Boundaries in Visualizing Mathematical Behaviour

Autor/in	Hare, Andrew Francis
Titel	Boundaries in Visualizing Mathematical Behaviour
Quelle	In: Collected Essays on Learning and Teaching, 6 (2013), S.60-64 (5 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2368-4526
Schlagwörter	Visualization; Mathematics Education; Mathematical Applications; Mathematical Models; Calculus; Graphs; Teaching Methods; Educational Practices + Suchen Sie Ihr Suchwort? Visualisation; Visualisierung; Mathematische Bildung; Angewandte Mathematik; Innermathematische Anwendung; Mathematical model; Mathematisches Modell; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Grafische Darstellung; Teaching method; Lehrmethode; Unterrichtsmethode; Bildungspraxis
Abstract	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. (As Provided).
Anmerkungen	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
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01