Decision making in the mathematical inquiry using technology and guide line for instructional design

在数学调查中使用技术，我们可以观察到更多的数据，我们可以使用更多的策略来解决问题。我们在数学研究中有很多选择；哪些数据是重要的，哪些策略是合适的，我应该如何解释数据和评估解决方案，以及哪种问题的重新表述是合适的。为明确这些原则，为利用技术进行数学调查课堂活动的教学设计提供指导，我们做了以下工作；(1)选取了20个利用技术进行数学调查的案例（主要是动态几何软件几何构造器）；(2)从教师决策的角度对我们的课程进行了两个案例分析；(3)在此基础上，提出了一些应用于数学教育本科和研究生课程的技术数学课程教学设计的指导方针；我们在附属初中设计了新的数学习题。

Using technology in mathematical investigation, we can observe more data, and we can use more strategies to solve the problems. We have many choices in mathematical investigation ; which data is important, which strategy is suitable, how should I interpret data and evaluate a solution, and which re-formulation of problem is suitable. To clarify them and to make guide line to make a instructional design of classroom activity about mathematical investigation using technology, we have done as follows ; (1) we made 20 case studies of mathematical investigations using technology (mainly, dynamic geometry software Geometric Constructor ), (2) we made two case studies of our lesson from viewpoint of teacher's decision making, (3) based on them, we made some guide-line for instructional design of mathematical lesson using technology, which was used in undergraduate and graduate program of mathematics education (4) and based on them, we have designed new mathematical investigations in our attached junior high school.