排列組合可在高一學習嗎？

Can First Graders of High School Learn Combination and Permutation?

劉康君(Kang-Jun Liu)

中原大學/人文與教育學院/教育研究所/碩士(2012年)

https://doi.org/10.6840/cycu201200476

摘要

本研究旨在探討適用「99課綱」的高一學生與適用「95暫綱」的高二學生在排列組合單元的學習表現、影響高中學生在排列組合的學習表現因素為何、暸解高中學生解排列組合的錯誤情形，以及瞭解現場教師對於高一學習排列組合的看法。
　　本研究採調查研究法，藉由1545位高中學生在研究者自編之「排列組合試卷」的成績，以及研究者依研究目的擬定問題，以半結構式訪談高中六位數學教師所得資料進行資料分析。茲將本研究的結論歸納如下：
一、在排列組合單元中，適用99課綱的高一學生的學習表現不亞於95暫綱的高二學生的學習表現，因此，高一是可以學習排列組合的。
二、取才程度高的學生在排列組合的學習表現優於取才程度低的學生。
三、男生在排列組合的學習表現優於女生。
四、高中數學教師認為高一學生可以學習排列組合。
五、高中學生在排列組合單元的錯誤情形如下：
（一）高中學生解「重複排列」、「組合」、「重複組合」的題型，答對率較低，且普遍容易犯下「重複分類、分類不完全」與「自行加入其他條件解題」的錯誤類型。
（二）教師指出高中學生在排列組合單元的學習時，統整型的概念（重複排列、組合與重複組合）較容易出現學習困難。
（三）教師指出高中學生在排列組合解題時，主要錯誤來自於學生無法辨識題意的訊息而做出正確判斷，應用適當的概念解題，進而導致錯誤情形產生。

關鍵字

99課綱 ； 學習表現 ； 排列組合

並列摘要

The purpose of this research aimed to examine 10th-grade students’ and 11th-grade students’ mathematics learning performance, potential factors on students’ learning performance and error patterns of Combination and Permutation, and investigate senior high school teachers’ perceptions on 10th-grade students’ learning Combination and Permutation under 99 Curriculum.

A survey was adopted as the research method in the crurrent study. Based on the theories, reviews of the relavent literature and empirical research, “Test Paper for Combination and Permutation” and “semi-structured interviews” were conducted as the research instruments. A total of 1,545 questionnaires were valid for “Test Paper for Combination and Permutation” and 6 Mathematics teachers of senior high school participated in the study. The results are as the following:

1. The 10th-graders’ learning performance of Combination and Permutation was not worse than the 11th-graders’. Hence, the 10th-graders were able to learn Combination and Permutation.
2. The high-scoring students of Basic Mathematic Competence Test performed better
on Combination and Permutation the low-scoring ones.
3. Male students’ learning performance of Combination and Permutation was better than female students’.
4. The teachers thought that 10th-grade students could learn Combination and Permutation.
5. Error patterns of Combination and Permutation made by the students are as following:
(1) Students’ problem-solving of “Combination with Repetition”, “Permutation” and “Permutation with Repetition” was less proficient.
(2) The teachers thought that the students were poor at integration.
(3) Based on conditions and restrictions offered by the questions, the students were unable to adopt their strategies to solve questions.

並列關鍵字

learning performance ； Combination and Permutation ； 99 Curriculum

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