本研究旨在運用學科領域知識空間、學習狀態與推薦系統，預測學生在數學科各知識點的學習狀況，並規劃適性化之學習路徑，取代傳統教科書章節排序單一路徑的教學方法，使學習路徑能對應學生的差異產生適性化。知識空間由臺南一所女子高中和一所男子高中的教師群共同定義，利用此知識空間產生符合先備(Prerequisite)關聯的學習路徑集。本研究以10題不同知識點的學習前試題測驗作為學習狀態，並以測驗結果做為輸入，經推薦系統演算法產生學生在其它知識點表現的預測值。推薦系統選擇基於使用者協同過濾(User-Based Collaborative Filtering, UBCF)演算法預測學生在各個知識點的學習表現，並對照知識空間與系統中的規劃策略，規劃出適性化且能提高學生學習動機的學習路徑。本研究共有108名來自台南兩所高中補修班的學生參與，兩校都使用適性化線上學習平台，兩校都有一個使用傳統教學路徑與一個適性化學習路徑的班級，並於相同授課時間的前後進行測驗。研究範圍包含高中數學科第一冊與第二冊的知識空間，研究利用推薦系統預測學生各知識點答對率，並比較學生學習前後的學習成績。首先，無論適性化路徑班或傳統路徑班，學生後測分數皆顯著高於前測分數，而且男子高中的適性化路徑班的後測分數顯著高於傳統路徑班的後測分數。此外，本研究也利用科技滿意度問卷、學習動機問卷與訪談蒐集學生回饋，研究發現學習動機變化與後測分數達顯著正相關。若學生偏好的學習策略符合適性化學習路徑的規劃策略，適性化學習路徑能提升學生學習動機和學科成績。未來研究可擴大使用平台的學生數量，蒐集更多學生使用的學習數據進行分析，讓推薦系統預測值能更精準，實現個人化獲得知識的效率與效果。

This study aims to apply the subject area knowledge space, knowledge state and recommender system to predict the learning situation of students in mathematics knowledge units, and plan adaptive learning paths to replace the traditional single path teaching method; thus, the learning paths can correspond and be adaptive to the differences of students. The knowledge space is jointly defined by the teachers from a girls’ senior high school and a boys’ senior high school in Tainan. Using Mathematics knowledge space, a set of learning paths with prerequisite can be generated. This study administers a pretest, including 10 different knowledge units as the learning state, and then provides the recommender system to predict the performance of other knowledge units of students. The recommender system selects a user-based collaborative filtering (UBCF) algorithm that predicts student performance based on students’ learning state and other students’ learning data in the past to plan suitable learning paths corresponding to the knowledge space.
In this study, a total of 108 students from the remedial classes of two high schools were recruited. They were individually divided into two classes, implementing the traditional learning path and the adaptive learning path. The high school mathematics knowledge spaces of 1st and 2nd semesters were developed. All participants used online learning platform, had the same learning time, and took the pretest and posttest. The research result indicated that the posttest scores are both significantly higher than the pretest scores in both traditional learning path and adaptive learning path. And, the posttest scores of the adaptive learning path class in the boys’ senior high school are significantly higher than those in the traditional learning path class. Besides, this study also used the survey of technology acceptance model, the learning motivation questionnaire, and the interview to collect student feedback. The result found that the changes in learning motivation are significantly positively correlated with the posttest scores. If the student’s preferred learning strategy is consistent with the adaptive learning path planning, his/her learning motivation and academic achievement are enhanced. Future research can expand the number of students using the platform, collect more learning data used by students for analysis, and make the predictions of the recommendation system more accurate, and achieve the efficiency and effectiveness of personalized knowledge.

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