Software‐based intervention with digital manipulatives to support student conceptual understandings of fractions
Authors: Bush Jeffrey B. 
Published: July 2021

Rational number and fractions concepts are inherently difficult; and lack of mastery often holds students back from success in subsequent mathematics courses. This paper describes design characteristics of a software based, adaptive, rational number tutor with virtual manipulatives, realistic contexts, and procedural feedback. Then, the paper presents findings from a randomized crossover trial designed to evaluate the impact of the described intervention on student fraction achievement. The trial was conducted in two districts in two states with 17 elementary school teachers and 297 4th and 5th grade students. Half of the participating classrooms replaced worksheet practice time (over 10 instructional hours) with Woot Math Adaptive Learning (WMAL), a digital tutor that incorporates dynamic digital manipulatives, video tutorials and automatic feedback to students and teachers. After 10 instructional hours the groups switched conditions for another 10 instructional hours so each student would have exposure to the treatment and control conditions. Analysis shows that regardless of treatment order, student performance gains on assessment items (mostly from NAEP and TIMMS) were statistically higher, (d = 0.39, F(1,589) = 5.73, p < 0.05), after 10 days of instruction with WMAL than they were after 10 days of business‐as‐usual instruction. This difference of 0.39 standard units corresponds to an improvement index of 10.9 (percentile point gain compared to non‐treatment). The results demonstrate how the described approach to software and instructional design can work together to support significant increases in student achievement in rational number domains by combining best practices in feedback, curricular design, and adaptive instructional sequences.

Practitioner notes

What is already known about this topic?

Fraction difficulties are common and compound into greater math difficulties and math anxiety.

Best practices for teaching fractions include the use of manipulatives and a focus on conceptual understanding. Feedback should focus on both the process of learning and the products that students produce.

Adaptive software systems have the potential to support student practice but there are limited studies in authentic classroom environments with comparable control groups.

Other adaptive systems have not implemented best practices in adaptability, design for feedback and curricular design.

What this paper adds?

Describes a software‐based intervention designed with best practices in curricular design for student development of conceptual understanding of fractions.

Describes adaptive features of the software intervention for pacing and automated feedback on both student responses and their work.

Reports on a randomised crossover study to evaluate the effectiveness of this intervention as compared to business‐as‐usual instructional methods for student practice time.

Implications for practice and/or policy?

Provides evidence to support curricular materials that use manipulatives and are designed to promote conceptual understanding in addition to procedural fluency.

Describes how technology can efficiently scale best practices and support teachers in helping students make sense of fractions.

Reports on how classroom technology can support and extend teaching through personalised learning and improved feedback used during independent practice time.