Process of change of teaching practice and children's proportional reasoning by making aware of a knowledge acquisition model

点击翻译按钮获取中文摘要

In this study, through a collaborative effort with a teacher in preparing, implementing, reflecting and revising lessons on ratio and proportion based on a knowledge acquisition model, opportunities were provided for the teacher with thinking about the relationship between teaching of terms, notations, calculations and/or formulas in the textbook on the one hand, and developing pupils' proportional reasoning on the other hand. The purpose of the study is to investigate the thinking process of the teacher when he faced a challenge in making aware of the model in his teaching.In 2003, based on a model of "pupils' internalization and creation of mathematical notations concerning ratio and proportion," we developed lesson plans on three content units : "quantity per unit," "multiplication by decimals," and "division by decimals" collaboratively. During the time that the teacher implemented the lesson plans in the classroom, several people including myself observed the lessons and studied t … More hinking processes and changes of some focused pupils intensively. Results of observation of these pupils were informed to the teacher as early as possible. After every lesson, the teacher reflected on his teaching and made a brief report about notices of pupils' thinking and notations and so on. We also had time for discussion about once in a week.In 2005, the data were summarized and analyses of the teacher and the pupils were made. With respect to the teacher, a jointly-created perspective "transformation of pupils in the classroom" provided a situation of discussion between the researcher and the teacher. At the same time, a proposal of letting the pupils draw figures by the researcher attracted the teacher's attention and contributed to deepening the discussion between us. This act of teaching produced situations in which we can learn about pupils' conceptions of learning mathematics and situations in which we can talk about pupils' transformations more concretely. It also produced situations in which the teacher's conception of mathematics teaching is manifested and reflected. With respect to the pupils, the teacher's attempts of letting the pupils draw figures enhanced their process of internalizing the figures as a tool of thinking and their norms of learning mathematics.One implication of this study for bridging gaps between the model, an outcome of research, and actual teaching practice, is the importance of pedagogical tools that serve to concretize the model in the teaching and bringing out teacher's conceptions for mathematics teaching in the discussion. In this study, to let pupils draw figures was such a tool. Less