Location of Repository

Students' mental prototypes for functions and graphs

By David Tall and Md. Nor Bakar

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

Topics: LB, QA
Publisher: Taylor & Francis Ltd.
Year: 1992
OAI identifier: oai:wrap.warwick.ac.uk:511

Suggested articles

Preview

Citations

  1. (1983). Concept definition, concept image and the notion of function”, doi
  2. (1988). Concepts and thought”, doi
  3. (1988). Difficulties Students have with the Function Concept”, The Ideas of Algebra,
  4. (1980). Historical and pedagogical aspects of the definition of function”, doi
  5. (1988). Prospective secondary mathematics teachers’ knowledge and understanding about mathematical function, unpublished Ph.D. thesis,
  6. (1982). Some aspects of the function concept in college students and junior high school teachers,
  7. (1985). Supergraph, (software for BBC compatible computers),
  8. (1990). The transition to advanced mathematical thinking: functions, limits, infinity and proof”,
  9. (1988). Understanding the Function Concept: Some Results of Interviews with

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.