Developing a Model for Describing Aspects of Knowledge in Statistical Inquiry Activity: Based on the Viewpoints of Symbols/Words and Complex System

Abstract

　　 Purpose of this paper is to identify the viewpoints for developing a model which represents aspects of a lot of statistical knowledge of children and to develop the model.   

　　 For this purpose, the author focused on Polanyi’s classification of knowledge in terms on symbols and words (Tacit Knowing・Explicit Knowing) and Hirabayashi’s classification of knowledge in terms on a complex organic system (Method Knowledge・Content Knowledge). 

　　 As a result, the author identified two viewpoints for developing a model: from Tacit Knowing to Explicit Knowing (Problem Solving), from Method Knowledge to Content Knowledge (Problem Posing).  Then, the author developed a matrix model representing aspects of statistical knowledge of children (Fig. 1) through integrating following two classification: Polanyi’s classification of knowing in terms on symbols and words (Tacit Knowing・Explicit Knowing), Hirabayashi’s classification of knowledge in terms on a complex organic system (Method Knowledge・Content Knowledge). At the same time of developing this model, I explained this generality for reasons of Hirabayashi’s mathematical analysis activity: <Vague Unity> → <Analysis> → <Defined Unity>.

Fig.1. A Matrix Model Representing Aspects of Statistical Knowledge of Children