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From Concrete Representations to Abstract Symbols |
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Abstract:
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We report on students who were introduced to standard combinatorial notation after they had already investigated concepts in combinatorics using their own representations. We show what strategies these students used to make sense of the notation and how they used this notation to expand and generalize their understanding of counting problems. |
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Association:
Name: North American Chapter of the International Group for the Psychology of Mathematics Education
URL: http://www.pmena.org
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Citation:
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MLA Citation:
| Uptegrove, Elizabeth. and Maher, Carolyn. "From Concrete Representations to Abstract Symbols" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada, Oct 21, 2004 <Not Available>. 2009-05-26 <http://www.allacademic.com/meta/p117569_index.html> |
APA Citation:
| Uptegrove, E. B. and Maher, C. A. , 2004-10-21 "From Concrete Representations to Abstract Symbols" Paper presented at the annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Delta Chelsea Hotel, Toronto, Ontario, Canada Online <.PDF>. 2009-05-26 from http://www.allacademic.com/meta/p117569_index.html |
Publication Type: Conference Paper/Unpublished Manuscript
Review Method: Peer Reviewed
Abstract: We report on students who were introduced to standard combinatorial notation after they had already investigated concepts in combinatorics using their own representations. We show what strategies these students used to make sense of the notation and how they used this notation to expand and generalize their understanding of counting problems. |
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| Document Type: |
.PDF |
| Page count: |
7 |
| Word count: |
3578 |
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| FROM CONCRETE REPRESENTATIONS TO ABSTRACT SYMBOLS Elizabeth B. Uptegrove and Carolyn A. Maher Rutgers University uptegrov@eden.rutgers.edu and cmaher@rci.rutgers.edu We report on the transition from personal representation to formal notation for a group of five students from a community of students engaged in doing mathematics for several years. The group was introduced to standard combinatorial notation after they had already investigated concepts in counting using personal representations that they built over several years. We describe the strategies used by the |
| East Anglia. Maher C. A. & Martino A. M. (1996). The development of the idea of Mathematical proof: A 5-year case study. Journal for Research in Mathematics Education 27 194-214. Muter E. M. & Maher C. A. (1999). Recognizing isomorphism and building proof: Revisiting earlier ideas. In Proceedings of the Twentieth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 20) (Vol. 2 pp. 461-467). Raleigh NC: North Carolina State |
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