A Feature of Mathematical Values in Selecting a Solution

Abstract

As mathematics was developed by people, the nature of mathematics is assumed to be important to the human development process. In this study, “mathematical values” means the value a person assigns to the nature of mathematics in evaluating it. Research identifies the nature of mathematics having been assigned mathematical values by people, and mathematical values are described in the literature. However, the context in which a person assigns mathematical values to the nature of mathematics need to be explored because what should be assigned a mathematical value depends on the context. Therefore, this study aims to reveal the features of mathematical values within such a context. This study focuses on evaluating the multiplicity of ideas. A problem of counting marbles was set with four different solutions to capture mathematical values; 45 pre-service teachers were asked to select which solution had mathematical values and to give an account of the reasons for their selection. As a result, there were different contexts for evaluating the mathematical character of a solution. This indicates that the contexts of mathematical values are not necessarily the same, even if mathematical values are assigned to the same nature of mathematics. The context needs to be explored more closely.