• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.59-74
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• 2015

It is an increasing research area to explore mathematics learning from discursive perspectives. However, there have been little studies conducted on why and how discursive perspectives in mathematics learning were adopted and developed. Especially, not much discussion has been done on the later Wittgenstein's philosophical stance in terms of the relationship between language and thought as a background of discursive approach to learning mathematics. This study aims to explore the later Wittgenstein on language to get better understanding about discursive approaches to mathematics learning. For the attainment of this aim, first the later philosophy is compared with the former philosophy in depth. Then the later philosophy is discussed focusing on how his point of view on the world and the language have been changed. After providing an account of his later philosophy, it is clarified that what is discursive approaches to learning mathematics and how this philosophy brace the approaches. This research concludes with implications and limitations, as well as suggestions for future researches.

• School Mathematics
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• v.18 no.1
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• pp.193-214
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• 2016

Teachers' questioning plays an important role in mathematics teaching and learning by asking students to react or to participate in mathematical discourse. Previous studies on teachers' questioning have not focused on how to questioning to formulate an effective mathematical discourse which is contributed by students because studies mostly analyzed and categorized teachers' questions according to cognitive levels of questions without consideration of context. Therefore, this study explored characteristics of teachers' questioning to formulate an effective characteristics of teachers' questioning to formulate an effective mathematical discourse in mathematics classrooms. By reviewing and analyzing mathematics discourse and studies on teachers' questioning theoretically, we presented openness, sharedness, and productivity as characteristics of teachers' questioning. Through a middle school mathematics teacher's case, we examined three characteristics were necessary to formulate an effective mathematical discourse. Based on results from theoretical analysis and case analysis, we discussed that openness, sharedness, and productivity would be useful as a framework to analyze teachers' questioning.