과정-대상 측면에서 본 ‘대수적 사고’ 연구

A study on the algebraic thinking: From the perspective of 'process' and 'object' aspects

In this paper, we deal with the algebraic thinking from the perspective of ‘process’and ‘object’ aspects. Generally, mathematical con-cepts have come from the concrete process. We consider the origin of algebra as the arithmetic calculations. Also, the concept of school arith-metic is beginning from actions or procedures. However, in order to develop the alge- braic thinking and to apply this thinking, we have to see the history of algebraic thinking, and find this duality. Next we investigate various researches relating to the ‘process-object duality’. Theses studies suppose that the concept formation and thinking process should be started from the process-object duality. Finally, we reinterprete many difficulties in algebra - equals sign, vari-ables, algebraic expressions, and linear equations, the principle of permanence of form- from the perspective of the process-object duality.