Representing Fractions with Standard Notation: A Developmental Analysis

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.