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Students' mental prototypes for functions and graphs
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Tall, David and Bakar, Md. Nor (1992) Students' mental prototypes for functions and graphs. International Journal of Mathematical Education in Science and Technology, Vol.23 (No.1). pp. 39-50. doi:10.1080/0020739920230105 ISSN 0020-739X.
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Official URL: http://dx.doi.org/10.1080/0020739920230105
Abstract
This research study investigates the concept of function developed by students studying English A-level mathematics. It shows that, while students may be able to use functions in their practical mathematics, their grasp of the theoretical nature of the function concept may be tenuous and inconsistent. The hypothesis is that students develop prototypes for the function concept in much the same way as they develop prototypes for concepts in everyday life. The definition of the function concept, though given in the curriculum, is not stressed and proves to be inoperative, with their understanding of the concept reliant on properties of familiar prototype examples: those having regular shaped graphs, such as x2 or sin*, those often encountered (possibly erroneously), such as a circle, those in which y is defined as an explicit formula in x, and so on. Investigations reveal significant misconceptions. For example, threequarters of a sample of students starting a university mathematics course considered that a constant function was not a function in either its graphical or algebraic forms, and threequarters thought that a circle is a function. This reveals a wide gulf between the concepts as perceived to be taught and as actually learned by the students.
| Item Type: | Journal Article | ||||
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| Subjects: | L Education > LB Theory and practice of education Q Science > QA Mathematics |
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| Divisions: | Faculty of Social Sciences > Institute of Education ( -2013) | ||||
| Library of Congress Subject Headings (LCSH): | Mathematics -- Study and teaching, Functions | ||||
| Journal or Publication Title: | International Journal of Mathematical Education in Science and Technology | ||||
| Publisher: | Taylor & Francis Ltd. | ||||
| ISSN: | 0020-739X | ||||
| Official Date: | 1992 | ||||
| Dates: |
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| Volume: | Vol.23 | ||||
| Number: | No.1 | ||||
| Page Range: | pp. 39-50 | ||||
| DOI: | 10.1080/0020739920230105 | ||||
| Status: | Peer Reviewed | ||||
| Access rights to Published version: | Open Access (Creative Commons) |
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