ERIC EJ1059073: Boundaries in Visualizing Mathematical Behaviour pdf

ERIC EJ1059073: Boundaries in Visualizing Mathematical Behaviour

More Book Details

Description of the Book:

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

• Creator/s: ERIC
• Date: 2013
• Year: 2013
• Book Topics/Themes: ERIC Archive, Visualization, Mathematics Education, Mathematical Applications, Mathematical Models, Calculus, Graphs, Teaching Methods, Educational Practices, Hare, Andrew Francis

An excerpt captured from the PDF book