Practical Research on the Development and Evaluation of the Teaching Materials for Students to Approach in a Trial-and-Error Method on Mathematics in National College of Technology

本研究的目的是搜集和发展学生需要尝试和错误接近的数学教材，并建立学生作业的评价方法。为了做到这一点，我们借给学生一个图形计算器，然后在暑假和寒假给他们布置家庭作业。例如，我们让学生思考毕达哥拉斯数、二项式系数或含有绝对符号的函数的图形等。调查是在一年级学生中进行的，许多学生表示思考这些作业很有趣，也很有帮助，而且这些言论与他们的成就和对数学的兴趣无关。开放式作业的教育意义在于：（1）许多学生，即使是成绩较差的学生，也能注意到数学的性质，并能享受数学学习的乐趣; (2)It我们在布置作业时没有必要改变数学教学大纲，我们遗憾的是没有建立起数学作业评价的方法，但我们可以从中得到一些启示，因此我们将继续研究建立数学作业评价的方法。

The aim of this study is to collect and develop the teaching materials on mathematics which Students need to approach by trial and error, and to establish the method of evaluation of students' homework. In order to do this, we lent students a graphing calculator and then, assigned them homework during summer and winter holidays. We made students think, for example, about Pythagorean numbers, binomial coefficients or graphs of functions containing an absolute sign, etc. The survey was carried out on the first year students.Many students said that thinking about these homework was interested and helpful, moreover, these remarks turned out to be independent of their achievements and their interest in mathematics. Then we studied relations among several evaluation items : the numbers of assignments, the levels of generalization about mathematics, and growing possibilities of their thinking, etc.The educational significance of these open-ended assignments is as follows :(1)Many students, even those who achieved poorly, can take notice of mathematical properties, and they can enjoy learning mathematics.(2)It is not necessary to change a syllabus for mathematics when we assign students homework.We regret that we could not establish the method of evaluation of homework, however, we could get some perspective to do it, so we shall continue to study to establish it.