Nancy Anderson, EdD

Mathematics Teacher ~ Author ~ Consultant

Ball, D.L., Thames, M.H. & Phelps, G. (2008). Content knowledge for teaching: What makes it special? *Journal of Teacher Education*, 59(5), 389-407.

Baroody, A. (2006). Why children have difficulties mastering the basic number combinations and how to help them. *Teaching Children Mathematics*, 13, 22-31.

Berger, W. (2016). *A more beautiful question*. London, UK: Bloomsbury.

Boaler, J. Youcubed at Stanford University. www.youcubed.org. Stanford University.

Boaler, J. (2016). *Mathematical mindsets*. San Francisco, CA: Jossey-Bass.

Bransford, J.D., Brown, A.L. & Cocking, R.R. (Eds.). (2000). *How people learn: Brain, mind, experience, and school* (expanded ed.). Washington, DC: National Academy Press.

Brown, P.C., Roediger, H.L., & McDaniel, M.A. (2014). *Make it stick*. Cambridge, MA: The Belknap Press of Harvard University.

Burton, L. (1999). The practices of mathematicians: What do they tell us about coming to know mathematics? *Educational Studies in Mathematics*, 37, 121-143.

Carey, B. (2015). *How we learn*. New York, NY: Random House.

Carpenter, T.P., Fennema, E., Franke, M.L., Levi, L.W., & Empson, S.B. (1999). *Children’s mathematics: Cognitively guided instruction*. Portsmouth, NH: Heinemann.

Chapin, S.H. & Johnson, A. (2006). *Math matters* (2nd ed.). Sausalito, CA: Math Solutions.

Chapin, S., O’Connor, C., & Anderson, N. (2009). *Talk moves: A teacher’s guide for using talk moves to support the Common Core and more* (3rd ed.). Sausalito, CA: Math Solutions.

Chapin, S. & O’Connor, C. (2004). Project Challenge: Identifying and developing talent in mathematics within low-income urban schools. Boston, MA: Boston University.

Chi, M.T.H. & Bassok, M. (1989). Learning from examples via self-explanations. In L.B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 251-282). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Cobb, P., Wood, T. Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B. & Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education, 22, 3-29.

Fennema, E., Carpenter, T.P., Franke, M.L., Levi, L., Jacobs, V.R. & Empson, S.B. (1996). A longitudinal study of learning to use children’s thinking in mathematics instruction. Journal for Research in Mathematics Education, 27, 4, 403—434.

Franke, M.L., Webb, N., Chan, A.G., Ing, M., Freund, D. & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60, 380-392.

Fuson, K. (2003). Toward computational fluency in multidigit multiplication and division. Teaching Children Mathematics, 9, 300-305.

Gray, E., & Tall, D. (1994). Duality, ambiguity, and flexibility: A “proceptual” view of simple arithmetic. Journal for Research in Mathematics Education, 25(2), 116-140.

Hattie, J. & Yates, G. (2014). *Visible learning and the science of how we learn*. London: Routledge.

Hembree, R. & Dessart, D. (1986). Effect of hand-held calculators in precollege mathematics education: A meta-analysis. *Journal for Research in Mathematics Education*, *17*, 83-99.

Hiebert, J. & Carpenter, T. (2007). Learning and teaching with understanding. In F. Lester, Jr. (Ed.), *Second handbook of research on mathematics teaching and learning*. Reston, VA: National Council of Teachers of Mathematics.

Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A. & Human, P. (1997). *Making sense*. Portsmouth, NH: Heinemann.

Hill, H., Rowan, B. & Ball, D.L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. *American Educational Research Journal*, 42(2), 371-406.

Hill, H.C., Blank, M.L., Charalambous, C.Y., Lewis, J.M., Phelps, G. C., Sleep, L. & Ball, D.L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. *Cognition and Instruction*, 26, 430-511.

Kieran, C. (2008). Learning and teaching algebra at the middle school through college levels: building meaning for symbols and their manipulation. In F.K. Lester, Jr. (Ed.), *Second handbook of research on mathematics teaching and learning*, pps. 707 – 762. Reston, VA: NCTM.

Kilpatrick, J., Swafford, J., & Findell, B. (Eds.) (2001). *Adding it up*. Washington, D.C.: National Academy Press.

Kling, G. & Bay-Williams, J. (2014). Assessing basic fact fluency. *Teaching Children Mathematics*, 8, 489-497.

Moser, J., Schroder, H., Heeter, C., Moran, T., and Lee, Y. (2011). Mind your errors: Evidence for a neural mechanism linking growth mind-set to adaptive posterror adjustments, *Psychological Science*, *22*, 1484-1489.

National Council of Teachers of Mathematics (NCTM). (2006). *Curriculum Focal Points for Prekindergarten through grade 8 mathematics: A quest for coherence*. Reston, VA: NCTM.

Otto, A.D., Caldwell, J.H., Lubinski, C.A., Hancock, S.W. (2011). *Developing essential understanding of multiplication and division, grades 3-5*. Reston, VA: NCTM.

Renkl, A. (2002). Worked-out examples: instructional explanations support learning by self-explanations. *Learning and Instruction*, 12, 529-556.

Schmidt, W., Houang, R., & Cogan, L., “A coherent curriculum: The case of mathematics,” *American Educator*, Summer 2002, 1-18.

Schwartz, K. (November 21, 2016). *What Neuroscience Can Tell Us About Making Fractions Stick*. Retrieved from www.kqed.org.

Sfard, A. (2008). *Thinking as communicating: Human development, the growth of discourses, and mathematizing*. Cambridge: Cambridge University Press.

Star, J.R. (2005). Reconceptualizing procedural knowledge. *Journal for Research in Mathematics Education*, *36*(*5*), 404-411.

Stein, M.K., Grover, B.W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. *American Educational Research Journal*, 3, 455-488.

Stigler, J. & Hiebert, J. (1999). *The teaching gap*. New York, NY: The Free Press.

Tugend, A. (2011). *Better by mistake*. New York, NY: Riverhead Books.

Usiskin, Zalman. “Why Elementary Algebra Can, Should, and Must Be an Eighth-Grade Course for Average Students.” In *Algebraic Thinking, Grades K – 12*, edited by Barbara Moses, pp. 40 – 48. Reston, Va.: National Council of Teachers of Mathematics, 1999.

von Glaserfeld, E. (1995). A constructivist approach to teaching. In *Constructivism in education*. Steffe, L.P. & Gale, J. (Eds.). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.

Webb, N.W. (1991). Task-related verbal interaction and mathematics learning in small groups. *Journal for Research in Mathematics Education*, 22(5), 366-389.

Webb, N.M. & Mastergeorge, A.M. (2003). The development of students’ helping behavior and learning in peer-directed small groups. *Cognition and Instruction*, 21, 361-428.Wu, H. (2007). Fractions, decimals, and rational numbers. University of California, Department of Mathematics. Retrieved on October 14, 2015 from http://math.berkely.edu/~wu.

Webb, N.M., Troper, J.D. & Fall, R. (1995). Constructive activity and learning in collaborative small groups. *Journal of Educational Psychology*, 87, 406-423.