臺灣博碩士論文加值系統

本研究的主要目的在於瞭解數學障礙學生在數學概念理解、數學推理能力及數學解題表現上的情形，並探討影響數學障礙學生數學概念理解、數學推理能力及數學解題表現之因素。
本研究以高雄市五所國小一年級學生為篩選對象，篩選出非閱讀缺陷/數學障礙學生27人，閱讀缺陷/數學障礙學生27人及一般學生39人，共計83名受試者。所有受試者均接受數學概念理解測驗、數學推理測驗、數學解題測驗及國民小學一二年級閱讀理解測驗等四項測驗。所得之測驗結果以描述統計、獨立樣本單因子共變數分析及多元迴歸分析等統計方法加以分析考驗。
研究結果顯示：
一、國小一年級數學障礙學生的數學概念理解能力、數學推理能力、數學解題表現顯著低於一般學生。
二、非閱讀缺陷/數學障礙學生和閱讀缺陷/數學障礙學生在數學概念理解、數學推理能力和數學解題表現上有一致的困難。
三、閱讀理解能力是數學概念理解能力發展的主要影響因素。
四、不同數學成就學生之數學推理能力，分別受智力、閱讀理解能力和數學概念理解能力的影響。
五、不同數學成就學生之數學解題表現，分別受閱讀理解能力、數學概念理解能力和數學推理能力的影響。
根據以上研究結果，本研究對未來在數學障礙的教育和研究上提出建議。

The purpose of this research is to realize the performance of students with mathematics disabilities(MD) in mathematical conception understanding, mathematical reasoning, and mathematical problem solving, and to discuss the factors which influence them.
The eighty three subjects were chosen from the first graders of five elementary schools in Kaohsiung City were sieved out twenty seven students with disabilities in mathematics but not in reading(MD-only), twenty seven students with disabilities in mathematics as well as in reading(MD/RD), and twenty nine normal students(NS). All students take four tests, including mathematical conception understanding test, mathematical reasoning test, mathematical problem solving test, and reading comprehension test for first and second grade students. The results were analyzed by the descriptive statistics, independent sample one-way analysis of convariance, and multiple regression analysis.
The main findings were summarized as follows:
1. The performance of students with MD in first grade is significantly lower than NS in mathematical conception understanding, mathematical reasoning, and mathematical problem solving performance.
2. The MD-only and MD/RD have consistent difficulty in mathematical conception understanding, mathematical reasoning, and mathematical problem solving performance.
3. The ability of reading comprehension is the main factor to influence the development in mathematical conception understanding.
4. The ability in mathematical reasoning of students with different achievement in math is affected by intelligence, reading comprehension, and mathematical conception understanding.
5. The mathematical problem solving performance of students with different achievement in math is affected by the ability of reading comprehension, mathematical conception understanding, and mathematical reasoning.
Theoretical and practical implication as well as suggestions for future researchers were discussed in the thesis.

目 次
中文摘要 ……………………………………………………………………… I

英文摘要 ……………………………………………………………………… II

謝 詞 ……………………………………………………………………… III

目 次 ……………………………………………………………………… IV

表 次 ……………………………………………………………………… VI

圖 次 ……………………………………………………………………… VI



第一章 緒論………………………………………………………………… 1
第一節 研究動機…………………………………………………………… 1
第二節 研究目的…………………………………………………………… 5
第三節 待答問題…………………………………………………………… 5
第四節 名詞解釋…………………………………………………………… 7

第二章 文獻探討…………………………………………………………… 12
第一節 數學能力的本質…………………………………………………… 12
第二節 數學障礙的成因…………………………………………………… 17
第三節 數學概念理解與數學解題之關係………………………………… 23
第四節 數學推理與數學解題之關係……………………………………… 27

第三章 研究方法與步驟…………………………………………………… 34
第一節 研究架構…………………………………………………………… 34
第二節 研究對象…………………………………………………………… 36
第三節 研究工具…………………………………………………………… 39
第四節 實施步驟…………………………………………………………… 45
第五節 資料分析…………………………………………………………… 47



第四章 結果與討論………………………………………………………… 48
第一節 受試者在數學概念理解測驗表現之差異………………………… 49
第二節 受試者在數學推理測驗表現之差異……………………………… 53
第三節 受試者在數學解題測驗表現之差異……………………………… 57
第四節 影響數學概念理解、數學推理、數學解題之相關因素………… 61
第五節 綜合討論…………………………………………………………… 65

第五章 結論與建議………………………………………………………… 73
第一節 結論………………………………………………………………… 73
第二節 限制………………………………………………………………… 76
第三節 建議………………………………………………………………… 78

參考書目 ……………………………………………………………………… 80

附錄一 數學概念理解測驗題目難度鑑別度指數一覽表………………… 92
附錄二 數學推理測驗題目難度鑑別度指數一覽表……………………… 96
附錄二 數學解題測驗題目難度鑑別度指數一覽表……………………… 99

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