What makes an explanation a good explanation? : adult learners' criteria for acceptance of a good explanation

Roberts, Rosemary (1999) What makes an explanation a good explanation? : adult learners' criteria for acceptance of a good explanation. Masters thesis, Memorial University of Newfoundland.

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Abstract

The problem that students have perceiving a need for proof is well-known to high school teachers and has been identified by researchers as a major problem in the teaching of proof. My research addresses the problem of teaching of proof, especially the role of proof as explanations for students. My study builds on Hoyles' (1997) and Reid's (1995a) studies to explore what qualities make an explanation a good explanation for the student. -- Through a questionnaire, classroom observations, and interviews with students and their teachers I researched the kinds of explanations students prefer, what constitutes a good explanation for students and teachers, and whether or not students mirror teachers' explanations or if they have their own style of explaining. -- Both quantitative and qualitative research methods were employed to collect and report the findings. A student questionnaire, set in two domains of mathematics, geometry and arithmetic/algebra, comprised the quantitative part of the study. To help determine the kind of explanation preferred the questionnaire offered deductive, inductive and analogical explanations. The student questionnaire was administered to adult learners who were enrolled in the trades, technician, business, applied arts, and Adult Basic Education (ABE) programs at the College of the North Atlantic, Happy Valley-Goose Bay campus. -- Interviews, participant observations and document analysis comprised the qualitative pan of the study. Person-to-person, semi-structured interviews were conducted with eight adult learners enrolled in the ABE program at the same college. The two ABE mathematics instructors also participated in the person-to-person interviews. Both students and their instructors were observed within their classroom setting. The interviews and observations helped to determine students' preference for a particular kind of explanation, what qualities make an explanation a good explanation for the student and for the teacher and whether or not students mirror teacher explanations. Document analysis involved an intense literature review of proof, proving, and the different purposes proving serves. -- Students showed an overall preference for multiple example explanation and analogical explanation. It was the form of the explanation, namely its familiarity and accessibility, that students used as criteria for acceptance. The logical structure of an explanation was what the teacher used as criteria for acceptance. Conforming to teacher expectations was seen as a motivation for proving in the classes observed.

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