Connecting Fractions and Decimals

Session Type: Paper Symposium

Abstract

Fractions and decimals are a critical but uniquely difficult topic in children's math learning. A central challenge in learning about fractions and decimals is understanding how they represent magnitudes that can be compared, ordered, and placed on a number line. Whereas much research has investigated children's understandings of fraction and decimal magnitudes separately, this symposium will investigate connections between fraction and decimal magnitude understanding and suggest ways in which such connections could facilitate learning about rational numbers.

Talks 1 and 2 describe longitudinal studies investigating concurrent development of fraction and decimal magnitude understanding. Talk 1 presents evidence that these forms of magnitude understanding share a parallel structure of partial understanding and that both independently predict math achievement. Talk 2 also delineates parallel levels of partial understanding of fraction and decimal magnitudes; within each level, understanding of decimals is superior to understanding of fractions, suggesting that it could be productive to leverage decimal magnitude understanding to help learn about fraction magnitudes.

Talks 3 and 4 explore the concept of cross-notation knowledge of rational numbers, that is, knowledge of relations between fractions and decimals. Talk 3 describes analyses demonstrating that cross-notation knowledge of rational number magnitudes (e.g., knowing that 3/4>0.5) predicts rational number arithmetic skill when controlling for within-notation knowledge (e.g., knowing that 3/4>1/2 or 0.75>0.50). Talk 4 describes a computer-game-based classroom intervention designed to improve cross-notation knowledge; the intervention proved more effective than business-as-usual instruction in a randomized classroom experiment.

Sub Unit

• Cognitive Processes

Chair

• David Braithwaite, Florida State University

Individual Presentations

• Development of Decimal Magnitude Understanding and its Relation with Fraction Magnitude Understanding and Mathematics Achievement - Presenting Author: Ilyse Resnick, University of Canberra; Non-Presenting Author: Luke Rinne, University of Delaware; Non-Presenting Author: Christina Areizaga Barbieri, University of Delaware; Non-Presenting Author: Nancy C Jordan, University of Delaware

• A Longitudinal Study Investigating Natural Number Based Reasoning in Rational Number Tasks - Presenting Author: Jo Van Hoof, Katholieke Universiteit Leuven (KU Leuven); Non-Presenting Author: Tine Degrande, KU Leuven; Non-Presenting Author: Eva Ceulemans, KU Leuven; Non-Presenting Author: Lieven Verschaffel, KU Leuven; Non-Presenting Author: Wim Van Dooren, KU Leuven

• Cross-Notation Knowledge of Rational Numbers Predicts Rational Number Arithmetic - Presenting Author: David Braithwaite, Florida State University; Non-Presenting Author: Jake McMullen, Turun yliopisto (UTU); Non-Presenting Author: Michelle A Hurst, University of Chicago

• Promoting Cross-Notation Rational Number Knowledge - Presenting Author: Jake McMullen, Turun yliopisto (UTU); Non-Presenting Author: Antti Koskinen, Tampere University; Non-Presenting Author: Tomi Kärki, University of Turku; Non-Presenting Author: Saku Määttä, University of Turku; Non-Presenting Author: Antero Lindstedt, Tampere University; Non-Presenting Author: Hilma Halme, University of Turku; Non-Presenting Author: Erno Lehtinen, University of Turku; Non-Presenting Author: Minna M Hannula-Sormunen, University of Turku; Non-Presenting Author: Kristian Kiili, Tampere University