National Academy of Sciences | 150 Year Anniversary

Questions? Call 800-624-6242

| Items in cart [0]

The National Academies Press

PAPERBACK
price:$34.95
add to cart

Rights & Permissions

topleft topright

Adding It Up: Helping Children Learn Mathematics (2001)
Center for Education (CFE)

Citation Manager

. "8 Developing Mathematical Proficiency Beyond Number." Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

Please select a format:

BibTeX EndNote RefMan


Page
300
bottomleft bottomright

The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy.


Adding + It Up: Helping Children Learn Mathematics

171.  

Tversky and Kahneman, 1974. See Shaughnessy, 1992, pp. 470–473, for a discussion.

172.  

Fey, 1989a, 1989b.

173.  

See, for example, Phillips, Gardella, Kelly, and Stewart, 1994.

References

Acredolo, C., O’Connor, J., Banks, L., & Horobin, K. (1989). Students’ ability to make probability estimates: Skills revealed through application of Anderson’s functional measurement methodology. Student Development, 60, 933–945.

Amir, G.S., & Williams, J.S. (1999). Cultural influences on children’s probabilistic thinking. Journal of Mathematical Behavior, 18, 85–107.

Arcavi, A. (1994). Symbol sense: Informal sense-making in formal mathematics. For the Learning of Mathematics, 14(3), 24–35.

Arzarello, F. (1992). Pre-algebraic problem solving. In J.P.Ponte, J.F.Matos, J.M. Matos, & D.Fernandes (Eds.), Mathematical problem solving and new information technologies (NATO ASI Series, vol. 89, pp. 155–166). Berlin: Springer-Verlag.


Ball, D.L., & Bass, H. (1999, June). What counts as an explanation in math class? Interdisciplinary analysis of teaching. Paper presented at the mathematics education seminar series of the Weizmann Institute of Science, Rehovot, Israel.

Ball, D.L., & Bass, H. (2001). What mathematical knowledge is entailed in teaching children to reason mathematically? In National Research Council, Knowing and learning mathematics for teaching: Proceedings of a workshop (pp. 26–34). Washington, DC: National Academy Press. Available: http://books.nap.edu/catalog/10050.html. [July 10, 2001].

Battista, M.T. (1999). Fifth graders’ enumeration of cubes in 3D arrays: Conceptual progress in an inquiry classroom. Journal for Research in Mathematics Education, 30, 417–448.

Battista, M.T., & Clements, D.H. (1998). Students’ understanding of three-dimensional cube arrays: Findings from a research and curriculum development project. In R. Lehrer & D.Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 227–248). Mahwah, NJ: Erlbaum.

Battista, M.T., Clements, D.H., Arnoff, J., Battista, K., & Van Auken Borrow, C. (1998). Students’ spatial structuring of 2D arrays of squares. Journal for Research in Mathematics Education, 29, 503–532.

Beaton, A.E., Mullis, I.V.S., Martin, M.O., Gonzalez, E.J., Kelly, D.L., & Smith, T.A. (1996). Mathematics achievement in the middle school years: IEA’s Third International Mathematics and Science Study (TIMSS). Chestnut Hill, MA: Boston College, Center for the Study of Testing, Evaluation, and Educational Policy. Available: http:// www.timss.org/timss1995i/MathB.html. [July 10, 2001].

Bednarz, N., Radford, L., & Janvier, B. (1995). Algebra as a problem-solving tool: One unknown or several unknowns? In L.Meira & D.Carraher (Eds.), Proceedings of the nineteenth international conference for the Psychology of Mathematics Education (vol. 3, pp. 160–167). Recife, Brazil: Federal University of Pernambuco. (ERIC Document Reproduction Service No. ED 411 136).

Behr, M., Erlwanger, S., & Nichols, E. (1980). How children view the equal sign. Mathematics Teaching, 92, 13–15.

Page
300