國中生數學內容知識與數學認知能力之混合Rasch模式分析研究

The Study of mixed Rasch model analysis on mathematical content knowledge and cognitive abilities for junior high school students

鄭蕙如(Huey-Ru Cheng)

指導教授 ： 林世華

國立臺灣師範大學/教育學院/教育心理與輔導學系/博士(2005年)

摘要

本研究目的為了解我國國中生之數學內容知識與數學認知能力之表現：首先，建立以國中基本學力測驗為基礎之數學科評量架構；其次，了解國中生之數學內容知識及數學認知能力的表現類型及各類型表現內涵。在研究方法上，蒐集並分析國內、外各大型專業評量機構對數學內容知識及數學認知能力之定義；並且使用混合Rasch模式，針對基本學力測驗數學科之作答反應資料，進行國中生數學內容知識與數學認知能力之分析研究。本研究之結果如下：一、就評量架構部分，在基本學力測驗數學科的基礎上，本研究建立以數學內容知識與數學認知能力為主軸之評量架構，其中數學內容知識下，又細分為若干數學學習單元。二、國中生在基本學力測驗數學科之整體表現方面，在資料分析統計與機率表現較佳、幾何與空間概念表現較差；在數學認知能力部分，則以概念理解、程序知識與執行表現較好，問題解決表現較差。三、就混合Rasch模式分析結果顯示，分屬於不同組別的國中生，數學內容知識與數學認知能力之試題平均答對率高低及結構並不一致。最後，研究者針對研究所得之結論，提出未來教學與研究之建議，並提出應持續針對國內國中生數學表現繼續深入探討及研究。

關鍵字

國中基本學力測驗 ； 數學內容知識 ； 數學認知能力 ； 項目反應理論 ； 混合Rasch模式

並列摘要

The purpose of this study is to understand the performance of junior high students’ mathematical content knowledge and cognitive abilities. The assessment framework of mathematics will be built and the performance types of students’ mathematical content knowledge and cognitive abilities will be understood based on the Basic Competence Test for Junior High School Students (BCTEST). In the research methods, we collect and analyze the definitions of mathematical content knowledge and cognitive abilities as defined by assessment institutes and use mixed Rasch model to analyze the students’ mathematical response patterns for the BCTEST. The findings were listed as follows: (a) a framework of mathematical content knowledge and cognitive abilities was built based on the BCTEST; (b)students had better performance in data analysis, statistics and probability than in geometry and spatial sense on the mathematical content knowledge; and on the mathematical cognitive abilities performed better in conceptual understanding, procedure knowledge and execution than in problem solving; (c)the results of mixed Rasch model showed that students had different performance in mathematical content knowledge and cognitive abilities who belong to different latent classes. Finally, some suggestions were provided in further instructions and researches based on the results.

並列關鍵字

The Basic Competence Test for Junior High School Students ； mathematical content knowledge ； mathematical cognitive abilities ； item response theory ； mixed Rasch model