Shaffer and Kaput (1998) wrote that technology has the power to transform the mathematical thinking that is possible in classrooms, giving students new ways of experiencing mathematics as a sense-making activity:
We suggest here that the ability to externalize the manipulation of formal systems changes the very nature of cognitive activity. These changes will have important consequences for mathematics education in coming decades. In particular, we argue that mathematics education in a virtual culture should strive to give students generative fluency to learn varieties of representational systems, provide opportunities to create and modify representational forms, develop skill in making and exploring virtual environments, and emphasize mathematics as a fundamental way of making sense of the world, reserving most exact computation and formal proof for those who will need those specialized skills. (p. 97)
My question is twofold:
- How have you used technology in your classroom in a way that created opportunities for students to reason mathematically?*
- What result, if any, did you note? (For example, did students express insights related to mathematical relationships represented within the technology? Or did you have a memorable interaction related to mathematical reasoning?)
[* Kaput (1992) describes four classes of mathematical activities in school mathematics:
- Syntactically constrained transformations within a particular notation system, with or without reference to any external meanings,
- Translations between notation systems, including the coordination of actions across notation systems,
- Construction and testing of mathematical models, which amount to translation between aspects of situations and sets of notations,
- The consolidation or crystallization of relationships and/or processes into conceptual objects or "cognitive entities" that can then be used in relationships or processes at a higher level of organization. (pp. 524-525)
Technology could play a role in any of these types of activities. I provide them in case they help people to consider what role technology might play with respect to the mathematics in their classrooms.]
Clarification: I'm primarily looking for people to share their personal experiences and impressions. Research you may have been involved with is, of course, also of interest.
Kaput, J. J. (1992). Technology and mathematics education. In D. Gurows (Ed.), Handbook of research on mathematics teaching and learning (pp. 515–556). New York, NY: Macmillan.
Shaffer, D. W., & Kaput, J. J. (1998). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37(2), 97–119.