A Study on the Algebraic Notations and Algebraic Thinking

대수적 사고와 대수 기호에 관한 고찰

In this paper, we start with the question "what is algebraic thinking\ulcorner". The problem is that the algebraic thinking is not exactly defined. We consider algebraic thinking from the various perspectives. But in the discussion relating to the definition of algebraic thinking, we verify that there is the algebraic notations in the core of algebraic thinking. So we device algebraic notations into the six categories, and investigate these examples from the school mathematics. In order to investigate this relation of algebraic thinking and algebraic notations, we present 'the algebraic thinking process analysis model' from Frege' idea. In this model, there are three components of algebraic notations which interplays; sense, expression, denotapion. Thus many difficulties of algebraic thinking can be explained by this model. We suppose that the difficulty in the algebraic thinking may be caused by the discord of these three components. And through the transformation of conceptual frame, we can explain the dynamics of algebraic thinking. Also, we present examples which show these difficulties and dynamics of algebraic thinking. As a result of these analysis, we conclude that algebraic thinking can be explained through the semiotic aspects of algebraic notations.