In response to the need for studies that focus on learning and writing in mathematics, this study examined changes in students' probabilistic thinking and writing during an instructional program that emphasized transactional writing in a problem-solving context. Although correlations between probabilistic thinking and writing levels at the end of the study were not significant, students did make significant gains in both probability reasoning and writing. Analysis of target students' journals revealed that their writing incorporated both writing symbols and mathematical symbols. These symbols were more complementary for those students whose writing increased to the higher levels during instruction. Moreover, this growth appeared to be promoted by the teacher herself, who systematically sought verbal explanations of solutions and written interpretations of diagrams and numerical patterns.
Get full access to this article
View all access options for this article.
References
1.
Abel, J.
, & Abel, F. (1988). Writing in the mathematics classroom. Clearing House, 62, 155-158.
2.
Acredolo, C.
, O'Connor, J., Banks, L., & Horobin, K. (1989). Children's ability to make probability estimates: Skills revealed through application of Anderson's functional measurement methodology. Child Development, 60, 933-945.
3.
Allen, B.
(1991). Using writing to promote students' metacognition in mathematics. Paper presented at the 14th Annual Conference of the Mathematics Education Research Group of Australasia, Perth, Australia.
4.
Azzolino, A.
(1990). Writing as a tool for teaching mathematics: The silent revolution. In T. J. Cooney, & C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990's (pp. 92-100). Reston, VA: National Council of Teachers of Mathematics.
5.
Biggs, J. B.
, & Collis K. F. (1991). Multimodal learning and the quality of intelligent behavior. In H.A.H. Rowe (Ed.), Intelligence: Reconceptualization and measurement (pp. 57-76). Hillsdale, NJ: Lawrence Erlbaum.
6.
Bogdan, R. C.
, & Biklen, S. K. (1992). Qualitative research for education: An introduction to theory and methods. Boston: Allyn and Bacon.
7.
Britton, J.
(1970). Language and learning. London: Allen Lane.
8.
Britton, J.
, Burgess, T., Martin, N., McLeod, A., & Rosen, H. (1975). The development of writing abilities. New York: Macmillan.
9.
Brown, J. S.
, Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning, Educational Researcher, 18, 32-42.
10.
Bruner, J. S.
(1964). The course of cognitive growth, American Psychologist, 19, 1-15.
11.
Case, R.
(1985). Cognitive development. San Diego, CA: Academic Press.
12.
Clarke, D. J.
, Waywood, A., & Stephens, M. (1993). Probing the structure of mathematical writing. Education Studies in Mathematics, 25, 235-250.
13.
Clements, M. A.
(1984). Terence Tao. Educational Studies in Mathematics, 15, 213-238.
14.
Connolly, P.
(1989). Writing and the ecology of learning. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 1-14). New York: Teachers College Press.
15.
Drake, B. M.
, & Amspaugh, L. B. (1994). What writing reveals in mathematics. Focus on Learning Problems in Mathematics, 16(3), 43-50.
16.
English, L.
(1993). Children's strategies for solving two- and three-stage combinatorial problems. Journal for Research in Mathematics Education, 24, 255-273.
17.
Falk, R.
(1983). Children's choice behavior in probabilistic situations. In D. R. Grey, P. Holmes, V. Barnett, & G. M. Constable (Eds.), Proceedings of the First International Conference on Teaching Statistics, Volume II (pp. 714-716). Sheffield, England: University of Sheffield.
18.
Fischbein, E.
, Nello, M. S., & Marino, M. S. (1991). Factors affecting probabilistic judgments in children in adolescence. Educational Studies in Mathematics, 22, 523-549.
19.
Freedman, S. W.
(1995). Crossing the bridge to practice. Written Communication, 12(1), 74-92.
20.
Jones, G. A.
, & Thornton, C. A. (1993). Vygotsky revisited: Nurturing young children's understanding of number. Focus on Learning Problems in Mathematics, 15(2&3), 18-28.
21.
Jones, G. A.
, Langrall, C. W., Thornton, C. A., & Mogill, A. T. (1997). A framework for assessing young children's thinking in probability. Educational Studies in Mathematics, 32, 101-125.
22.
Jones, G. A.
, Thornton, C. A., Langrall, C. W., & Mogill, A. T. (1996). Using children's probabilistic thinking to inform instruction. In L. Puig & A. Guitierrez, (Eds.), Proceedings of the 20th Conference of the International Group for the Psychology of Mathematics Education, 3 (pp. 137-144). Valencia, Spain: University of Valencia.
23.
Keith, S.
(1989) Exploring mathematics in writing. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 132-146). New York: Teachers College Press.
24.
Layzer, D.
(1989). The synergy between writing and mathematics. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 122-133). New York: Teachers College Press.
25.
Miles, M. B.
, & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (3d ed.). Thousand Oaks, CA: Sage.
26.
Piaget, J.
, & Inhelder, B. (1975). The origin of the idea of chance in children. (L. Leake, Jr., P. Burrell, & H. D. Fischbein, Trans.). New York: Norton.
27.
Shepard, R. G.
(1993). Writing for conceptual development in mathematics. Journal of Mathematical Behavior, 12, 287-293.
28.
Shuell, T. J.
(1990). Phases of meaningful learning. Review of Educational Research, 60, 531-547.
29.
Siegel, S.
, & Castellan, N. J., Jr. (1988). Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill.
30.
Starr, A.
(1994). Writing to learn while learning to write. Teaching English in the Two-Year College, 21, 134-135.
31.
Tarr, J. E.
, & Jones, G. A. (1997). A framework for assessing middle school students' thinking in conditional probability and independence. Mathematics Education Research Journal, 9, 39-59.
32.
Tobias, S.
(1989). Writing to learn science and mathematics. In P. Connolly, & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 48-55). New York: Teachers College Press.
33.
Van Zoest, L. R.
, & Walker, R. K. (1997). Racing to understand probability. Mathematics Teaching in the Middle School, 3, 162-170.
34.
Vygotsky, L. S.
(1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
35.
Waywood, A.
(1994). Informal writing-to-learn as a dimension of a student profile. Educational Studies in Mathematics, 27, 321-340.
36.
Yerushalmy, M.
(1997). Mathematizing verbal descriptions of situations: A language to support modeling. Cognition and Instruction, 15, 207-264.
