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January 2004, Volume 35, Issue 1

FEATURES

Mathematical Discourse in Shared Storybook Reading
Ann Anderson, Jim Anderson, Jon Shapiro
The purpose of the study reported in this article was to explore the mathematical discourse in which four dyads engaged while sharing the storybook One Snowy Night (Butterworth, 1989) while at home or in other locations (e.g., day care centers). Each dyad consisted of a mother and her four-year-old child. Various discourse patterns were evident, and while there were commonalities across dyads, each pair shared the book in unique ways. In two of the dyads, the mother initiated the mathematical discourse; in the other two, the child did. Size, subitizing, and counting were the most common mathematical concepts that emerged. One dyad attended to a single concept  of size, and the other dyads attended to more than one mathematical idea. Some parents scaffolded particular   problem-solving strategies; others provided more generic support. Based on our findings, we discuss insights and issues and make suggestions for further research.

Metaphor and Numerical Diagrams in the Arithmetical Activity of a Fourth-Grade Class
Adalira Sáenz-Ludlow
Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of splitting an object into parts and the mental action of splitting a number into units. Such a resemblance, evoked by the word split as used by the students, can be considered to be a metaphor in the Peircean theory of signs. This spontaneous metaphor mediated students' constructions of numerical strategies. Students communicated such strategies through different signs like numerical diagrams, verbal numerical arguments, and other idiosyncratic arithmetical notations. Students presented the same   solution strategy using signs in different semiotic systems and translated signs in one system into signs of another system. Students' arithmetical activity indicated a shift from an instrumental understanding of basic arithmetic to a relational understanding mediated by their symbolic initiative. The article contains an analysis of the collective construction of this metaphor and its role in mediating the semiotic and arithmetical activity of the students.

Statistical Significance, Effect Size Reporting, and Confidence Intervals: Best Reporting Strategies
Robert M. Capraro
A Forum for Researchers Statistical Significance, Effect Size Reporting, and Confidence Intervals: Best Reporting Strategies Robert M. Capraro, Texas A&M University.