連結原理與實例：抽象內容與複雜解答的效果

Connecting Principled Information and Worked Examples: Effects of Content Abstractness and Solution Complexity

本研究透過兩個實驗調查抽象內容（實驗1）與複雜解答（實驗2）對連結原理與實例的影響。未曾學習過特定機率分配的大學生研讀某原理與兩個實例。在實驗1中，參與者完成原理－實例映對以及實例－實例映對作業。整體而言，他們在原理－實例映對的表現低於實例－實例映對的表現。與實例－實例映對相較，他們也犯了較多一對多錯誤，而且在原理－實例映對作業上對比出較少對等的內容但較多非對等的內容。然而，當實例－實例作業中一個例題較為複雜時，這些效果變得較為微弱。在實驗2中，參與者完成原理－簡單實例以及原理－複雜實例映對作業。結果發現，他們在後者的表現低於前者。此外，參與者在後者犯了較多一對多錯誤，並且對比較少的對等內容但稍多的非對等內容。這項研究為文獻增加了關於連結原理與實例之歷程的直接證據。與實例－實例映對相比，抽象性確實導致原理－實例映對的困難。部分原因是該原理中的一般元素可以對應到實例中幾個可能的候選者。這種效果的結果是原理和實例之間的相應元素的映對不太準確。然而，原理－實例映對為學習者提供了檢驗未出現於實例中的元素的機會，並且與實例－實例映對相比這種學習往往較為準確。（儘管總體而言，原理－實例映對不如實例－實例映對準確。）另一方面，原理－實例映對也受到實例的解決方案複雜性的影響。將簡單實例與原理配對似乎有助於學習對等內容，而將複雜實例與原理配對則傾向於促進對非對等內容的學習。文末針對這些發現的意涵進行討論。

Two experiments were conducted to investigate the effect of content abstractness (Experiment 1) and solution complexity (Experiment 2) for connecting principled information and worked examples. College students who had not learned the selected statistical distribution studied the principled information and two examples. In Experiment 1, the participants completed tasks for principle-example mapping and example-example mapping. Overall, their performance in principle-example mapping was lower than that in example-example mapping. They also committed more one-to-many errors and mapped fewer parallel contents and more nonparallel contents in principle-example mapping in comparison with those in example-example mapping. However, these effects were weaker when one example in the example-example pair was relatively complex. In Experiment 2, the participants completed tasks for principle-simple example mapping and principle-complex example mapping. Their performance in principle-complex example mapping was lower than that in principle-simple example mapping. In addition, the participants made more one-to-many errors and mapped fewer parallel elements and slightly more nonparallel elements. This study adds direct evidence to the research literature concerning the process of connecting a principle to its example. Abstractness causes principle-example mapping difficulty but not example-example mapping difficulty. Because a general element in the principle may be mapped onto several possible candidates in the example, mapping of corresponding elements between the principle and example is less accurate. However, principle-example mapping provides learners an opportunity to examine elements not demonstrated in the examples, and such learning tends to be more accurate in comparison to example-example mapping. Furthermore, pairing a simple example with the principle appears to facilitate learning of the parallel content, whereas pairing a complex example with the principle tends to promote learning of the nonparallel content. The implications of these findings are discussed.