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March 2005, Volume 36, Issue 2

FEATURES

Equity in School Mathematics Education: How Can Research Contribute?
NCTM Research Committee
The NCTM Research Committee has prepared this article as a means to raise the awareness about equity and issues surrounding equity from a research perspective as well as to support the NCTM's commitment to the Equity Principle. The committee discusses the concept of equity from three perspectives: as a subject of research, as a "critical lens" with which to examine research, and as a cross-disciplinary theme. Equity issues offer a unique opportunity to unite research and practice within mathematics education and across other disciplines.

Initiating and Eliciting in Teaching: A Reformulation of Telling
Joanne Lobato, David Clarke, Amy Burns Ellis
We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative  consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as pedagogical implications of constructivism. In response, we advance a theoretical reformulation of telling as the set of teaching actions that serve the function  of stimulating students' mathematical thoughts via the introduction of new ideas into a classroom conversation. We reformulate telling in three ways: (a) in terms of the function (which involves attention to the teacher's intention, the nature of the teaching  action, and the students’ interpretations of the action) rather than the form of teachers'  communicative acts; (b) in terms of the conceptual rather than procedural content of the new information; and (c) in terms of its relationship to other actions rather than as an isolated action. This reformulation resolves some of the concerns with teaching as telling and helps establish the legitimacy of providing new information within a constructivist perspective on learning.

Representing Fractions with Standard Notation: A Developmental Analysis
Geoffrey B. Saxe, Edd V. Taylor, Clifton Mcintosh, Maryl Gearhart
This study had two purposes: (a) to investigate the developmental relationship between students' uses of fractions notation and their understandings of part-whole relations; and (b) to produce an analysis of the role of fractions instruction in students' use of  notation to represent parts of an area. Elementary students (n = 384) in 19 classes participated  in the study. Pre- and posttests were administered before and after fractions instruction, and key lessons were recorded with videotape and field notes. Students' written responses were coded in two ways: for the forms of the notations (e.g., use of  numerator, denominator, and separation line), and for the concepts captured by the notations (e.g., part-whole, part-part, or other kinds of relations). The lessons captured on videotapes and in field notes were rated with respect to their alignment with principles  supported by reform frameworks in mathematics education (e.g., opportunity to build understanding of fractions concepts, ongoing assessment of student understanding). Our analyses indicated (a) notation and reference were acquired somewhat independently, and (b) classroom practices that built on students’ thinking were more likely to support shifts toward normative uses of notation.