2023 Volume 47 Issue 3 Pages 281-289
Expectation is one of the most important concepts in learning probability. The purpose of this paper is to construct a process of conceptualization of expectation. The theoretical framework is a process of conceptualization based on negation theory. As a result, the process of conceptualization of expectation is developed as follows: [1] to recognize that the simple average may produce an average that is insufficient to be considered balanced; [2] to reconsider as expectation a model that does not assume that the certainty of each value is equal; [3] the simple average is, for example, “a model that does not consider the difference in certainty of each value” and “cannot be applied to situations where the certainty of each value is different”; [4] to recognize that the expectation may not allow selection taking into account variables (e.g., the amount of money won). In addition, we analyzed five Japanese high school mathematics A textbooks from the viewpoint of the process of forming the process of conceptualization of expectation that we constructed. We derived four issues in teaching expectation and proposed problems and activities to overcome them.
