【作 者】：
权国龙，顾小清，姚媛媛， 龚晋瑜
【关 键 词 】：
图解设计；图示应用；数学概念；数学模型；行动研究
【栏 目】：
课程与教学
【中文摘要】：
数学是信息时代学生学习的重要科目，因其抽象性也成为基础教育中的“难点科目”。“解题无思路”是学生数学应用问题解答中遇到的普遍问题。研究试图描绘理论上可行的可视设计：拟象图形与结构图表如何用来帮助学生理解并运用数学概念，进而解答数学应用题目。通过行动研究中的观察与评估，初步发现拟象图形与结构图表在数学应用解答中有一定效力。结构图表可以帮助学习者更好地理清应用情境中事物的关系和量的关系，而拟象图形在还原性技术条件齐备时，可以更好地辅助学习者理解情境和知识概念。研究分析认为，教学中合理的图解设计与运用可以辅助学生对数学知识的理解与掌握，并增强其将之运用于应用问题解答的技能。研究也发现，类化题型与模型化解题，是帮助学生获得并运用数学概念和掌握解题模型图解方法的可行方式。
【英文摘要】：
Mathematics is an important subject for students especially in information age, but it is also a difficult subject in basic education because of its abstractness. "Solving math problems without ideas" is a common problem for many students. This study attempts to depict the visual design like simulation graphics and structure charts, which is theoretically feasible, to help students understand and apply mathematical concepts to solve math problems. Through the observation and evaluation in action research, it is found that the simulation graphics and structure chart are effective in math problem solving. Structure chart helps students understand the relationships between objects and qualitative relations in math problems clearly; imitation graphics can assist students to understand the context and concepts better when technical conditions are ready for use. The study results prove that the reasonable design and application of diagram in teaching can help students understand and grasp mathematical knowledge, and enhance their skills to use them in math problem solving. The study also finds that classified problems and modeling problem solving are feasible ways to help students to obtain and apply mathematical concepts and grasp how to use the problem solving model.