本研究旨在探討數位學習環境、引導策略及先備知識對高中生數學遞迴關係的學習成效與動機之影響。研究對象為高中二年級學生，採因子設計之準實驗研究法，有效樣本96人。自變項包含數位學習環境、引導策略及先備知識，數位學習環境分為擴增實境及虛擬實境；引導策略分為程序引導及反思引導；先備知識依學習者課前具備之能力分為高先備知識及低先備知識。依變項為學習成效與學習動機。
研究結果顯示：(1)在學習成效方面，就知識理解而言，擴增實境學習環境組在知識理解表現優於虛擬實境學習環境組，程序引導組優於反思引導組，且高先備知識組優於低先備知識組；就知識應用而言，擴增實境學習環境組在知識應用表現優於虛擬實境學習環境組，高先備知識組優於低先備知識組，而程序引導組及反思引導組在知識應用表現則無顯著差異。(2)學習動機方面，各實驗組對學習活動皆抱持正向的學習動機；其中，在期望成功面向，擴增實境學習環境組表現優於虛擬實境學習環境組、反思引導組優於程序引導組、而在先備知識二組間則無顯著差異。

The purpose of this study was to investigate the effects of type of digital learning environment, guiding strategy and prior knowledge on senior high school students’ learning performance and motivation in learning of recursion. A quasi-experimental design was employed and the independent variables were type of digital learning environment, guiding strategy, and prior knowledge. The participants were the eleventh graders and the effective sample size was 96. While the digital learning environments consisted of the augmented reality and the virtual reality, the guiding strategies included the procedural guidance and the reflective thinking guidance; the prior knowledge involved high and low prior knowledge. The dependent variables were the students’ learning performance and motivation.
The results showed that: (a) for knowledge comprehension performance, the augmented reality group outperformed the virtual reality group, the procedural guidance group outperformed the reflective thinking guidance group, and the high prior knowledge group outperformed low prior knowledge group; as for the knowledge application, the augmented reality group outperformed the virtual reality group and the high prior knowledge group outperformed the low prior knowledge group, whereas there was no significant difference between the procedural guidance group and the reflective thinking guidance group; and (b) as for learning motivation, all participants showed positive motivation toward the employed learning environments; in particular, regarding learner’s expectancy for success, the augmented reality group showed more positive effect than the virtual reality group did, and the reflective thinking guidance group showed more positive effect than the procedural guidance group did while there was no significant difference between the high prior knowledge group and the low prior knowledge group.

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