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This question already has an answer here:

I am in need to find references for my thesis proposal. My topic is "Virtual manipulative versus physical manipulative: which way do students learn faster?".

Do you know any authors that worked on this topic or books about it?

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marked as duplicate by Benjamin Dickman, Joel Reyes Noche, Brendan W. Sullivan, Amy B, yoniLavi Sep 3 '16 at 20:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ What is a cyber manipulative? Do you mean something in the direction of embodied cognition? E.g., Dor Abrahamson (faculty page) does research on embodied design as related to math teaching/learning. Or do you mean math education software more generally? Or do you mean something like a FitBit? Or...? (I know what "physical manipulative" refers to -- e.g., base 10 blocks -- but its prefix is related to hands, and I'm not sure how that transfers to a "cyber" setting...) $\endgroup$ – Benjamin Dickman Aug 17 '16 at 8:59
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    $\begingroup$ Perhaps you mean virtual manipulatives. I've never heard anyone in my school call them cyber manipulatives which might be what @BenjaminDickman and others were asking. Virtual Manipulatives are often used in K-9 with the Smart Board. For example, instead of using actual coins or base 10 blocks (physical manipulatives), the teacher might slide around coins on the smart board to make change or regroup using by moving base 10 blocks on the Smart Board. I suggest you change cyber manipulatives to virtual manipulatives and give examples or links to virtual manipulative sites. $\endgroup$ – Amy B Aug 17 '16 at 19:14
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    $\begingroup$ matheducators.stackexchange.com/questions/10722/… $\endgroup$ – Jessica B Aug 18 '16 at 5:51
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    $\begingroup$ @JoelReyesNoche the age group that I am interested is in grades 8 and 9. And in the Mathematical domain of Geometry. $\endgroup$ – Airen Ercika Soberano Aug 23 '16 at 5:05
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    $\begingroup$ @AirenErcikaSoberano, it seems that you're interested in the same age group and mathematical domain as those in the other question, so I'm voting to close your question as a duplicate. Do not take this as a judgment that your question is "bad;" I am voting to close it to avoid duplication of effort of those answering. $\endgroup$ – Joel Reyes Noche Aug 23 '16 at 6:34
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Here's a piece comparing virtual manipulatives to traditional teaching without manipulatives, in the context of community college remedial courses:

Violeta Menil and Eric Fuchs, "Teaching Pre-Algebra and Algebra Concepts to Community College Students through the Use of Virtual Manipulatives", Improving Undergraduate Mathematics Learning, CUNY Office of Academic Affairs, 2012. (Link)

Statistically significant improvements were found regarding exam performance and student attitude for prealgebra/arithmetic classes. None are found for either in elementary algebra classes.

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