Studies of Mathematical Problem Solving Processes by Using Hypermedia

本研究的研究结果如下：(1)将算术应用题的解题过程分解为翻译、整合、计划与监控、执行四个子过程，结果表明，与其他三个子过程相比，整合子过程与算术应用题解题精度的关系最为密切。学生们接受了评估每个子过程的每一项测试。(2)上述类似的实验是使用Macintosh计算机进行的，其程序是用HyperCard编写的。每道字词题都是在Macintosh彩色经典计算机上提出的，它被开发为一道评估四个子过程中的每一个的计算机。结果表明，关系图组的学生在难字题上的成绩优于其他两组(图表组和控制组)的学生。关系图组的学生可以通过Macintosh计算机操作比率的部分和整体之间的关系，从而很容易地建立起应用题的图式。(3)关系图组的学生在没有看到关系图的情况下，能否在同一水平上解决困难的应用题还不清楚。这个问题还需要更多的研究。

The results of this research were as follows :(1) When processes of arithmetic word problem solving are broken down into four subprocesses, translation, integration, planning and monitoring, and execution subprocesses, we showed that an integration subprocess is associated with solution accuracy in arithmetic word problems most closely than other three subprocesses. Students received each test which evaluated each subporcess.(2) A similar experiment stated above was conducted by using a Macintosh computer whose program was written in HyperCard. Each word problem was presented on a Macintosh color classic computer, which was developed as one evaluating each of four subprocesses. The results showed that the students in the relational picture group outperformed the students in the other two groups(the diagram group and the control group) on hard word problems. The students in the relational picture group could easily build schema of word problems by operating the relation between the part and the whole of the ratio via a Macintosh computer.(3) It is not clear whether the students in the relational picture group can solve hard word problems at the same level when they are not presented relational pictures. More research is needed to this issue.