以鷹架輔助坡里亞式思考方式之進行-使用者介面研究

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

李坤金(Kun-Chin Lee)

指導教授 ： 夏延德

中原大學/工學院/資訊工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200353

摘要

現今學校教育中，為了順應考試求高分的期望，數學的教學常背離了數學的實用性與探究的過程，強塞給學生許多零碎片段的知識，此舉不僅抹煞了數學學習的本質，也削弱了學生的學習慾望。教育界最近幾年來一直強調建構主義，為的就是要發展學生的思考能力、增進他們的學習成就、以及培養他們在學習數學上的正面態度。
數學科的作業中，最令學生害怕的的就是應用題了。普通的運算練習，當然也不一定容易指導學生作出所有正確的計算。但一到應用題，就特別困難。首先是解題，先不提字裏行間可能會有的一些較陌生少用的文字，就是要將題意掌握清楚亦並非每題都這般順利；而且還要孩子自己列算式，將要用的數據資料連結起來，寫出一個正確的運算式，更是難題所在。因此很多學生都害怕應用題，而很多家長和教師也覺得這是一個難關。
本篇論文的目的希望能活化小學數學應用題的教學模式，藉著將「問題解決」策略及探索式學習融入電腦多媒體的教學設計，在Web上設計一個Polya-Style Thinking的使用者界面來訓練學生養成養成這種思考的習慣，並且希望學生在解題的時候，可以依照Polya所提出的解題四步驟的方法，其中我們也加上一些建構主義者的方法在系統裡面，讓學習者可以主動的、自主的去探索這個問題的解題策略,藉由這樣鼓勵他多方面的思考解決問題的方法，並希望藉由其在探索的過程當中，找到最適合自己的解題策略，建構屬於自己的知識。期望藉此來培養學生對於學習數學的正確態度，提高學生的學習興趣，並最終提升學生的學習成就與高層次思考能力（higher-order thinking skills）。

關鍵字

鷹架理論 ； 探索式學習 ； 坡里亞式思考方式 ； 建構主義

並列摘要

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.

並列關鍵字

scaffolding theory ； constructivism ； Nuffield Discovery Approach ； Polya-Style Thinking

參考文獻

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