A study on learning mathematics from the viewpoint of sense making

从建构主义认识论出发，首先指出在学生与他人一起学习数学的情境中存在着不同层次的意义建构。然后，本研究将重点放在数学知识的意义建构阶段，即问题情境的意义建构与话语的意义建构的互动阶段，并将数学学习视为一种社会文化情境，从意义建构的角度探讨话语对学习者数学学习过程的影响。对部分学习者在数学课堂上的学习过程进行了录像和分析。分析表明，在他们的学习过程中，以下两个过程是相互交织的：学习者将他们理解问题情境的要素放入新的语境中，这些语境是由醚类话语所暗示的;学习者试图根据自己的理解来理解醚类话语。 ...更多信息 在采用数学学习是将数学知识作为文化工具的过程的观点后，进一步分析了这种意义的形成过程。新记录并分析了跨越4至5节课的学习过程。这一分析表明，从上述观点来看，醚类话语对学习过程的影响可以表现为新旧思想融合的混合体的构建。研究还表明，这种混合结构的构建可能伴随着较长的时间滞后，学习者需要意识到自己的意义构建的不可行性，才能迁移到更好地反映他人意义构建的混合结构中。通过对它们的分析，提出了教师在教学中如何将复合思想分离出来，使学习者了解每一个复合思想，并将它们联系起来的可能性。少

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