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ERIC Number: EJ1059073
Record Type: Journal
Publication Date: 2013
Pages: 5
Abstractor: As Provided
Reference Count: 9
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A