直覺法則對於數學及科學學習的影響
--以國小四、五、六年級學生為對象
中 文 摘 要
本研究的主要目的有二：（一）針對以色列學者們研究所提出的直覺法則：More A--More B、 Same A--Same B、「無限細分法則」以及「有限細分法則」。設計相關的評量工具，以測試國內國小學生在這些評量工具上是否也隨從這些直覺法則來作反應。（二）探討是否有新的直覺法則的存在，並嘗試收集實證資料以驗證這些新的法則，以強化直覺法則預測的力量。
本研究的研究樣本為南投國小四、五、六年級學生共310人，透過四份評量工具的測試，以探討國小學生是否在數學及科學的學習上受以色列學者們所提出的直覺法則的影響。另本研究探討是否存在兩個新的直覺法則：（一）「習慣化法則」（二）More A--More A法則，透過兩份評量工具的測試，先以量的分析，探討此兩個法則是否有存在的根據，再透過質的分析，以進一步確認。
關於第一個研究目的，研究結果顯示，學生在More A--More B的評量工具上的反應，隨從直覺法則More A--More B反應的百分率有隨年級增加而下降的趨勢。在溫度相關概念的評量工具上的反應亦有類似的結果，學生隨從直覺法則More A--More B反應的百分率有隨年級增加而下降的趨勢。
在Same A--Same B的評量工具中有部分題目的測試結果顯示，若問題的外在特徵會活化Same A—Same B法則的話，則四年級的學生會比五、六年級學生較少隨從該法則。相反的，若問題的外在特徵會活化More A—More B法則的話，四年級學生會比五、六年級的學生較多隨從該法則。四年級的學生會傾向於根據題目的外在特徵來做反應，而較高年級的學生則較會採用邏輯推理。
在連續細分型問題的評量工具上的測試結果顯示，國小學生在連續細分型的問題上主要是採取有限的反應，亦即「有限細分法則」在國小學生具有主導性。
關於第二個研究目的，在「習慣化法則」評量工具上的測試結果顯示，四、五、六年級的學生將算法操作習慣化的情況似有隨年級增加而上升的趨勢。由大部分的學生會有將算法操作習慣化的事實來研判，似乎支持「習慣化法則」存在的可能性，顯示了「習慣化法則」的存在，而對於學生訪談的質的分析結果也進一步支持了這點。
而在More A--More A評量工具上的測試結果顯示。四、五、六年級學生在先後比較一些事物或概念時，都會針對該事物或概念中某一個屬性先後作不同的比較，且這現象有隨年級增加而增加的趨勢。這個現象顯示了More A--More A直覺法則存在的可能性，而對於學生訪談的質的分析結果也支持了這點。
然而，本研究在這兩個新的直覺法則上，只是作初步的探討，目前研究的結果仍含有有其他詮釋的可能性。這方面的研究有待後續更深入的探討，而學生在這兩個工具上確實犯了某一種型式的錯誤，這些都是值得提出來供教師教學及學生學習時多加留意的。
根據前述研究之結果及心得，研究者針對教師教學與學生學習、課程規劃與安排、教科書的呈現、測驗的編製等四方面，提出一些建議。關於教師教學與學生學習方面，教師宜多鼓勵學生從事批判性的思考、鼓勵學生一題多解，研究者並探討一些可行的方式，以減少學生隨從直覺法則反應，最後並建議學生對於直覺應該抱持正向的態度。關於課程規劃與安排方面，研究者建議，打折的問題應可從六下提前到五年級來實施、初步的負數的概念應可提前到國小階段來實施、溫度是內涵量的教學應可提前到國小六年級來實施。關於教科書的呈現方面，研究者建議，教科書的呈現應該要考慮到直覺法則的影響、在除法文字題的呈現上應可納入被除數小於除數的題型。關於測驗的編製上，研究者建議，測驗的編製應考慮直覺法則的影響，而直覺法則理論因具有預測的力量，因此，教師在檢驗試題的難易度時應將直覺法則的觀點也納入來做評估。最後則針對未來研究方向，提出研究者的看法，以供後續研究者之參考。

The Influences of the Intuitive Rules on Learning Mathematics
and Science for 4th, 5th and 6th Graders in Taiwan
Wen - Chan Hsieh
Abstract
There are two main purposes for this study. The first one is to verify if the four intuitive rules as identified by Stavy and Tirosh (2000) can also be observed among the four-to-six graders in Taiwan. The second purpose of this study is an attempt to find out if there exist any intuitive rules other than those identified by our Israel colleagues. A total of six instruments were developed to achieve these purposes.
A total of 310 four-to-six graders were involved in this study. The first part of this study focused on how this group of students performed on the tools that were related to the four established intuitive rules, namely, "More A-More B", "Same A-Same B", "Everything comes to an end" and "Everything can be divided by two". The second part of this study tried to establish the existence of two new rules, namely, "habituation rule" and "More A-More A".
In this study, quantitative analysis was the primary means for data analysis. Subsequent qualitative analysis was also pursued in order to supplement the findings.
Regarding the first purpose, the following results were obtained:
With respect to the "More A--More B" test tool, it was found that the percentages of students who responded in line with the "More A--More B" rule would drop as their grades increase. The same result was also found on their responses to the "temperature" test tool.
On the "Same A—Same B" test tool, some items in the test could solicit responses in accordance to both the Same A-Same B and the More A-More B rules. It was found that the 4th graders responded less in line with the Same A—Same B rule than the 5th and 6th graders if the apparent features of the items could activate the Same A—Same B rule. On the contrary, the 4th graders responded more in line than the 5th and 6th graders with the “More A—More B” rule if the apparent features of the items could activate the “More A—More B” rule. The 4th graders were more inclined to solve the problems according to the problems’ apparent features. It was also found that the higher the grades of the students, the more they would respond according to their logical reasoning. As regard the successive division tests, it was found that most students responded in accordance with the "Everything comes to an end" rule.
With respect to the second purpose, the following results were obtained:
On the "habituation rule" test tool, we found that most students applied the algorithms they had just learned to items that appeared to have the same formats. This phenomenon increased as their grades increased. This result seems to lend support to the existence of the "habituation rule". Subsequent qualitative analysis by way of interviews with some of the students provided further evidence to this claim.
As regards the "More A--More A" test, we found that most students would first compared the attributes between the concepts or events before they compared the concepts or events themselves. Furthermore, the higher the grades, the more prominent the phenomenon. This result together with the subsequent interviews seems to provide some evidence in support of the claim that "More A--More A " rule exists as yet another intuitive rule.
However, it is emphasized that this study represents a preliminary exploration into the existence of two new intuitive rules. There may well be some other interpretations to the research outcomes than those provided in this report. Hence the findings are only tentative for the time being. Further studies are needed to investigate into these two new intuitive rules. The types of mistakes made by the students should also be addressed.
Based on the above findings, the following suggestions were made:
1. The instruction of the teacher and the learning of the
students:
Teachers should encourage their students to exercise critical thinking and try to solve problems in several ways. It was suggested that students should keep a positive attitude towards their intuition. Some feasible ways for students to minimize their dependence on the intuitive rules were also discussed in the study.
2. The planning and the arrangement of the curriculum:
It was suggested that the concepts of discount could be covered in the 5th grade, while the fundamental concepts of negative numbers could be covered in elementary school.
3. The presentation of the textbook
Presentations in mathematics and sciences textbooks should take the influences of the intuitive rules into consideration.
4. The compilation of general test items
Teachers, while compiling test items for their regular classes, should always take the influences of the intuitive rules into consideration.
Finally, several suggestions were made for further study in the future.

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