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ERIC Number: EJ1059073
Record Type: Journal
Publication Date: 2013
Pages: 5
Abstractor: As Provided
Reference Count: 9
ISBN: N/A
ISSN: ISSN-2368-4526
Boundaries in Visualizing Mathematical Behaviour
Hare, Andrew Francis
Collected Essays on Learning and Teaching, v6 p60-64 2013
It is surprising to students to learn that a natural combination of simple functions, the function sin(1/x), exhibits behaviour that is a great challenge to visualize. When x is large the function is relatively easy to draw; as x gets smaller the function begins to behave in an increasingly wild manner. The sin(1/x) function can serve as one of their first counterexamples, helping them to better appreciate the tamer functions that they normally encounter. I see three boundaries here. First, a boundary erected by mathematicians between "nice" versus "wild" functions--captured for example by the concept of continuity. Second, a boundary between those functions that are most often studied in calculus and pre-calculus classrooms, and those that are more rarely looked at. Third, the boundary between the drawable and the undrawable. In this example, we can witness this last boundary first-hand even as we attempt to sketch the curve. Yet, we can also continue the visualization in our mind's eye beyond what we can represent on paper.
Society for Teaching and Learning in Higher Education. 1280 Main Street West, Mills Library Room 504, Hamilton, Ontario L8S 4L6, Canada. Tel: 905-525-9140; Web site: http://www.stlhe.ca
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A