数学教育における推論主義の可能性 ― 学力調査で求められる実践的知識としての統計的概念に関する批判的考察 ―

抄録

　　This study examines the applicability of inferentialism to mathematics education in Japan.  Inferentialism, which R. Brandom originally proposed in pure philosophy and J. Derry introduced to educational contexts, has been applied to mathematics education, and especially in statistics education.  In this paper, we identified four characteristics of Derry’s inferentialism: 1) it denies representationalism, namely, conceptual platonism; 2) it entails that understanding a concept is defined as possessing practical know-how for making inferences and that a process of making knowledge explicit is interpreted as a process of conceptualization; 3) it is assumed that using a concept requires us to understand many other concepts from a holistic perspective; 4) judgements in learning environments are considered important opportunities for learning.  We then drew two findings from these characteristics: 1) inferentialism is highly consistent with mathematics education research in Japan, which focuses on know-how in learning environments; 2) we should value not only mathematical (context-free) concepts but also context-specific concepts in both research and practice.  

　　Considering these findings, we analyzed the ski jump problem from the 2012 National Assessment of Academic Ability, a well-known statistical word problem.  We found that the problem lacked information necessary for determining a unique optimal solution.  Our findings imply that teachers should consider how we treat non-statistical concepts in statistical word problems and how we teach statistical activities.  As a future research task, we propose to contrast inferentialism with existing epistemologies in mathematics education such as constructivism or the theory of commognition.