Studies of Mathematical Problem Solving Processes by Using Hypermedia

研究结果表明：(1)将算术字词问题求解过程分解为翻译、整合、计划与监控和执行四个子过程，发现整合子过程与算术字词问题求解精度的关系最为密切。学生们接受了评估每个子过程的每个测试。(2)用一台用HyperCard编写程序的Macintosh计算机进行了上述类似的实验。每个字问题都是在麦金塔经典彩色计算机上呈现的，这台计算机被开发成一个评估四个子过程中的每一个的问题。结果表明，关系图片组的学生在难题上的表现优于其他两组（图表组和对照组）的学生。关系图组的学生可以通过Macintosh计算机操作比例的部分和整体之间的关系，很容易地构建字词问题的图式。(3)关系图片组的学生在不呈现关系图片的情况下，是否能够解决相同水平的难词问题尚不清楚。这个问题需要更多的研究。

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.