國家教育研究院

　　本研究兩年期計畫，本報告是第一年的研究成果。本計畫目的是建置數學個別化補救教學平臺。主要是以分析學科知識地圖，將學科知識地圖和認知診斷模式結合，編製認知診斷測驗，根據學科知識地圖進行補救教學設計，最後建置個別化補救教學平臺。?式是為代數學習而準備的，是方程式與多項式概念發展的先備知識，而乘除兩步驟併式記錄在經驗及困難度比較之下，比「加減併式」問題相對困難很多。另由TASA的施測結果顯示，小四學生對於兩步驟問題中，乘除併式的記法的應用能力不足；四年級學童在分數的能力指標通過率僅約五成，顯示學童在學習乘除兩步驟併式記錄和分數有其困難度。本計畫進行「解決兩步驟問題，並學習併式的記法」的研究。第一年成果報告已完成已訂好評量架構、乘除兩步驟併式記錄學科知識地圖、命題與修審以及根據學科知識進行腳本設計。在分數的部分，已編製完成試題和補救教學動畫腳本，學生對於分數的加法與減法概念較為精熟，以及較能列出單步驟問題的算式並解決；對於分數的定義較不瞭解，且對於解決兩步驟問題較有困難。本計畫第一年已完成「乘除兩步驟併式記錄」80道題；「分數」165題，分別組成「乘除兩步驟併式記錄」20題、「基礎分數」30題和「等值分數」25題的正式試卷。經由認知診斷模式分析「基礎分數」30題，信度是0.88，試題參數良好。本計畫政策建議如下:

1.精進教師評量技能。 老師如能編製認知診斷測驗並輔以認知診斷統計模式，可透過認知模式之估計，提供詳細的評量回饋，對教師而言，能立即調整教學方案或設計對應的補救教學方案；對學生而言，能知道自己的學習的強項與落後點。然而，認知診斷測驗編製歷程複雜，建議可透過研習或工作坊，以小組或區域聯盟的方式，讓教師們實地編製認知診斷測驗並運用於教學上，精進評量技能。

2.結合科技輔具提供差異化補救教學。 教師實施補救教學時，最常見的作法是採用團班的方式，然而學生的學習落後點不盡相同，如能透過電腦快速演算之輔助，針對每一位學生提供差異化的診斷報告，進而提供差異化的補救教學。

　　This study is proposed for two-year period of research implementation. The results from the first-year of research implementation are presented .The purposes of first-year of this study are to build an individualized remedial mathematics instruction platform and to develop items and animation scripts in some subject domains. In the first year, based on the perspective of practical setting, the knowledge map in specific subject matter are combined with cognitive diagnosis model respectively to develop diagnostic assessments and to support remedial instruction.The construction is prepared for algebraic learning. It is a prerequisite knowledge of the development of concepts of equations and polynomials. The multiplication and division of two steps is more difficult than addition and subtraction in the comparison of experience and difficulty. By TASA results showed that the application of capacity of the 4th grade students are insufficient for the two-step problem related to multiplication and division of the notation. Therefore, it is proposed to carry out the study of two-step solution to the problem, and learning the notation of construction. At present, the framework of evaluation, knowledge map of construction records of multiplication and division of two steps as well as items designed and revised has been set up. In addition, script design has been finished according to the subject knowledge. The results in Fraction showed that most of the grades four students master fraction addition and subtraction and can solve one-step problems, but they do not understand the basic definition of fraction and have some obstacles in solving two-step problems. The performance of the cognitive diagnostic assessment designed in this study was well, which can be a good practical example. The jobs mentioned in the proposal of the first year are done.For policy recommendations, enhancing the skills of developing diagnostics assessments of teachers and combining the technology with assessment and remedial instruction are suggested.