國家教育研究院

　　傳統評量理論並無法提供有效的訊息，讓教師對學生的錯誤概念進行診斷的評量，認知診斷評量著眼於探討學生的潛在知識結構與其作答反應過程的關係，應用於診斷評量具有顯著的成效。本研究擬依循Asiala等人所提出的數學課程發展與研究的三元循環論，運用APOS理論來分析有關國小三角形面積、梯形面積概念的內容與能力指標，以發展此二單元的起源分解結構、教學活動內容架構及評量架構，以此為基礎進行命題、修審、施測，再以認知診斷評量分析，了解教學成效與學生概念或技能的精熟程度，並評估適合每一試題的認知診斷模式，提供解題時所需概念、技能間的交互影響訊息，給教學設計者，作為教學改進，進而建立以結合APOS理論的有效教學模式與認知診斷評量，做為後續推廣與應用。

　　Traditional assessment theory is unable to provide effective information that teachers can diagnose the wrong concepts of students. Cognitive Diagnostic Assessment (CDA) focuses on the relationship between the latent knowledge structure and the response process of students and has significant outcomes. The study plans to follow the mathematics curriculum development and research provided by Asiala et al. and applies APOS theory to analyze the concept and competence indices of triangle area and trapezoidal area in elementary school. The study will use the above as base to design frame of genetic decomposition, instruction activity, and assessment framework of triangle area and trapezoidal area. After that, the study will design items, revise items, implement test, and use CDM to analyze data in order to understand the instruction effects and master proficiency of students’ concepts or skills. In addition, the study will evaluate the appropriate cognitive diagnostic model (CDM) for every item to provide interaction between concept and skill in each item. Teachers can improve the instruction by the item CDM information. In the long run, the study hopes to build effective instruction model and CDA in order to promotion and application in future.