在數位學習的教學環境中，學習和教學方法都受到技術的影響。以往的研究表明，在教學方面，由於教學缺乏“個體化的認知診斷”機制，適性學習受到限制。此外，對於技術輔助的適性教學，基於概念診斷的教學策略使用也面臨著不足的數據分析和實證研究。
上述認知診斷的局限性可能會影響學與教的深度。概念學習的研究問題側重於學習與診斷之間的相互作用。我們進行了一系列的實證研究，以探討認知診斷對適性學習的影響。本研究為學生設計了三種具有認知診斷能力的適性學習環境，其中包括四個子研究。首先，本研究開發認知診斷評估系統並分析診斷的準確性。然後，實施線上認知診斷結合電子書包和適性形成性評量、線上認知診斷的適性動態評估多媒體學習以及基於線上認知診斷的適性遊戲化學習。關於實證研究的研究方法，我們採用了單因子共變數分析，量化內容分析和質化分析。透過實證觀察，我們探索了學習深度和誤解糾正的效果，這使我們能夠探索和比較在線上認知診斷下採用不同策略的不同學習活動的實際狀況及其應用的局限性。

以下是此研究中的四個實證研究的結果：
（1）在研究I中，結果顯示，本研究開發的線上診斷系統的平均識別率為95.72％，99.10％，98.73％，99.02％和98.96％；此系統可以有效地自動檢測學生犯下的錯誤的類型。

（2）在研究II中，結果顯示，兩組在學習效果或學習態度方面（電子書包結合即時認知診斷系統和形成性評量相較於傳統數學課堂教學）沒有顯著差異。然而，調整後的統計數據分析顯示，實驗組的後測平均值和標準差皆優於對照組。儘管前測分數較低，但實驗組的後測分數仍高於對照組。

（3）在研究III中，結果顯示，適性學習的學生表現出的學習成績和誤解矯正率均高於對照組。透過分析，我們發現近一半的非適性學習學生未能選擇適當的學習內容來糾正他們的誤解。此外，兩組學生在學習上所花費的時間明顯不同。適性學習的學生在學習上的時間明顯少於非適性學生，從而顯示出更高的學習效率。

（4）在研究IV中，結果顯示，在實驗1中，線上認知診斷系統的準確性分別達到90.8％（專家判斷）和88.29％（專家訪談）。實驗2中，透過體驗式遊戲化學習的實驗結果顯示，在基於純遊戲的體驗式學習中，適性化遊戲的體驗式學習（帶有概念診斷）顯著提高了學生的學習成果，矯正率和心流經驗。實驗3中，接受基於遊戲的體驗學習任務的學生的適性學習成果要優於接受適性多媒體學習任務的學生。結果顯示，基於遊戲的體驗學習確實在幫助學習概念與矯正錯誤概念方面發揮了重要作用。具有認知診斷機制的基於遊戲的體驗式學習明顯改善所獲得的學習成果、學習動機與心流經驗。

由上述結果我們了解認知診斷運用於適性化數學學習的面向與策略，並於文中進而提出模擬式操作由具象輔助抽象概念的形成、遊戲機制中製造認知衝突、策略設計與認知診斷結合、人工智慧手寫辨識結合認知診斷、潛藏性認知診斷以及認知診斷結合智慧型代理人技術等未來可能的各種輔助建議。

此一系列實徵研究有助於探究認知診斷與適性化學習環境下學生知識概念的演進與轉變，其中包含適性化學習策略的整合與結合量化與質化的分析結果，對於適性化數學學習與認知診斷的評估與發展期待能有重要的參考價值。

In the teaching environment of e-learning, both learning and teaching methods are affected by technology. Previous studies have shown that in terms of teaching and learning, adaptive learning is limited because teaching lacks the mechanism of "individualized cognitive diagnosis". In addition, for technology-assisted adaptive teaching, the use of teaching strategies based on concept diagnosis also faces a lack of sufficient data analysis and empirical research.

The limitations of the above cognitive diagnosis may affect the depth of learning and teaching. The research question of conceptual learning focuses on the interaction between learning and diagnosis. We conducted a series of empirical studies to explore the impact of cognitive diagnosis on adaptive learning. This research designed three adaptive learning environments with cognitive diagnosis for students, including four sub-studies. First, develop a cognitive diagnostic assessment system and analyze the accuracy of diagnosis. Then, real-time cognitive diagnosis is integrated into e-schoolbag and adaptive formative assessment, online adaptive dynamic assessment multimedia learning, and adaptive experimental game-based learning. As for the research methods of empirical research, we adopted single-factor covariate analysis, quantitative content analysis, and qualitative analysis. Through empirical observations, we explored the effect of learning depth and misconception correction, which enabled us to explore and compare the actual status of different learning activities with different strategies under cognitive diagnosis, as well as the limitations of their applications.

The following are the results of the four empirical studies in this study:

(1)In study I, the result indicates that the mean recognition rates of the computerized diagnostic system developed in this study are 95.72 %, 99.10 %, 98.73 %, 99.02 %, and 98.96 %; this system can effectively and automatically detect the types of mistakes that students make.

(2)In study II, the results showed no significant differences between the two groups (e-schoolbag integrated model combined with real time cognitive diagnostic system and formative assessment vs. traditional mathematics classroom teaching) with regard to learning effectiveness or attitudes towards learning. However, analysis of adjusted statistics showed that the mean and standard deviation of the experimental group were superior to those of the control group. Despite having a lower pre-test score, the experimental group still produced a higher post-test score than the control group.

(3)In study III, the results revealed that the adaptive learning students exhibited learning performance and misconception correction ratios superior to those of the students of the control group. Through analysis, we discovered that nearly half of the non-adaptive learning students failed to select appropriate learning content for correcting their misconceptions. In addition, the time spent on learning by the students in the two groups was significantly different; the adaptive learning students spent significantly less time on learning than the non-adaptive students, thus exhibiting higher learning efficiency.

(4)In study IV, the results showed that the accuracy of the concept diagnosis system was up to 90.8% (expert judgement) and 88.29% (expert interview) in the experiment 1. In the experiment 2, the game-based experimental results showed that adaptive game-based experiential learning (with concept diagnosis) significantly improved students’ learning outcomes, correction rates, and flow experience in pure game-based experiential learning. Similarly, in the experiment 3, the adaptive learning outcomes of students given game-based experiential learning tasks were superior to those given adaptive multimedia learning tasks. The results implied that game-based experiential learning did play an important role to help learning conception. Moreover, the game-based experiential learning with cognitive diagnosis mechanism will obviously improve the learning obtained, achievement, learning motivation, and flow experience.

Based on the above results, we understand the aspects and strategies of cognitive diagnosis applied to adaptive mathematics learning, and in this article, we propose that the simulation operation assists the formation of abstract concepts by concreteness, the creation of cognitive conflicts in game mechanisms, the combination of strategy design and cognitive diagnosis, and artificial intelligence handwriting recognition combined with cognitive diagnosis, latent (tacit) cognitive diagnosis, and cognitive diagnosis combined with intelligent agent technology and other possible future auxiliary suggestions.

This series of empirical studies helps to explore the evolution and transformation of students’ knowledge concepts in the context of cognitive diagnosis and adaptive learning. It includes the integration of adaptive learning strategies and the combination of quantitative and qualitative analysis results. The evaluation and development of cognitive diagnosis are expected to have important reference value.

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