• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.43-58
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• 2006

An objective of this paper is to discuss the didactical contracts which have been conceptualized by Brousseau. He modelled mathematics instruction as a game. In such game, didactical contracts existed as its own hidden rules which teacher and student should obey Brousseau introduced it to reveal certain hidden rules which regulates mathematics instruction. Those rules are implicit and reciprocal. In particular, it is not revealed until students break. He defined didactical contracts as teacher's behaviour and corresponding students 'behaviour in order to define it operationally. He he did not define it in psychological and epistemological dimension. But it is necessary to discuss teacher's belief system and epistemology, since teacher's behaviour in instruction is affected by them. He also did not discuss fully teacher's breaking of didactical contracts.

• The Mathematical Education
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• v.60 no.4
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• pp.509-527
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• 2021

We investigated whether and how pre-service teachers took the realistic contexts seriously in the course of solving word problems; additionally, we investigated how pre-service teachers evaluated students' realistic and non-realistic answers to word problems. Many pre-service teachers, similar to students, solved some of the realistic problems unrealistically without taking the realistic contexts seriously. Besides, they evaluated students' non-realistic answers higher than the realistic answers. Whether the pre-service teachers could solve problems realistically or not, they did not appreciate students' realistic considerations for the reasons that those were not fitted to the intentions of the word problems, or those were evidence of the flaws of the problem. Furthermore, the analysis of premises implied in the pre-service teachers' evaluation comments showed the implicit didactic contracts about realistic word problem solving that they accepted and also anticipated students to follow. Our analysis of the pre-service teachers' conceptions of realistic word problems can help teacher educators design the teacher program to challenge and revise pre-service teachers' folk pedagogy.