解題時機與範例類型對學習成效與認知負荷的影響

Effects of Problem Solving and Example-Based Learning on Cognitive Load and Performance

十二年國民基本教育課程綱要強調在課程中實施探索活動的重要性，如何實施探索活動，達到有效的教學目標，便成為在職老師的重要課題。本研究以數學科的「基本量與比較量」單元為實驗主題，國小六年級學童為實驗對象，以實驗研究法探討兩個因子：探索解題的時機（先解題／先閱讀）與範例學習的類型（比較範例／解題練習），對學習成效與認知負荷的影響。首先，研究者以兩因子來設計畫線段圖、操作線段圖，以及解基準量與比較量問題三個部分的實驗教材。其次，將105名學童隨機分派至四個不同的組別進行實驗操作。而在每個部份的教材學習完成後，以認知負荷量表來量測學童所感知的內在與外在認知負荷。最後，以學習成效測驗來評估學童在畫線段圖、操作線段圖，以及解基準量與比較量問題的表現。統計分析後，得到以下的結果：第一，兩因子間在認知負荷的感知以及測驗成績的表現上皆沒有顯著的交互作用；第二，先解題組學童在學習解基準量與比較量問題時感知的內在負荷顯著高於先閱讀組，先解題組學童在學習操作線段圖與解基準量與比較量問題時所感知的整體認知負荷顯著高於先閱讀組，而比較範例組與解題練習組在三個學習內容所感知的內在、外在，及整體認知負荷皆沒有顯著差異；第三，不同探索解題時機分組在三個學習內容的測驗成績上皆沒有顯著差異，而比較範例組在畫線段圖的測驗成績顯著優於解題練習組。最後，依據研究結果提出教學上的建議。

The 12-year Basic Education Curriculum guidelines emphasize the importance of discovery activities in the curriculum. Therefore, methods of implementing discovery-based learning in the classroom and achieving effective teaching goals have become a major topic for current teachers. Alfieri et al. (2011) conducted a meta-analysis of 164 studies and reported that allowing students to only perform pure discovery activities may be detrimental to learning; however, assisted discovery learning, including feedback, worked examples, and self-explanation prompts, can benefit learning. Studies on assisted discovery learning, have provided empirical results regarding the integration of problem solving and example learning. These studies have indicated that learners who cooperate in solving problems before receiving direct teaching or seeing examples perform better than those who first receive direct teaching or examples and then solve problems. However, the findings of these studies only demonstrate that solving problems cooperatively and then studying examples is a more favorable approach than studying the examples individually and then practicing solving the problems. With inconsistent experimental conditions (i.e., cooperative vs. individual), distinguishing the effects of the variables of the timing of problem solving and the type of example learning on teaching effectiveness is impossible. Sweller and Paas (2017) also indicated that most of these studies did not control variables appropriately and that they changed multiple variables simultaneously. Therefore, the experimental designs of these studies were fundamentally flawed and could not isolate the effects of specific variables. Although some studies on the integration of problem solving and example learning have analyzed the learning process from the perspective of cognitive load theory, this is only a theoretical discussion. Studies have not conducted actual measurements of the cognitive load perceived by the learner during the learning process (Kapur & Bielaczyc, 2012; Loibl & Rummel, 2014). In addition, for studies in which the experimental participants were elementary school students, only one item was used to evaluate cognitive load, such as “How much effort did you use in the process of learning just now?”; in general, this cognitive load could not be accurately measured (Huang & Shie, 2016 ; Wong et al., 2012). Furthermore, if the intrinsic and extraneous cognitive loads perceived by the learner during learning cannot be known, cognitive load theory cannot be used to effectively analyze the learner’s cognition and information processing during learning (Leppink et al., 2013). Therefore, this study excluded the effect of cooperative learning and allowed learners to learn materials individually to avoid confounding variables. The “basic quantity and comparative quantity” unit of mathematics was used for the experiments in this study. The researcher conducted an experiment to study the effects of two factors on learning outcomes and perceived cognitive load: Problem-solving timing (problem solving first or reading an example first) and the type of example (comparative example or problem-solving practice). The multidirectional scale developed by Leppink and van den Heuvel (2015) was used to measure intrinsic and extraneous cognitive loads perceived during learning, and an objective reference value was used for the learning outcome to observe germane cognitive load. Therefore, on the basis of cognitive load theory and the relevant literature, the research questions verified in this study were as follows: 1. Does the timing of problem solving and the type of worked-out example affect the intrinsic, extraneous, and overall cognitive load when students learn to draw line segments, operate line segments, and solve reference and comparison quantity problems? 2. Does the timing of problem solving and the type of worked-out example affect the test scores when students learn to draw line segments, operate line segments, and solve the reference and the comparison quantity problems? The researcher first used two factors (timing of problem solving and type of worked-out example) to design an experiment involving three exercises: drawing line segments, operating line segments, and solving a reference and comparison quantity problem. Second, 105 sixth-grade children were randomly assigned to four groups for the experiment: reading examples first then comparing examples (group 1), solving problems first then comparing examples (group 2), reading examples first then practicing problem solving (group 3), and solving problems first then practicing problem solving (group 4). After each exercise was completed, the cognitive load scale was used to measure the students’ perceived intrinsic load and extraneous load. Finally, a learning test was used to evaluate the students’ learning performance in drawing line segments, operating line segments, and solving the reference and the comparison quantity problems. The answers to the first three questions of the cognitive load scale indicated the perceived intrinsic load, and the answers to the last three questions indicated the perceived extraneous load. Factor analysis with the timing of problem solving and type of worked-out example as independent variables and the test scores and cognitive load indicators as the dependent variables was performed. The two-factor multivariate analysis revealed no significant interaction effect between the timing of problem solving and the type of example on the students’ perceived cognitive load or the three test scores. The analysis also indicated that the perceived intrinsic load of the students who solved problems first was significantly higher than that of the students who read examples first when solving the reference and the comparison quantity problems. The overall perceived cognitive load of the students who solved problems first was also significantly higher than that of those who read examples first when operating line segments and solving the reference and comparison quantity problem. No significant difference was observed between the comparative example condition and the practicing problem solving condition in the students’ perceived intrinsic, extraneous, or overall cognitive load No significant difference in test scores was observed between the different problem-solving timing conditions in the three tests; however, the test scores of the students who had seen a comparative example were significantly higher than those of the students who practiced problem solving when drawing line segments. Four sets of materials were designed to study the effects of problem-solving timing and worked-out examples on learning effectiveness and perceived cognitive load. The researcher used the multidimensional cognitive load scale to successfully measure the students’ perceived intrinsic load and extraneous load. When the experimental conditions were controlled for and the cooperative learning variable was excluded, the experimental results were determined to be consistent with those of previous research regarding worked examples (Kalyuga et al., 2003; Renkl & Atkinson, 2003). The learning performance of group 2 was not higher than that of group 1. Different learning examples may be suitable for learning different types of knowledge. Therefore, on the basis of the findings of this study, the researcher proposes the following strategies for educators. First, because of the nature of problem-solving activities, learners may perceive a higher cognitive load; therefore, learning materials suitable for the level of learners should be carefully designed when implementing a strategy that involves solving problems. Second, the comparison of examples is suitable for learning conceptual knowledge, and practicing of problem solving is suitable for learning procedural knowledge. Finally, when designing teaching materials for comparative examples, educators should add incorrect examples to the materials. The correct and incorrect examples should be compared, and the learner must be asked to explain why the incorrect examples are wrong; doing so can repair the learners’ knowledge and enable them develop the correct concept.