Use of Virtual Manipulatives in Developing Grade Six Students' Proportional Reasoning Skills

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Blessing, Stephen Wayne
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Middle Tennessee State University
The lack of development of proportional reasoning skills has long been recognized in the literature as a mathematical topic needing specific attention. Also, several studies demonstrated the use of virtual manipulatives as an effective tool in the development of certain mathematical concepts; however, few researchers have pursued the application of virtual manipulatives to develop proportional reasoning skills. This study aimed to determine the impact of the use of virtual manipulatives on the development of proportional reasoning in grade six students, focusing upon the potential effect of gender, technology-input modality, and interaction effect between these two factors.
Two virtual manipulatives, Thinking Blocks and Number Pieces, were included as part of a mixed-method approach incorporating a convergent parallel design. During a ten-day period, a group of 56 participants completed a pre-test/post-test instrument measuring proportional reasoning, including a survey to determine touchscreen experience and preference of modality; in addition, five performance tasks involving proportional reasoning were completed at regular intervals. Finally, a group of six target students were observed during the data-gathering process as they worked during class time, being interviewed individually as they completed two additional tasks before and after instruction.
Findings from this research revealed participants who used Thinking Blocks and Number Pieces made greater gains on the post-test when compared to the participants who did not; however, these gains did not demonstrate statistical significance. No statistical significance was found in the performance of participants with respect to gender or technology-input modality; also, the researcher noted no interaction effect between gender and technology-input modality.
Participants demonstrated growth as shown on the work generated from the first task to the fifth, but performance levels fluctuated from one task to another. Participants tended to revert to an additive approach when encountering a non-integral value in a proportional setting. All six target students used an additive approach when completing the pre-instruction interview task. However, the use of academic vocabulary and informal expressions of proportional reasoning concepts exhibited during the post-instruction interviews by the four target students who used Thinking Blocks and Number Pieces provided additional support for the premise of virtual manipulatives as effective tools to develop proportional reasoning skills.
Block Modeling strategy, Proportional Reasoning, Proportional tasks, Virtual Manipulatives