1. Doing mathematics is about making sense of and thinking deeply about fundamental concepts.
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2. Persistence is critical to success in problem-solving and doing mathematics.
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3. Teachers need to establish a classroom culture that develops students’ curiosity and imagination.
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4. Communication between students and teachers is critical for learning.
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Eggleton, P. J., & Moldavan, C. (2001). The value of mistakes. Mathematics Teaching in the Middle School, 7(1), 42-47.
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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.
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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.