A Cross-Cultural Research on the Influence of the Teacher of Problem-Solving

“解决问题”是日本和美国数学教育中最重要的主题。了解学生解决问题的策略和困难是提高学校数学问题解决教学的必要条件。这些策略和困难似乎受到一些文化因素的很大影响，如语言、日常生活方式等。这一跨文化研究的结果如下：(1)这里使用的困难和问题类型与两国的典型问题不同。我们试图分析学生的数学思想和策略，而不是成绩。这些变化发生在学生发现模式的过程中，随着他们在不同年级的进步，根据文化差异进行识别。日本每个年级的一些学生都能找到数学上理想的策略，而美国的学生却做不到这一点。日本和美国的共同调查问题是许多学生使用解决问题的策略。(2)在计算估计中，日本学生对问题解决策略的识别和表征均有所提高。更具体地说，本研究旨在确定和描述五年级和八年级最好的估计者使用的计算估计过程。(3)本研究的目的是为了准确了解参与问题解决的教师与学生的教与学互动的效果。日本和美国的教师必须更加意识到教学过程，包括教师的解释和学生解决问题的方法之间的策略和困难。通过本研究，我们相信可以在日本和美国的数学教育中获得一些有益的发现。

'Problem Solving' was the most important topics of mathematics education in both Japan and the USA. The research on understanding students' strategies and difficulties in problem solving was considered indispensable to improving the teaching of problem solving in school mathematics. It seemed that these strategies and difficulties were influenced greatly by some cultural factors, such as languages, daily life-styles and so on. Result of this cross-cultural research was as follows:(1) The difficulties and types of problems used here are different from typical problem in both countries. We tried to analyze the students' mathematical ideas and strategies rather than achievements. These changes occurring in the process of students' pattern-finding as they progress through the various grade levels, were identified according to the cultural differences. Some students at each grade level in Japan could find mathematically desirable strategies, while no student in the USA could do the same things. What Japan and the USA had in common survey problems were that many students used strategies of problem-solving.(2) In computational Estimation, both identification and characterization of the strategies of problem-solving possessed by Japanese students were found. More specifically, this research was clarified to identify and describe computational estimation processes used by the best estimators in grade 5th and 8th.(3) This study was done to make exact the effects of teaching and learning-of interactions of the teacher and students who engaged in problem-solving. Japan and USA teachers had to become more aware of the teaching processes which consisted of the strategies and difficulties between the teacher's explanations and the students' approach to problem-solving. Through this research, we believed that we could obtain some useful findings in mathematics education for both Japan and the USA.