비례 추론 관점에서 비례배분 형식화 과정 분석

Abstract

The aim of this study is to offer suggestions to improve proportional reasoning ability for teaching and learning proportional distribution and to derive the proportional distribution formalization process on the perspective of proportional reasoning, and analyze the formalization process on the perspective of teaching mathematical expressions. In other to attain these purposes, we have established a framework that can analyze the proportional distribution formalization process on multiple-batches perspective and variable-parts perspective, which is the perspective of proportional reasoning, four proportional distribution formalization types(MU, MB, VN, VS) was derived through theoretical consideration. In the light of such theoretical consideration and analytical results of the derived formalization process on the perspective of teaching mathematical expressions, this study provided suggestions for teaching the proportional distribution as follows: The importance of clear recognition of the ‘ratio term’, which shows (whole), 1st formalizing process is division and 2nd process are connected with multiplication, the importance of understanding the meaning of division quotient in solving the proportional distribution problem, and various perceptions of the ‘ratio term’ indicating (part) and (whole). Importance of 1st objectification and a progressive disentanglement(2nd objectification), and the possibility of using the general expressions, which is the result of proportional distribution formalization and the commutative property of multiplication that can be found during comparative analysis by type, the need for teaching that strengthens the connectivity of proportional distribution and division.