數學障礙學生數學概念理解、數學推理能力與數學解題表現之關係分析研究

A Study of the Relations among Mathematical-Concept Understanding%2C Mathematical Reasoning and Mathematical Problem Solving Performance in Students with Mathematical Disabilities

本研究的主要目的在於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29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、閱讀理解能力是數學概念理解能力發展的主要影響因素。二、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。三、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，本研究提出：閱讀理解能力、數學概念理解能力和數學推理能力，對於不同亞型數學障礙學生的解題能力有不同的影響力。因此，建議教師在提升閱讀缺陷／數學障礙學生的解題能力時，應優先注意其閱讀理解能力；非閱讀缺陷／數學障礙學生則需注意其數學概念理解能力；一般學生則需注意其數學推理能力。

The purpose of this study was to explore the factors which influence the performance of students with mathematical disabilities(MD) in mathematical-concept understanding， mathematical reasoning， and mathematical problem solving. The eighty three subjects were selected from first graders in five elementary schools in Kaohsiung City， composed of twenty seven students with disabilities in mathematics only (MD-only)， twenty seven students with disabilities both in mathematics and reading(MD/RD)， and twenty nine normal students (NS). All students took four tests tapped on mathematical-concept understanding， mathematical reasoning， mathematical problem solving， and reading comprehension for first and second grade students. The results were obtained with the multiple regression analysis and path analysis. The main findings were summarized as follows: 1. The ability of reading comprehension is the main factor influencing the development of mathematical-concept understanding. 2. The performance of mathematical reasoning of students with different level of mathematical achievement is affected by intelligence， reading comprehension， and mathematical-concept understanding. 3. The performance of mathematical problem solving of students with different level of mathematical achievement is affected by the abilities of reading comprehension， mathematical-concept understanding， and mathematical reasoning. The results of the study suggested that reading comprehension， mathematicalconcept understanding， and mathematical reasoning are contributed differentially to the performance of different subtypes of mathematical disabled students. It was implied for mathematical teaching that reading comprehension， mathematical-concept understanding， and mathematical reasoning should be emphasized to improve respectively for students with MD-RD， students with MD only， and for normal students during mathematical instruction.