Elementary students’ fraction reasoning: a measurement approach to fractions in a dynamic environment

ABSTRACT

In this study, we examine students’ mathematical reasoning within a technological environment designed to support understanding of relationships between quantities with adjustable measuring units. In particular, we provide a cross-sectional snapshot of how 30 elementary students (Grades 3–5) engaged in a series of fraction-as-measurement tasks using a “Dynamic Ruler” that could continuously dilate unit sizes. Screencast recordings were collected from a task-based clinical interview and analyzed to investigate children’s mathematical actions and mathematical ideas. Students’ reasoning patterns were characterized using four distinct types (low attending, holistic estimating, determining, and commeasuring) based on their solution strategies. Findings suggest that the Dynamic Ruler tool can elicit rich conceptions of fractions and even prompt novel approaches such as commeasurement. We conclude by drawing insights into how elementary students might use dynamic technology meaningfully.

KEYWORDS:

• Fraction as measure
• dynamic technology
• instrumental genesis
• semiotic mediation

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research received no specific grant from any funding agency.

Notes on contributors

Sheunghyun Yeo

Sheunghyun Yeo is an Assistant Professor of mathematics education at the University of Alabama in the Department of Curriculum and Instruction. His research examines the development of fractional understanding through the use of dynamic technology, the establishment of dialogic instructions, the enhancement of preservice teacher’s high-leverage teaching practices, and the comparisons of international textbooks. Corey Webel is an Associate Professor at the University of Missouri in the Department of Learning, Teaching, and Curriculum. He typically teaches mathematics courses for prospective elementary teachers and is the director of the Elementary Mathematics Specialist certification program. His research explores how individual and institutional factors can support and inhibit improvements to mathematics teaching, and he is interested in studying how online tools and school structures could be used to facilitate teacher collaboration and learning across contexts.

Twitter: @CoreyWebel