國小加減法數學文字題歷程導向解題診斷評量題組之編製發展與功能分析研究

The Development and Function of Process-Oriented Diagnostic Assessment Battery for First Graders' Learning on Word Problem Solving

本研究旨在參照數學解題歷程模式進行成份（認知、後設認知）分析，並搭配學習內容分析，編製歷程導向單步驟加減法文字題解題診斷評量題組。採合目標與叢集取樣抽取嘉義縣市一年級學生共477人，施測後進行統計分析。在項目分析方面，平均表現水準約75%，單題、各成份及全題組的內部相關與極端組t考驗結果良好。在效度分析方面，主成份、試探性及驗證性因素分析均發現題組的二成份三因子結構（認知成份含基本解題及數量辨識技巧、後設認知成份含檢核技巧），且共同向度性、因素萃取、抽取變異比及模式適配度均屬良好，並具良好之效標關聯及預測效度。在信度分析方面，內部一致性係數及組合信度亦屬良好。而在個案剖面訊息方面，亦具診斷處方功能。

The purpose of this study was to develop the Process-Oriented Diagnostic Assessment Battery (PODAB) for single-step word problem of addition and subtraction through componential and content analyses. Participants were composed of 477 first graders from Chiayi by convenient and cluster sampling. Participants were administered the PODAB. Item analysis suggested good passing percentage， internal correlation and critical ratio， regardless whether in single items， sub-battery or the whole battery. As for construct validity， three factors were suggested by exploratory factor analysis and confirmatory factor analysis (basic solving， quantity identification， and checking skills)， and there were appropriate dimentionality， variance proportions of factor extraction， model fit， as well as criterion-related and predictive validity. For reliability， results showed appropriate internal consistency coefficient and composite reliability. Finally， because of individualized information， the battery could provide diagnostic profile and subsequent prescriptions.