Visualized Case Design Of Mathematical Thinking

With the development of science and technology, the research of visualized teaching are increasingly concerned. In the field of mathematics, visualized teaching are gaining more and more attention, but look at mathematical visualization research, research on the visualization of mathematical thought are rare. They play an important role in mathematical knowledge, which reflect the nature and essence of mathematics. However, mathematical thought have highly abstraction and complexity, they are not easy for teachers to explain and students are also difficult to understand. Based on this, the visualization of mathematical thought is very necessary and important. The main purpose of this study is to make use of information technology to achieve visualization of mathematical thought cases, in order to better highlight the teaching in primary mathematics, thus we can experience the convenience of mathematical thought visualization.In this paper, the research combine literature analysis with design method, from the point of visualization, basis to curriculum standards, through search relevant literature, understand the status of mathematical thought visualization, explore the value and significance of achieving mathematical thought visualization. Next, the author makes a definition of related concepts about mathematical thought visualization, discusses from Intuitive Teaching Theory, Audio-visual Teaching Theory and Constructivist Teaching Theory, analyzes the characteristics of mathematical thought visualization. Then, the author introduces two types of mathematical thinking visualization tools: general visualization tool—Flash and professional mathematical visualization tool—Geometer’s Sketchpad. Meanwhile, with visualization tools, the author explores general process to achieve mathematical thinking visualization: select mathematical thinking, clear visualization tools and case design. So the author designs three cases. One case is limit thinking which make use of "Liu Hui’ cyclotomic method" and design flash animation to achieve graphical representation. Another case is about the thought of combination of numeral and form that can learn from "the discovery of irrational numbers 2and π" and design teaching plan included dynamic process. The last one is mathematical modeling thought which is connected with practical application of trigonometric model by the use of Geometer’s Sketchpad or graphing calculator. At the same time, the author discussed the benefits of mathematical thought visualization. Finally, the author Make a conclusion and put forward some suggestions.