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Additional Readings

Baek, J. (1998). Children’s invented algorithms for multidigit multiplication problems. In L. J. Morrow (Ed.), The teaching and learning of algorithms in school mathematics (pp. 151-160). Reston, VA: National Council of Teachers of Mathematics.

Behrend, J. L. (2001). Are rules interfering with children’s mathematical understanding? Teaching Children Mathematics, 8(1), 36-40.

Campbell, P. F., Rowan, T. E., & Suarez, A. R. (1998). What criteria for student-invented algorithms? In L. J. Morrow (Ed.), The teaching and learning of algorithms in school mathematics (pp. 49-55). Reston, VA: National Council of Teachers of Mathematics.

Carroll, W. M., & Porter, D. (1997). Invented strategies can develop meaningful mathematical procedures. Teaching Children Mathematics, 3, 370-374.

Chambers, D. (1996). Direct modeling and invented procedures: Building on students’ informal strategies. Teaching Children Mathematics, 3, 92-95.

Creative Publications. (1996). Smart arithmetic [video]. Mountain View, CA: Author.

de Groot, C., & Whalen, T. (2006). Longing for division. Teaching Children Mathematics, 12(8), 410-418.

Heuser, D. (2005). Teaching without telling: computational fluency and understanding through invention. Teaching Children Mathematics, 11(8), 404-412.

Hope, J. A., Leutzinger, L. P., Reys, B. J., & Reys, R. E. (1988). Mental math in the primary grades. Palo Alto, CA: Dale Seymour.

Hope, J. A., Reys, B. J., & Reys, R. E. (1987). Mental math in the middle grades. Palo Alto, CA: Dale Seymour.

Hope, J. A., Reys, B. J., & Reys, R. E. (1988). Mental math in the junior high school. Palo Alto, CA: Dale Seymour.

Kamii, C. (1994). Young children continue to reinvent arithmetic: 3rd grade. New York: Teachers College Press.

Kamii, C., & Dominick, A. (1997). To teach or not to teach algorithms. Journal of Mathematical Behavior, 16, 51-61.

Kamii, C., & Lewis, B. A. (1993). The harmful effects of algorithms in primary arithmetic. Teaching K-8, 23(5), 36-38.

Kouba, V. L., & Wearne, D. (2000). Whole number properties and operations. In E. A. Silver, & P. A. Kenney (Eds.), Results from the seventh mathematics assessment of the National Assessment of Educational Progress (pp. 141-162). Reston, VA: National Council of Teachers of Mathematics.

Li, Y., & Silver, E. (2000). Can younger students succeed where older students fail? An examination of third graders’ solutions of a division-with-remainder (DWR) problem. Journal of Mathematical Behavior, 9, 233-246.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.

Randolph, T. D., & Sherman, H. J. (2001). Alternative algorithms: Increasing options, reducing errors. Teaching Children Mathematics, 7(8), 480-484.

Reys, B. J. (1991). Developing number sense in the middle grades: Addenda series, grades 5-8. Reston, VA: National Council of Teachers of Mathematics.

Reys, B. J., & Reys, R. E. (1998). Computation in the elementary curriculum: Shifting the emphasis. Teaching Children Mathematics, 5, 236-241.

Schifter, D., Bastable, V., & Russell, S. J. (1999a). Developing mathematical understanding: Numbers and operations, Part 1, Building a system of tens (Casebook). Parsippany, NJ: Dale Seymour Publications.

Schneider, S. B., & Thompson, C. S. (2000). Incredible equations develop incredible number sense. Teaching Children Mathematics, 7, 146-148, 165-168.

Skinner, P. (1999). It all adds up! Engaging 8-to-12-year-olds in math investigations. Sausalito, CA: Math Solutions Publications.

Trafton, P. R., & Hartman, C. L. (1997). Developing number sense and computational strategies in problem-centered classrooms. Teaching Children Mathematics, 4, 230-233.

Wickett, M. & Burns, M. (2001). Teaching arithmetic: Lessons for extending multiplication, grades 4-5. Sausalito, CA: Math Solutions Publications.

Whitenack, J.W., Knipping, N, Novinger, S., & Underwood, G. (2001). Second graders circumvent addition on subtraction difficulties. Teaching Children Mathematics, 8,228-232.






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