Abstract
Abstract: Nowadays, mathematical reasoning and making proof have taken importance for all students from the grade level of elementary education to university. More specifically, mathematical induction (MI) is a kind of proof and reasoning strategy taking place nearly all grade levels. Moreover, teachers are important factors affecting student learning and they can acquire necessary knowledge and skills developmentally in their teacher education programs. This paper makes contributions to domain of research by investigating the development of PMT’s conception of MI in the context of written argumentations encouraging MI. In other words, the purpose of this multiple case study is to explore how PMT’s conception of mathematical induction develop through their written argumentations. These cases show that there exist improvements in PMT’s written argumentations, conception of MI and proof construction activities related to MI. In other words, the more organized and structured they produced written argumentation, the more successfully they use and make mathematical induction.
Highlights
There exist many research examining the relationship between the teaching and learning of proof and justification of people in mathematics education in different contexts such as by argumentation (Krummheuer, 2000; Yackel, Cobb, & Wood, 1991; Zack & Graves, 2001), by conception of proof (Harel & Sowder, 1998) and by the construction of proofs (e.g., Weber, 2001; Martin & McCrone, 2003; Weber & Alcock, 2004), there are limited research examining mathematical induction (MI) as a strategy of reasoning and proof especially for basic mathematics concepts (Stylianides, Stylianides, & Philippou, 2007)
This paper explains the written argumentation schemes, conceptions of MI of preservice mathematics teachers (PMTs) through engaging in proof construction activities related to MI proof strategy and presents evidence of a developmental process of these skills with treatments in teacher education programs
It was found that the PMTs solved the proof construction problems in this stage by considering proof writing that they did in previous lessons or looking the solutions of similar solved problems
Summary
There exist many research examining the relationship between the teaching and learning of proof and justification of people in mathematics education in different contexts such as by argumentation (Krummheuer, 2000; Yackel, Cobb, & Wood, 1991; Zack & Graves, 2001), by conception of proof (Harel & Sowder, 1998) and by the construction of proofs (e.g., Weber, 2001; Martin & McCrone, 2003; Weber & Alcock, 2004), there are limited research examining mathematical induction (MI) as a strategy of reasoning and proof especially for basic mathematics concepts (Stylianides, Stylianides, & Philippou, 2007). The skills related to teaching and learning proof, writing argumentation and forming the conception of proof can be developed efficiently with the help of the lessons designed and implemented effectively by providing necessary knowledge, it is needed to investigate developmentally. With this motivation, this paper explains the written argumentation schemes, conceptions of MI of preservice mathematics teachers (PMTs) through engaging in proof construction activities related to MI proof strategy and presents evidence of a developmental process of these skills with treatments in teacher education programs.
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