# Talk:Tanyas Links

### From MathWiki

Response to Mordy's post on Liping Ma's research study

“Imagine that one of your students comes to class very excited. She tells you that she has figured out a theory that you never told the class. She explains that she has discovered that as the perimeter of a closed figure increases, the area also increases. She shows you this picture to prove what she is doing: [a 4cm by 4 cm square and a 4cm by 8cm rectangle, with respective perimeters and areas calculated correctly, and “in support” of her claim]. How would you respond to this student?”

Please give this some thought, I will post some of Ma's analysis of the teachers' approaches in a couple of days.

Mordy wrote: I was curious about which software was used for the "computer constructions and explorations" section of the Geometric Structures textbook? Was it just Sketchpad? As well, do the authors give any indication/suggestion as to how to best use "virtual manipulatives" together with real hands-on manipulatives (i.e. equal time allocated to each, or more time with real, less time with virtual)?

Professor Whiteley wrote: "My own experience / general proposal is that the ideal way to use the physical materials in the practice of (my types of) mathematics is to weave back and forth among physical, virtual, and algebraic and not discard any of these as a source of insight and understanding"