工作範例之教學順序對學生學習成效與認知負荷影響之研究——以面積覆蓋活動為例

The Effect of Instructional Orders of Worked Examples for Students' Learning Achievement and Cognitive Load in Area Covering

本研究以認知負荷的觀點，探討不同教學順序之工作範例對「學習成效」與「認知負荷」的影響，其中教學順序方式包括「先看範例再練習(W-P)」及「先自己解題再看範例(P-W)」兩種。本研究採實驗研究法，研究的教材內容為國小幾何教材中之面積覆蓋。教材依認知負荷理論的教學設計原則設計，特別是工作範例原則。研究對象為國小四年級104名學生，將其隨機分配為「先看範例再練習組」與「先自己解題再看範例組」。研究工具包含兩節數位教材及認知負荷量表。實驗過程是先進行前測，再將學生分兩組學習兩節的數位教材課程，一週後進行後測，再隔一週進行延後測，在學習活動後及測驗階段後均進行認知負荷的問卷調查。研究結果發現如下：一、後測及延後測時，P-W組的學習成效顯著優於W早在且。二、在認知負荷之花費心力面向，P-W組在數位教材第一節及延後測時與W-P組有顯著差異，且P-W組花費心力多於W-P組。三、在面積覆蓋題型中，被覆蓋物是方形的通過率高於三角形:覆蓋物以4平方公分正方形通過率最高，0.5平方公分的等腰直角三角形最困難。記得幾年前，在教科書（或教科書出版社的刊物、參考書等）常常看到這樣一個問題：一質點以初速v。在兩個不同光滑軌道上運動，一個是直線軌道，另一個是在直線軌道的途中經過一段圓弧軌道，如圍1所示，則那一個軌道可以便質點比較快到達終點C？數學是自然科學、社會科學，以及科技課程等各類學科的基礎，其內容包含了許多職業所需的相關知能，如邏輯思維、管理與經營、科技使用等(TIMSS and PIRLS International Study Center, 2011 )。「玩具(toy)」是伴隨見童成長過程中不可或缺的物件(Swiniarski，1991)，因此在教育的功能也廣為學者所肯定，例如賀慧玲(1992)指出玩具帶給孩子歡樂、陪伴及自主，能敏銳幼見廠覺、激發幼見好奇心、增進幼見的記憶力、想像力、培養幼兒的審美能力和增進幼兒的注意力。李戊益(2002)也認為對見童成長學習的過程有莫大的影響力，可以促進學童在學習過程中快樂的學習。在高中教材中有「已知三角形的三邊長的面積公式」，「已知三角形三頂點的面積公式」等作法求三角形的面積，若條件為已知三角形三邊所在直線方程式，則常見的作法為先求三頂點，再利用「已知三角形三頂點的面積公式」來求面積，本文中利用高中所習的概念，討論直接利用三邊所在直線方程式的條件來求面積。

The purpose of this study was to design instructional material based on the cognitive load theory, and to investigate the consequences of learning achievement and cognitive load caused by different instructional orders. The instructional orders used in this study included the “worked example-problem solving (W-P) and “ problem solving-worked example (P-W)' orders. This study adopted an experimental design. The content was the “area covering' in the elementary school geometry. The teaching material was designed by applying the instructional principles of cognitive load theory, especially the principles of worked-examples. The participants were 104 fourth graders of an elementary school. They were randomly assigned to either the “ worked example-problem solving' (W-P) 。r the 'problem solving-worked example' (P-W) group. The research instruments included two multimedia lessons and a cognitive load questionnaire. A pretest was taken prior to dividing the participants into groups. Then two multimedia lessons were given, followed by a post-test one week later, and a delay post-test after another week. The cognitive load questionnaire was given after each learning lesson and test. The results were as follows: 1. The learning achievement of P-W group was much better than W-P group in both the post-test and delay post-test. 2. The P-W, however, perceived higher level of mental effort than the W-P and reached a significant difference in the first lesson and the delay post-test. 3. In the area covering problems, the students did better in squares than in triangles; they did best in 4 cm2 squares and worst in 0.5 cm2 triangles.