A Study of the Interface Design for Scaffolding Polya-Style Thinking

• Main Authors: Kun-Chin Lee, 李坤金
• Other Authors: Yen-Te Hsia
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/08791782692324121964

碩士 === 中原大學 === 資訊工程研究所 === 90 === In Taiwan, it is common to see that students are routinely “stuffed” with fragmentary knowledge for the purpose of obtaining high scores in examinations. This is a wrong thing to do, especially in the case of mathematics education. It not only violates the principles of mathematics education, but also deprives the students of their potential interests in mathematics. This is one reason why in recent years, influential educators are advocating constructivism in education. It is hoped that the students’ thinking abilities can be improved. It is also hoped that the students’ level of achievement can be alleviated, and that the students’ attitude toward learning mathematics can become more positive. For elementary students, word problems are often considered to be more difficult than “pure” calculation exercises involving, say, addition, subtraction, multiplication, and division. Firstly, there is the problem of understanding the problem statement. Apart from the possibility of encountering unfamiliar words or phrases in the problem statement, there is also the problem of having to fully understand the statement itself. Secondly, the students will have to identify (correctly) the relation or relations among the known quantities and unknown quantities. Only after the first and second steps are successfully completed can the students enter the “pure” calculation part of the solution process. This is what makes word problems so frightening for many elementary students. Even the instructors themselves may find it difficult to teach word problem solving to the students. In this thesis, we make use of appropriate computer technology to add problem-solving strategies into the solution process. The system runs on the Web, and there is a problem-solving interface that encourages the use of Polya-style thinking during problem solving. By using this interface, the students can readily follow the four problem solving steps that Polya suggested. The students can also actively explore solution hints that are based on various Polya’s ideas, including problem transformation, problem simplification, sub-problem identification, visual representation, and analogy. It is hoped that through the use of this interface, the students can find problem solving strategies that are most suitable for themselves, and that the students can also construct their own knowledge. This way, we may be able to (a) cultivate the “right” attitude toward mathematics learning, (b) alleviate the students’ interest in mathematics, and (c) train higher-order thinking skills.