桃園縣國小低年級學生位值概念及數學學習成就相關性之研究

The Study of Relationship between Concepts of Place Value and Academic Achievement of the First and Second Graders in Elementary School in Taoyuan County

林秀卿(Hsiu-Ching Lin)

指導教授 ： 袁媛

中原大學/人文與教育學院/教育研究所/碩士(2013年)

https://doi.org/10.6840/CYCU.2013.00132

摘要

本研究目的是為瞭解低年級學生的位值概念辨認情形，及其與數學學習成就表現之相關性。研究樣本為桃園縣兩個國小之一年級學生326人及二年級學生340人，並以「低年級位值概念測驗」及「數學學習成就測驗」收集研究資料，其中的位值概念測驗題型是依表徵方式區分為實物表徵問題、錢幣表徵問題及古氏積木表徵問題。
研究結果發現：
一、 一年級學生的位值概念多處於只認識數字卻不知其表徵意義，而二年級學生位值概念則多已建構二位數系統。因此，二年級學生的位值概念比一年級學生佳。
二、 低年級學生在不同表徵的位值概念問題有表現差異，其中學生在實物表徵問題與錢幣表徵問題的表現並無差異，但在古氏積木表徵問題的表現較差。
三、 低年級學生在不同表徵的位值概念問題成績與數學學習成就皆有顯著正相關，但只有在實物表徵問題的表現對一、二年級數學學習成就具有預測力。
最後根據研究結果提出建議，以供教材、教學及未來相關研究之參考。

關鍵字

低年級數學 ； 位值 ； 表徵 ； 數學學習成就

並列摘要

The purposes of this study were to investigate the development of the first and second graders’ concepts of place value and to explore the relationship between concepts of place value and academic achievement. The subjects were students selected from 326 first and 340 second graders of two elementary schools in Taoyuan County, and using place value concept test and academic achievement test as examining tools. One of the tests, place value concept test, this study divides questions by three representations: Cuisenaire representation, coin representation, and physical representation.
The results of this study were as follows:
1. At the concept of place value aspect, the first graders knew number symbol, but almost didn’t understand the meaning of number representation. However, the second graders already constructed two-digit system. Therefore, the second graders performed better than the first graders.
2. Significant differences were found among the three representations of the place value concept test for the first and second graders. In fact, no performance differences were found between questions in coin representation and physical representation. It was more difficult to understand Cuisenaire representation for the first and second graders.
3. There were significantly positive correlations between the grades on the three representations of the place value concept test and academic achievement in mathematics. And the physical representation was the important predictor to influence the academic achievement in first and second graders.

Finally, based on the findings of this study, suggestions for improving teaching and future research were discussed.

並列關鍵字

academic achievement ； representation ； place value ； math of first and second grader

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