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.
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Notes
This is the classic approach to deductive reasoning, which is also adopted in this paper. There are also other approaches; the main one is based not on formal rules of inference but on manipulations of mental models representing situations (Johnson-Laird 1999).
When referring to non-mathematical situations the interviewees (of both approaches) did not differentiate among different domains. Instead, they talked in general terms and illustrated their claims with examples, usually from daily life situations. Some interviewees did refer to specific domains, like art, science, literature, and law in order to illustrate a general point. However, these references were not presented as specific to the referred domain. Rather, all examples were treated as instances of general principles, and no comparisons were made among the nature of logical rules in different domains.
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Ayalon, M., Even, R. Deductive reasoning: in the eye of the beholder. Educ Stud Math 69, 235–247 (2008). https://doi.org/10.1007/s10649-008-9136-2
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DOI: https://doi.org/10.1007/s10649-008-9136-2