Using Open-Response Fraction Items to Explore the Relationship Between Instructional Modalities and Students’ Solution Strategies

Jessica F. Shumway, Patricia S. Moyer-Packenham, Joseph M. Baker, Arla Westenskow, Katie L. Anderson-Pence, Stephen I. Tucker, Jennifer Boyer-Thurgood, Kerry E. Jordan
540 363


The purpose of this study was to explore the relationship between instructional modality used for teaching fractions and third- and fourth-grade students’ responses and strategies to open-response fraction items. The participants were 155 third-grade and 200 fourth-grade students from 17 public school classrooms. Students within each class were randomly assigned to two instructional treatment groups: a virtual manipulatives representations (VMR) instruction group and a physical manipulatives and textbook representations (PMTR) instruction group. A conversion mixed methods analysis was used to examine quantitative and qualitative data. The quantitative analysis showed achievement outcomes were the same for both groups. The qualitative analysis revealed shifts in learning that were otherwise hidden with solely quantitative achievement results. Specifically, the results indicated VMR group success in understanding fractions as relationships and PMTR group success in maintaining conceptualization of the whole. Overall, the results of this study corroborate previous research indicating the importance of both types of instructional modalities, showing that virtual manipulatives and physical manipulatives are effective instructional tools with positive effects on student learning. The study expands existing research by offering an opportunity to explore the nuances of students’ fractions understanding and provide a window into students’ shifts in fraction learning.

Full Text:



  • There are currently no refbacks.

Copyright (c) 2017 International Journal of Education in Mathematics, Science and Technology


International Journal of Education in Mathematics, Science and Technology (IJEMST) 
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Editors: Mack Shelley & Ismail Sahin

Place of Publication: Turkey & Name of Publisher: Ismail Sahin

ISSN: 2147-611X (Online)