Abstract
The purpose of this study is to investigate characteristics of limit concepts through the simultaneous use of historical and experimental epistemologies. Based on a historical epistemology which is an investigation of historical developments in a mathematical concept raised in the history of mathematics, four different developments of limit concepts were considered. Through an experimental epistemology which is an analysis of students’ different stages in the development of their understanding of the mathematical concept, diverse developmental levels were scrutinized to find out how the students performed. Nine pairs of students in total were recruited and three representatives were presented. Results indicate that both historical and experimental epistemologies are useful methods for teaching mathematics along with the unpacking process and that experimental epistemologies are effective because mathematics learning is continuous.
Highlights
Since the nineteenth century, the concept of limit has been foundational to how calculus and mathematical analysis deal with other notions such as continuity, differentiability, and integration
We analyzed a mathematical structure of limit concepts on the basis of four historical epistemologies
Historically the limit concept has been developed through four different epistemologies: intuitive finitism, infinitism in the context of infinitesimals, infinitism in the context of variables, and actual infinitism
Summary
The concept of limit has been foundational to how calculus and mathematical analysis deal with other notions such as continuity, differentiability, and integration. In the high school curriculum, the concept of infinity is expanded to include differential and integral calculus, the limit definition of a series, the convergence and divergence of infinite series, and the limit and continuity of functions (Hwang et al, 2010; Lee et al, 2010; Lew et al, 2010a, 2010b). A historical epistemology is a structural analysis of the developmental stages of a mathematical concept in the history of mathematics, whereas an experimental epistemology refers to an examination of different developmental levels of students in learning the concept
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
