A study on learning mathematics from the viewpoint of sense making

点击翻译按钮获取中文摘要

Starting from the constructivist epistemology, it was first noted that there are various levels of sense-making in the settings where students learn mathematics with others. Then the focus of this research was laid upon the following : the phase where making-sense of mathematical knowledge is developing through interactions between making-sense of problem situations and making-sense of ethers' utterances.Then, seeing learning mathematics as a kind of socio-cultural settings, it was investigated how ethers' utterances influence learning processes of learners from the viewpoint of sense-making. Learning processes of some learners in mathematics classrooms were video recorded and were analyzed. The analysis showed that the following two processes were intermingled in their learning processes : learners put the elements of their making-sense of problem situations into new contexts that were suggested by ethers' utterances ; learners tried to make sense of ethers' utterances based on their … More making-sense of the problem situations.Such a kind of sense-making processes was further analyzed, after adopting the viewpoint that learning mathematics is a process of appropriating mathematical knowledge as cultural tools. Learning processes that extended across 4 to 5 lessons were newly recorded and analyzed. This analysis demonstrated that from the above-mentioned viewpoint, the influence of ethers' utterances upon learning processes can take the form of construction of hybrids where old and new ideas are inosculated. It also showed that this construction of hybrids can be accompanied by long time-lag and that learners need to realize the in viability of their sense-making in order to transfer to hybrids which reflect others' sense-making better.Taking account of such features of sense-making, learning processes extending across one unit were analyzed. Through the analysis of them, it was presented as a possible useful supports by teachers to separate compounding ideas and make learners aware of each of ideas and relate them. Less