ERIC Number: ED370766
Record Type: RIE
Publication Date: 1993
Reference Count: N/A
Reasoning by Analogy in Constructing Mathematical Ideas.
English, Lyn D.
A powerful way of understanding something new is by analogy with something already known. An analogy is defined as a mapping from one structure, which is already known (the base or source), to another structure that is to be inferred or discovered (the target). The research community has given considerable attention to analogical reasoning in the learning of science and in general problem solving, particularly as it enhances transfer of knowledge structures. Little work, however, has been directed towards its role in children's mathematical learning. This paper examines analogy as a general model of reasoning and discusses its role in several studies of children's mathematical learning. A number of principles for learning by analogy are proposed, including clarity of the source structure, clarity of mappings, conceptual coherence, and applicability to a range of instances. These form the basis for a critical analysis of some commonly used concrete analogs (colored counters, the abacus, money, the number line, and base-ten blocks). The final section of the paper addresses more abstract analogs, namely, established mental models or cognitive representations that serve as the source for the construction of new mathematical ideas. A reference list contains 78 citations. (MKR)
Descriptors: Abstract Reasoning, Analogy, Basic Skills, Cognitive Structures, Constructivism (Learning), Elementary Secondary Education, Foreign Countries, Learning Processes, Manipulative Materials, Mathematical Models, Mathematics Education, Mathematics Skills, Schemata (Cognition), Thinking Skills
Publication Type: Opinion Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Analogue Models