The University of Montana
Department of Mathematical Sciences

Technical report #18/2010

Conjecturing via reconceived classical analogy

Kyeonghwa Lee, Seoul National University, Korea
Bharath Sriraman, The University of Montana

Abstract

Reasoning and conjecturing by analogy is a fundamental human trait. One encounters excellent examples of this propensity to “analogize” in ancient Greek philosophy. If an ancient Greek philosopher were asked: why do we create analogies? The answer would simply be to create a framework by which we could better understand the dimensions of human experience (Sriraman, 2005). An important finding of English (2004) was that teachers must understand analogies themselves and know how to use them effectively (and also know which analogies are appropriate and which aren’t when it come to their use). They sometimes have to make the relationships explicit for the child. The OCA framework we have developed through reflective discourse practices by the teacher Seo, illustrate that analogies arising in mathematics are quite different from those arising in a discipline such as the life sciences where spontaneous analogies work well because children have a much larger a priori linguistic base, whereas in mathematics children’s pre-existing knowledge base is limited. This necessitates that both practitioners and researchers are sensitive to the major role that the knowledge base plays in the use of analogies for mathematics learning. The present study makes an important contribution for following this line of mathematical thinking initiated by the likes Newton, Euler and Polya. Further research is needed on a more typical classroom-type group of students. Another limitation relates to the limited content area. The focus of this paper was a triangle. Further studies involving a variety of OCA problems in different content areas are encouraged to verify the possibility of including OCA in mathematics learning. Finally, it will be necessary to not only identify but also clarify the kinds of norms or teaching interventions essential for effective integration of OCA into mathematics lessons.

Keywords: Analogical reasoning; Lakatos; Conjecturing; Classical Analogy; OCA framework

AMS Subject Classification: 97

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