整合技术的数学问题解决框架及其应用

A Framework on Mathematical Problem Solving with Technology and Its Applications

信息技术融入数学问题解决是促进信息技术与数学教学深度融合的途径之一.整合技术的数学问题解决框架为此提供了行动指南,它包括3阶段9环节:准备阶段(理解问题含义、抓住关键信息、思考技术功效)、解答阶段(实现问题条件、探索可能结论、制定解题方案、实施解题方案、书写解题过程)和反思阶段(分享解题思维).以上述框架为主线、以符号中介理论与工具化理论为桥梁,采用测试调查、任务式访谈和文档收集等方法收集数据,分析一个中学生使用动态数学软件GeoGebra实现数学问题解决的过程.研究发现:该生在整合技术的数学问题解决过程中充分展示了整合技术的数学流畅性;数学教育技术对于学生是一种心理工具,对于作为研究者的教师是一种起中介作用的人工制品.研究启示:夯实数学基础知识,提高学生数学问题解决能力;开展数学软件培训,提升学生数学教育技术素养;运用动态数学软件,发展学生整合技术的数学流畅性.

Integrating information technology into mathematical problem solving is one way to promote the deep infusion of information technology in mathematics teaching.The framework Mathematical Problem Solving with Technology(MPST)provides an action guide for this purpose and consists of three stages and nine steps:Preparation phase(understand the meaning of the problem,grasp key information,consider technology affordances),solution phase(realize the condition of the problem,explore possible conclusions,plan the solution approach,implement the solution approach,write the solution process),and reflection phase(share the problem-solving thinking).Using the MPST framework as the main basis for the study and the theory of semiotic mediation and instrumentation theory as bridges,numerous data were collected of a secondary school student via test survey,interview survey,and document collection for analyzing the process of mathematical problem solving using GeoGebra.The research results showed that the student’s techno-mathematical fluency was fully embodied in the process of mathematical problem solving with technology;in addition,technology in mathematics education is an instrument for students and a mediating artifact for teachers as researchers.The research implications include the following:tamping basic mathematical knowledge to promote students’problem-solving ability,launching mathematical software training to improve students’literacy in technology in mathematics education,and applying dynamic mathematical software to develop students’techno-mathematical fluency.