Design And Implementation Of Mathematical Activities Promoting Understanding

Under the new idea of curriculum reform, there are all kinds of mathematical activities emerging in the mathematics classroom: Mathematical research-based learning, mathematical inquiry-based learning, and mathematical task-based learning and so on. In this thesis, the autor focus on not only theory but also practice on these kinds of mathematical activities. On one hand side, basing on literature review on "mathematics understanding" and "Teaching and learning for understanding", the author analyzed the goal and the key ingredients of mathematical activities promoting understanding. On the other hand side, deriving from practices, the author summarized the strategies on how to design and implementate mathematical activities develop students' mathematical understanding.The goal of mathematical activities promoting understanding is to help students construct sound cognitive structure of mathematical knowledge and obtain the abilities to use the mathematical knowledge flexibly.Mathematical activities promoting understanding contains three key ingredients: worthwhile mathematical tasks, flexible scaffold, and effective communication and reflection. Thereinto, worthwhile mathematical tasks are the foundation of mathematical activities promoting understanding; flexible scaffold is the bridge between students and mathematical activities; effective communication and reflection are the important guarantee to develop students' mathematical understanding in the activities.Deriving from practices, we got some strategies on how to design andimplement mathematical activities to develop students' mathematical understanding:1) Using mind manager to manage self-knowledge and analyze activity tasks can help teacher design worthwhile mathematical tasks.2) Use demonstrations, dialogue, and worksheet to scaffold students' thinking and performing so that the students are engaged in the mathematical activities.3) Creating safe environment and developing in-depth mathematical communication so that the students are engaged in the effective communication and reflection.