Abstract
In this article, we suggest an instructional intervention to help students understand statements involving multiple quantifiers in logical contexts. We analyze students' misinterpretations of multiple quantifiers related to the ε-N definition of convergence and point out that they result from a lack of understanding of the significance of the order of the quantifiers in the definition. We introduce the Mayan activity which is designed to cause and then to help resolve students' cognitive dissonance. In particular, the Mayan stonecutter story in the activity is presented in an understandable and colloquial form so that students can recognize the independence of ε from N in the ε-N definition. Consequently, the Mayan activity can be regarded as a useful instructional intervention to study statements related to the ε-N definition of convergence.
| Original language | English |
|---|---|
| Pages (from-to) | 685-698 |
| Number of pages | 14 |
| Journal | PRIMUS |
| Volume | 21 |
| Issue number | 8 |
| DOIs | |
| State | Published - Nov 2011 |
Bibliographical note
Funding Information:The first author was supported by the National Science Foundation under grant #0837443. The authors thank Sigrid Wagner for her helpful comments on an earlier version of this article.
Keywords
- Mayan activity
- Multiple quantification
- cognitive dissonance
- instructional intervention
- ε-N definition