The Role of Regression in the History of Mathematical Induction and Its Didactical Implications

수학적 귀납법의 역사에서 하강법의 역할 및 교수학적 논의

  • Park, Sun-Yong (College of Education, Seoul National University) ;
  • Chang, Hye-Won (Dep. of Math. Education, Chinju National University of Education)
  • Published : 2007.11.30

Abstract

This study begins from posing a problem, 'formal introduction of mathematical induction in school mathematics'. Most students may learn the mathematical induction at the level of instrumental understanding without meaningful understanding about its meaning and structure. To improve this didactical situation, we research on the historical progress of mathematical induction from implicit use in greek mathematics to formalization by Pascal and Fermat. And we identify various types of thinking included in the developmental process: recursion, regression, analytic thinking, synthetic thinking. In special, we focused on the role of regression in mathematical induction, and then from that role we induce the implications for teaching mathematical induction in school mathematics.

Keywords

mathematical induction;infinite recursion;regression;analysis;synthesis