Construction Scheme of Proof Based on Assimilation and Accommodation Processes: Theorem of Number Theory

Abstract

Number theory is a branch of mathematics that deals with the properties of natural numbers, aimed at finding interesting and unexpected relationships of various types of numbers, then proving that the relationship is true. Problem solutions and proof theorems of number theory often require a strong mathematical background. Weak background, such as: giving examples only applies to definitions not to theorems and lemmas, understanding of the definitions and proven theorems, ways of looking at new theorems built on definitions, and previous theorems, and knowledge of when a definitions or lemma-theorems can be used; enough to affect the ability to solve the problem of number theory. So it is necessary to explore the possibility of other problems in the activity of constructing proof, which in this study uses the framework of the process of assimilation and accommodation, followed by interviews based on student responses. The results obtained are 3 groups of construction schemes, namely: 1) schemes using definitions and theorems, 2) schemes using theorems, and 3) schemes using definitions. Within the three groups there are variations of the problem found that the diantranya occurs is dis-equilibrium in the construction scheme group with theorems and definitions; and group construction schemes by definition only. His advice is to reflect on the ability to understand definitions, theorems and lemmas; and the development of lecture designs that can make the activity of constructing proof into routine activities.