Abstract
Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs’ interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler’s rules were used in analyzing PSTs’ responses to balance tasks to help determine each PST’s level of abstraction achieved regarding balance, equilibrium, or equivalence. Specifically, the data were analyzed regarding 3 different aspects: (a) the PSTs’ understanding of balance, (b) what previous knowledge was exhibited by the PSTs throughout the enactment of the tasks, and (c) the mathematics utilized by the PSTs as they problem-solved with the virtual balance applet. The results showed PSTs relying on visual cues to implement procedures that were often inappropriate for the task at hand. When confronted with missing value balance tasks, 47 % of the PSTs attempted an incorrect procedure using direct proportions, and some (35 %) employed an incorrect fractional method. One PST systematically solved tasks, where he invented an inverse proportions model. However, most interviewees relied on guess-and-check reasoning. Implications of this study advise the need for purposeful experiences within education programs that lead to better connections across disciplines of big ideas such as balance.
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Appendix
Appendix
Clinical Interview Protocol—Developed by the author, 2009
Name________________________ Date______________
Balance Exploration Using an Interactive Applet
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1.
Where should I add one weight, so the board would be balanced? (note: Weight is shown in the first box and position is shown in the second box. For example, the object in the figure below has a weight of 50 units and a position of 120 units).
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2.
The following board is balanced.
If I move the blue (shown above as dark black) object 30 units to the right, how would I have to move either the red (shown above as light black) or the yellow (shown above as white) object in order to maintain balance?
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3.
The following board is balanced.
If we were to move the blue (shown above as dark black) weight 100 units to the left, how would we need to move one of the other three weights to maintain balance?
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Wilhelm, J., Matteson, S. & She, X. INVESTIGATING PRESERVICE TEACHERS’ UNDERSTANDING OF BALANCE CONCEPTS UTILIZING A CLINICAL INTERVIEW METHOD AND A VIRTUAL TOOL. Int J of Sci and Math Educ 11, 1209–1231 (2013). https://doi.org/10.1007/s10763-012-9371-y
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DOI: https://doi.org/10.1007/s10763-012-9371-y