Annotated Bibliography & NRP

Clarke, D. M. & Roche, A. (2009). Students’ fraction comparison strategies as a window

into robust understanding and possible pointers for instruction. Educational Studies in

Mathematics, 72 (1), 127-138.

This article is written by researchers who conducted a study in an Australian primary school to examine students’ perceptions of fraction size. The researchers used interviews conducted by primary school teachers to gauge students’ understandings and misunderstandings of fraction size by having students describe their strategies for selecting the fraction with the largest value from a pair of fractions. The researchers found that the strategies used successfully by students who appeared to have a more conceptual understanding of the size of fractions weren’t the common strategies used by teachers in the schools. Additionally, students were confused by the use of terms such as “more” and “greater,” missing distinctions between “more pieces” and “greater-sized pieces.” Overall, the researchers found that generalizations students picked up on during instruction on whole numbers were being misapplied to fractions.

This article, while dealing primarily with fractions, is important for educators reviewing comparisons between whole numbers and decimals because the research indicates that children may over-generalize mathematics rules. Additionally, as suggested by the researchers, educators need to put sufficient focus on the meaning of rational numbers rather than devoting all attention toward the manipulations of rational numbers. Without more practice estimating or approximating numbers and without classroom discussions of strategies, students may not gain sufficient understandings of the number system. It is important for pre-service and current teachers alike to realize the importance of allowing students to explore numbers, both whole and otherwise, for numbers sake without only focusing on what can be done with numbers.