stigler, J. W. (1992). *The Learning Gap: Why our schools are failing and what we can learn from Japanese and Chinese education*. New York: Summit Books.

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Warshauer, M., and Fischer, J., “Mathworks: An Innovative Approach to Systemic Change in Mathematics Education,” *The Journal of the Society of Educators and Scholars*, Carolyn Morales, Chief Editor, Inter American University of Puerto Rico, San Juan, Puerto Rico, March 26, 2003.

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White, A., and Van Dyke, F., (2004). “Examining Students’ Reluctance to Use Graphs*,”* *Mathematics Teacher,* Vol. 98, 110.

Wiliam, D. (2007). Keeping learning on track: Classroom assessment and the regulation of learning. In J. Frank K. Lester (Ed.), *Second handbook of research on mathematics teaching and learning* (pp. 1051-1098). Charlotte, NC: Information Age Publishing.

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**3.*** Teachers need to establish a classroom culture that develops students’ curiosity and imagination.*

Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin & D. Schifter (Eds.), *A Research Companion to Principles and Standards for School Mathematics* (pp. 27-44). Reston, VA: National Council of Teachers of Mathematics.

Bass, H. (2005). Mathematics, mathematicians, and mathematics education. *Bulletin of the American Mathematical Society, 42*(4), 417-430.

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Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. *Journal for Research in Mathematics Education, 29*(1), 41-62.

Carter, S. (2008). Disequilibrium & Questioning in the Primary Classroom: Establishing routines that help students learn. *Teaching Children Mathematics, 15*(3), 134-138.

Dewey, J. (1910, 1933). *How we think*. Boston: Heath.

Doyle, W. (1988). Work in Mathematics Classes: The context of students’ thinking during instruction. *Educational Psychologist, 23*(February 1988), 167-180.

Fennema, E., Carpenter, T. P., Franke, M. L., & Carey, D. A. (1993). Learning to use children’s mathematical thinking: A case study. In R. B. Davis & C. A. Maher (Eds.), *Schools, mathematics, and the world of reality* (pp. 93-117). Boston: Allyn & Bacon.

Herbel-Eisenmann, B. A., & Breyfogle, M. L. (2005). Questioning our patterns of questioning. *Mathematics Teaching in the Middle School, 10*(9), 484-489.

Hiebert, J., & Wearne, D. (1993). Instructional tasks, discourse, and students’ learning in second-grade arithmetic. *American Educational Research Journal, 30*(2), 393-425.

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Kennedy, M. M. (2005). *Inside teaching: How classroom life undermines reform*. Cambridge, MA: Harvard University Press.

Lampert, M. (2001). *Teaching problems and the problems with teaching*. New Haven, CT: Yale University Press.

Pool, P. (2003). What do you do when you don’t know what to do? *Mathematics Teaching, 182*(March), 42-44.

Rittle-Johnson, B., & Koedinger, K. R. (2005). Designing Knowledge Scaffolds to Support Mathematical Problem Solving. *Cognition and instruction, 23*(3), 313-349.

Rogoff, B., & Wertsch, J. V. (1984). Children’s learning in the “zone of proximal development”. In B. Rogoff & J. V. Wertsch (Eds.), *Children’s learning in the “zone of proximal development”* (pp. 102). San Francisco: Jossey-Bass.

Romberg, T. A. (1994). Classroom instruction that fosters mathematical thinking and problem solving: Connections between theory and practice. In A. H. Schoenfeld (Ed.), *Mathematicl thinking and solving*. Hillsdale, NJ: Lawrence Erlbaum Associates.

Schoenfeld, A. H. (1994). Reflection on doing and teaching mathematics. In A. Schoenfeld (Ed.), *Mathematical thinking and problem solving* (pp. 53-69). Hillsdale, NJ: lawrence Erlbaum Associates.

Smith, M. S., Bill, V., & Hughes, E. K. (2008). Thinking through a lesson: A key to successfully implementing high-level tasks. *Mathematics Teaching in the Middle School, 14*(3), 132-138.

Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. *Educational Research and Evaluation 2*(October, 1996), 50-80.

Stein, M. K., Lane, S., & Silver, E. A. (1996). *Classrooms in which students successfully acquire mathematical proficiency: What are the critical features of teachers’ instructional practice?* Paper presented at the Annual Meeting of the American Educational Research Association.

Stein, M. K., Smith, M. S., Henningsen, M., & Silver, E. (2000). *Implementing Standards-Based Mathematics Instruction: A casebook for professional development*: Teachers College Press.

Stigler, J. W., & Hiebert, J. (2004). *The Teaching Gap: Best ideas from the world’s teachers for improving education in the classroom*. New York: Free Press.

Sullivan, P., Tobias, S., & McDonough, A. (2006). Perhaps the decision of some students not to engage in learning mathematics in school is deliberate. *Educational Studies in Mathematics, 62*(1), 81-99.

vanZee, E., & Minstrell, J. (1997). Using questioning to guide student thinking. *The Journal of the Learning Science, 6*(2), 227-269.

Vygotsky, L. S. (1978). *Mind in Society: The development of higher psychological processes *Cambridge, MA: Harvard University Press.

**4.**** Communication** between students and teachers is critical for learning.

Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. *American Educational Research Journal, 26*, 499-531.

Cobb, P., Wood, T., Yackel, E., & McNeal, E. (1993). Mathematics as procedural instructions and mathematics as meaningful activity: The reallity of teaching for understanding. In R. B. Davis & C. A. Maher (Eds.), *Schools, mathematics, and the world of reality*. Boston: Allyn & Bacon.

Eggleton, P. J., & Moldavan, C. (2001). The value of mistakes. *Mathematics Teaching in the Middle School, 7*(1), 42-47.

Ellis, A. B. (2007). The influence of reasoning with emergent quantities on students’ generalizations. *Cognition and instruction, 25*(4), 439-478.

Kahan, J. A., & Schoen, H. L. (2009). Visions of problems and problems of vision: Embracing the messiness of mathematics in the world. *Journal for Research in Mathematics Education, 34*(2), 168-178.

O’Connor, M. C., & Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. *Anthropology and Education Quarterly, 24*(4), 318-335.

Sfard, A. (2001). *Learning mathematics as developing a discourse.* Paper presented at the Proceedings of the twenty-third annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Snowbird, UT.

Sherin, M. G. (2002). A balancing act: developing a discourse community in a mathematics classroom. *Journal of Mathematics Teacher Education, 5*, 205-233.

Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, & autonomy in mathematics. *Journal of Mathematical Behavior, 21*, 423-440.

**5.*** Additional References*

Bryk, A., Sebring, P., and Allensworth, E., (2010). *Organizing Schools for Improvement: Lessons from Chicago*, University of Chicago Press.

Kawanaka, T., Stigler, J. W., & Hiebert, J. (Eds.). (1999). *Studying mathematics classrooms in Germany, Japan, and the United States: Lessons from the TIMSS Videotape study*. Philadelphia, PA: Falmer Press.

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). *Adding it up: Helping children learn mathematics*. Washington, D. C.: National Academies Press.

Loucks-Horsley, S., Stiles, K. E., Mundry, S. E., Love, N. B., & Hewson, P. W. (2010). *Designing Professional Development for Teachers of science and mathematics* (3rd ed.). CA: Corwin.

National Commission on Mathematics and Science Teaching for the 21st Century. (2000). *Before It’s too late: A report to the nation from the national commission on mathematics and science teaching for the 21st century*. Washington. D. C.: Department of Education.

National Council of Teachers of Mathematics (NCTM). (1991). *Professional **Standards for Teaching Mathematics*. Reston, VA: NCTM.

National Council of Teachers of Mathematics (NCTM). (2000). *Principles & **Standards for School Mathematics*. Reston: NCTM.

National Council of Teachers of Mathematics (NCTM), & Association of State Supervisors of Mathematics (ASSM). (2005). *Standards and Curriculum: A View from the Nation*. Reston, VA: National Council of Teachers of Mathematics (NCTM)

National Mathematics Advisory Panel. (2008). *Foundations for Success: The final report of the national mathematics advisory panel*. Washington, D. C.: U. S. Department of Education.