2019 年 43 巻 4 号 p. 333-344
The purpose of this paper was to clarify junior high school student validation processes in solving word problems for simultaneous equations. We proposed and demonstrated new hypotheses through the observation of an 8th-grade mathematics class from the following two viewpoints: validation of real results in solving word problems in mathematical modeling and an implicit requirement for learners referred to as the fictionality of word problems. Fictionality is described as the fact that when learners solve word problems, they cannot avoid constructing nonexistent fictional worlds in their minds from the problems and engage in modeling activities in these fictional worlds. Analyzing the classroom observations, we found that even if learners are aware of the fictionality of a word problem, it is when they obtain mutually exclusive multiple real results that they feel the necessity of validating their results. It is suggested that a condition of word problems as teaching materials for supporting learners’ realization of the necessity of validating their results is that the problems must allow them to generate multiple real models.