Characterizing Different Difficulties with Mathematical Induction in Terms of Proof Reading Comprehension: By Means of a Questionnaire Survey Targeting Nineteen Undergraduate Students

Abstract

　　 The purpose of the study is to consider a framework of proof reading comprehension specific to mathematical induction and to illustrate levels and difficulties of mathematical induction by means of the framework.  There are two main ideas used in this study: the idea of “Mathematical Theorem” posed by Mariotti et al. (1997) and the theoretical model of proof reading comprehension formulated by Yang & Lin (2008) and Mejia-Ramos et al. (2012).  In this study, the author will combine these two theoretical ideas in order to consider a framework of proof reading comprehension specific to mathematical induction.  Data are collected through the nineteen undergraduate students’ writing responses to a set of “scripted  statements and proofs” and “scripted  dialogue”.  As a result, different difficulties are characterized in terms of the three levels: meaning of terms and statements (first level), logical status of statements and proof framework (second level), and justification of claims (third level), in the following ways.  A difficulty at first level can be seen as a presupposition that a given statement is always true.  One of the difficulties found at second level is related to a weak understanding of connections between the statement and its proof.  Lastly, at third level, there is a misunderstanding of the proof of implication statement.  Some implications for further researches and teaching practices are also discussed.