Deductive Reasoning in Mathematics Education

Matematiksel Muhakeme Üzerine 2007-2021 Yılları Arasında Türkiye’de Yapılan Lisansüstü Tezlerin İncelenmesi

“…It was also a very interesting result that there was no thesis written for the aim of examining deductive reasoning. It is thought that this situation may have caused deductive reasoning to be taken as synonymous with proving (Harel and Weber, 2020) in the literature.…”

“…However, as stated in the section where the results obtained regarding the aims of the theses were discussed, it was a striking result that a thesis focusing on deductive reasoning was not reached in the examined theses. As mentioned above, the reason of this situation was deductive reasoning and proof were equated (Harel and Weber, 2020). In addition, considering the importance in mathematics education, the lack of a thesis focusing on analogical and abductive reasoning was another remarkable result.…”

Styles of reasoning for mathematics education

“…Not surprisingly, different forms of reasoning play a central part in mathematics education research. A search for the term "reasoning" in Lerman's (2020) most recent 916-pages long Encyclopedia of Mathematics Education, which I assume to present contemporary and influential theories in the discipline, yields entries on "deductive reasoning" (Harel & Weber, 2020), "mathematical proof, argumentation, and reasoning" (Hanna, 2020), and "quasi-empirical reasoning" (Sriraman & Mousoulides, 2020), as well as further mentions of more than 30 other forms of reasoning, including algebraic reasoning, diagrammatic reasoning, functional reasoning, geometric reasoning, inductive reasoning, mathematical reasoning, multiplicative reasoning, scientific reasoning, and statistical reasoning. 2 Although we find "mathematical reasoning" alone mentioned in 28 of the 216 entries of the Encyclopedia, it remains unclear what is meant by the term.…”

“…These Encyclopedia entries share a formalist position in the philosophy of mathematics, where mathematical objects are conceived of as sign games and proofs do not produce "truth" (in a realist sense) but merely "deducibility". For example, Harel and Weber (2020) reported that "contemporary mathematicians view axiom systems as being a freestanding system of relationships between undefined terms" (p. 185, my emphases), and Umland and Sriraman (2020) stated that, in mathematics, "the validity of an argument in its final form is judged solely on whether it is logically consistent" (p. 61, my emphases).…”

The Proof Schemes of Preservice Middle School Mathematics Teachers and Investigating the Expressions Revealing These Schemes

“…Bu ispat şemalarını sergileyen öğrencilerin aslını anlama ve diğerlerini ikna etme durumları dışsal kaynaklıdır. Bu kaynaklar öğretmen ya da bir kitaba dayanan bir otorite (otoriter ispat şeması), bir argümanın biçimi ya da görünümü (alışkanlık edinilmiş ispat şeması) veya sembollerin anlamsız manipülasyonu (sembolik ispat şeması) olarak ortaya çıkabilir (Harel, 2014;.…”