The digit-correspondence instructional tasks used in this study are "worthwhile" as defined in the NCTM Professional Teaching Standards (National Council of Teachers of Mathematics, 1991). By presenting a few digit-correspondence tasks in a problem solving mode and allowing students to exchange points of view, teachers may be able to help more students in grades three through five construct an understanding of the meanings of the digits in a multidigit numeral.
In the NCTM's Mathematics for the Young Child, Thompson recommends that teachers use digit-correspondence tasks to interview individual students as a way to diagnose place-value understanding (1990, 106-107). Teachers of older students may find the whole-class, written format described in this study to be a useful alternative.
Understanding place value is important to achieving good number sense, estimating and mental math skills, and to an understanding of multidigit operations. The results of this study contribute to a growing body of evidence that students can construct important mathematical concepts and structures through social interaction and communication with their peers about worthwhile mathematical tasks.
Fuson, K. C., & Smith, S. (April, 1994, ). Supporting Latino First Graders' Ten-Structured Thinking in Urban Classrooms. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans.
Hiebert, J., & Wearne, D. (1992). Links between teaching and learning place value with understanding in first grade. Journal for Research in mathematics Education, 23(2), 98-122.
Kamii, C. (1989). Young Children Continue to Reinvent Arithmetic, Second Grade: Implications of Piaget's theory. New York: Teachers College Press.
Kamii, C., & Lewis, B. (1993). The Harmful Effects of Algorithms in Primary Arithmetic. Teaching Pre K-8, 23(4), 36-38.
Kamii, M. (1982). Children's graphic representation of numerical concepts: a developmental study. Unpublished doctoral dissertation, Harvard University.
National Council of Teachers of Mathematics. (1991). Professional Standards for Teaching Mathematics. Reston, VA: National Council of Teachers of Mathematics.
Ross, S. H. (April, 1986). The Development of Children's Place-Value Numeration Concepts in Grades Two through Five. Paper presented at the Annual Meeting of the American Educational Research Association, San Francisco CA.
Ross, S. H. (1990). Children's acquisition of place-value numeration concepts: The roles of cognitive development and instruction. Focus on Learning Problems in Mathematics, 12(1), 1-17.
Thompson, C. S. (1990). Place value and larger numbers. In J. N. Payne (Ed.), Mathematics for the Young Child, (pp. 89-108). Reston VA: National Council of Teachers of Mathematics.
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