Infinite Iterative Processes: The Tennis Ball Problem
| Dublin Core | PKP Metadata Items | Metadata for this Document | |
| 1. | Title | Title of document | Infinite Iterative Processes: The Tennis Ball Problem |
| 2. | Creator | Author's name, affiliation, country | Kirk Weller; University of Michigan - Flint; United States |
| 2. | Creator | Author's name, affiliation, country | Cindy Stenger; University of North Alabama |
| 2. | Creator | Author's name, affiliation, country | Ed Dubinsky; United States |
| 2. | Creator | Author's name, affiliation, country | Draga Vidakovic; Georgia State University; United States |
| 3. | Subject | Discipline(s) | Math Education |
| 3. | Subject | Keyword(s) | infinite iterative processes (26A18), APOS theory (97C50), countable sets (11B99), natural numbers (11B99), student learning and thinking (97C20) |
| 3. | Subject | Subject classification | 97C20 |
| 4. | Description | Abstract | Iterative processes are central to the undergraduate mathematics curriculum. In [4], Brown et al. used a problem situation calling for the coordination of two infinite processes to analyze student difficulties in understanding the difference between the union over k of sets P({1,2,…,k}) (P is the power set operator) and the set P(N) of all subsets of the set of natural numbers. In this paper we study students’ thinking about the Tennis Ball Problem which involves movement of an infinite number of tennis balls among three bins. Here, there are three coordinations of infinite processes. As in [4], our analysis uses APOS Theory to posit a description of mental constructions needed to solve this problem. We then interviewed 15 students working in groups on the problem and we detail the responses of five of them, which represent the full range of comments of all the students. We found that only one student was able to give a mathematically correct solution to the problem. The responses of the successful student indicated that he had made the mental constructions called for in our APOS analysis whereas the others had not. The paper ends with pedagogical suggestions and avenues for future research. |
| 5. | Publisher | Organizing agency, location | JPAM |
| 6. | Contributor | Sponsor(s) | |
| 7. | Date | (YYYY-MM-DD) | 2007-12-14 |
| 8. | Type | Status & genre | Peer-reviewed Article |
| 8. | Type | Type | |
| 9. | Format | File format | |
| 10. | Identifier | Universal Resource Indicator | http://www.ejpam.com/index.php/ejpam/article/view/48 |
| 11. | Source | Journal/conference title; vol., no. (year) | European Journal of Pure and Applied Mathematics; Vol 1, No 1 (2008) |
| 12. | Language | English=en | en |
| 13. | Relation | Supp. Files | |
| 14. | Coverage | Geo-spatial location, chronological period, research sample (gender, age, etc.) | |
| 15. | Rights | Copyright and permissions | Upon acceptance of an article by the journal, the author(s) will be asked to transfer copyright of the article to European Journal of Pure and Applied Mathematics. The Copyright Transfer Agreement, which will be provided by the journal, should be signed by the appropriate person. The transfer of copyright does not take place until the manuscript is accepted for publication. If necessary, authors are responsible for obtaining permissions to reprint previously published figures, tables, and other material. |