Deductive reasoning: in the eye of the beholder

Abstract

This study examines ways of approaching deductive reasoning of people involved in mathematics education and/or logic. The data source includes 21 individual semi-structured interviews. The data analysis reveals two different approaches. One approach refers to deductive reasoning as a systematic step-by-step manner for solving problems, both in mathematics and in other domains. The other approach emphasizes formal logic as the essence of the deductive inference, distinguishing between mathematics and other domains in the usability of deductive reasoning. The findings are interpreted in light of theory and practice.

Using Different Questioning Strategies in High School English Literature and Mathematics Classes

“…On the other hand, mathematics as a discipline is bound by rules and concepts as well as a limited range of problemsolving procedures that focus mainly on the achievement -the answers; it"s believed to be based on deductive and logical reasoning, as noted by Ayalon and Even [38],deductive reasoning is a mathematical thinking synonym, with no room for creation. Therefore, a convergent questioning strategy seems appropriate to a limited extent; it might als o be reasonable to remark that the nature of mathematical tasks demands mastery of both convergent and divergent thinking.…”

Monitoring and Guiding Pupils' Problem Solving

“…This is a process of inferring conclusions from the known information (premises) based on formal logic rules, whereby the conclusions are necessarily derived from the given information, and there is no need to validate them by experiments (Ayalon & Even, 2008). Although there are also other accepted forms of mathematical proving, a deductive proof is still considered as the preferred tool in the mathematics community for verifying mathematical statements and showing their universality (Hanna, 1990;Mariotti, 2006;Yackel & Hanna, 2003).…”

Mathematics Educators’ Views on the Role of Mathematics Learning in Developing Deductive Reasoning

“…In a previous study (Ayalon & Even, 2008), we examined approaches of people involved in mathematics education to the use of deductive reasoning in and outside of mathematics. This group consisted of mathematics teachers at various levels (from secondary school teachers to research mathematicians who teach undergraduate or graduate university mathematics), curriculum developers, teacher educators of prospective and practicing mathematics teachers, and researchers in mathematics education.…”

“…And how do people with different approaches to deductive reasoning and to the usability of deductive reasoning outside mathematics view the role of learning mathematics in the development of deductive reasoning? This study builds on the data and the findings from a previous study (Ayalon & Even, 2008) mentioned above that investigated approaches of mathematics educators to deductive reasoning and to its usability inside and outside mathematics. In this paper, we focus on these mathematics educators' views regarding the role of mathematics learning in developing deductive reasoning.…”

“…The 21 interviewees participating in this study were the same people who participated in the previous study (Ayalon & Even, 2008). Most of them (17) belonged to different sub-communities in the field of mathematics education.…”