In this article, we focus on a group of 39 prospective elementary (grades K-6) teachers who had rich experiences with proof, and we examine their ability to construct proofs and evaluate their own constructions. We claim that the combined “construction–evaluation” activity helps illuminate certain aspects of prospective teachers’ and presumably other individuals’ understanding of proof that tend to defy scrutiny when individuals are asked to evaluate given arguments. For example, some prospective teachers in our study provided empirical arguments to mathematical statements, while being aware that their constructions were invalid. Thus, although these constructions considered alone could have been taken as evidence of an empirical conception of proof, the additional consideration of prospective teachers’ evaluations of their own constructions overruled this interpretation and suggested a good understanding of the distinction between proofs and empirical arguments. We offer a possible account of our findings, and we discuss implications for research and instruction.
- Sharing some thoughts about the process of settling down in Ann Arbor. #Sabbatical fulbright.no/grantee-experi… 2 months ago
- RT @velonews: Time trials can be a snooze, but the elite men’s ITT championship race was quite the opposite. velonews.com/2017/09/news/b… 2 months ago
- RT @UMichFootball: It’s GAME DAY! And we’re back home! #GoBlue https://t.co/2D0LrxW26l 3 months ago
- RT @UMichFootball: Tomorrow, the Wolverines return to The Big House. “You get chills.” #GoBlue https://t.co/syU3YHTUxn 3 months ago
- RT @SpringerEdu: Special Issue from ZDM! Digital Curricula in Mathematics Education. Interested? Check this out link.springer.com/journal/11858/… htt… 3 months ago