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Are there any existing research on the effectiveness of computer simulation and/or interactive visualization for the learning of mathematical concepts?

I ask because:

  1. There has been some efforts in developing "virtual laboratories" in the physical sciences and part of the justification is that virtual laboratories are better than no laboratories: this is especially the case for things like environmental sciences where it may not always be possible to travel to a destination with the right sort of environment.

    By extension one may expect there to be certain benefits derived from giving students "hands-on" access to mathematical/geometric objects. But is there any research that actually qualifies/quantifies the benefit?

  2. I've seen lots of people pushing the use of things like Desmos: one of the great things I like about it is that the graphs can interactively depend on adjustable parameters. Intuitively I would say that these kinds of models with visual feedback are more effective than simply a graph drawn on a black board. But is this supported by research evidence?

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This is not a knowledgeable answer, just one citation, perhaps not the most relevant (as it is a decade old):

Rösken, Bettina, and Katrin Rolka. "A picture is worth a 1000 words–The role of visualization in mathematics learning." Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education. Vol. 4. 2006. (PDF download.)

I mention this primarily because (a) it reviews related work, and (b) because of this interesting quote in its conclusion:

These aspects highlight the ambivalence of visualization as Tall (1994, p. 37) points out: “It is this quality of using images without being enslaved by them which gives the professional mathematician an advantage but can cause so much difficulty for the learner.”

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