| "visualization" made its first appearance as a professional term in February,1987 when the National Science Foundation convened a symposium. With the development of computer technology, visualization has attracted the attention of lots of researchers in Mathematics Education, especially at present when computer technology to a large extent makes visual display possible. Mathematical Visualization can be understood as: representing the abstract mathematical learning objects (abstract principles, symbolic representation, structural relations, thinking, etc.) in visible and clear form of presentation, such as graphics, images, animation and so on, thus to enable people to have a visual, intuitive and overall understanding of those objects. "Mathematical Visualization" has been a hotspot of education research on mathematics, and it has also been one of the study subjects in International Group for the Psychology of Mathematics Education (PME) in recent sessions.A look at those Mathematical Visualization researches both at home and abroad indicates that visual teaching have been paid more and more attention to in education field and its role has been fully affirmed. The researches on visual teaching in mathematics were directed mainly at areas of higher mathematics, but seldom in Elementary or Secondary Mathematics.The researchers at home and abroad also analyzed the problems of mathematical visualization in teaching, they found the difficulties mainly came from social, cognitive and cultural challenges. However, such issues as how to overcome the difficulties of visual teaching, and what conditions would make mathematics visual teaching better, were not analyzed or explored in depth. This paper proposed five principles on how to design the content of visualization teaching, based on the analysis of cognitive load theory, combining with the practice of mathematics teaching. They are:1) chunking principle-to promote in-depth learning; 2) spatial and temporal contiguity principle-to reduce split-attention; 3)consistency principle-to avoid redundancy effects; 4)double-channel principle-to expend working memory capacity; 5)signal principle-to enhance selective attention. On this basis, this paper re-designs the current teaching materials, conducting an empirical study of mathematical visualization in teaching which adopts the simple linear programming as the carriers and is carried on in a senior middle school in Long You County, Zhejiang Province. Two classes of grade one with 86 students in total have been selected. Students at similar level in these two classes are then matched according to the average of their scores of mid-term exam and monthly exams, and also by combining with their teacher's identification. After such adjustments,70 students were finally chosen for further data-collection, including 20 students in high-level group,30 students in middle-level group, and 20 students in low-level group. Then, a case study of visualteaching on linear function is conducted, taking three low-achievement students of grade eight in Nan Yuan School in Jinhua, Zhejiang Province as experimental subjects. The two empirical studies above make a deeper exploration from some sides on how to make use of multimedia technology to realize the visualization of the abstract principle, symbolic representation, structural relations, thinking, etc. At the same time, the two empirical studies partly verify the five principles mentioned above.Finally, conclusions are drawn on the basis of teaching practice and relevant experiments:compared with the traditional mathematics teaching, visual teaching, which based on the optimized visual teaching content, significantly reduces students'cognitive load in the learning process and markedly improves students'mathematics learning effects. Being subject to the limited research time, methods and sample size, these conclusions still need further verification.
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