應用認知負荷理論的數學解題教學實驗

The Application of Cognitive Load Theory to Mathematical Problem-Solving Instruction

自1980年代起，以認知負荷理論（cognitive load theory）為理論依據，所進行的數學解題教學實驗中，大多顯示有助於提升學生的數學解題能力。認知負荷理論主張人類的認知資源是有限的，如果學習活動所需的認知資源，超出學習者所能運用的認知資源，則會造成學習者的認知負荷過重，導致學習活動的失敗。認知負荷理論認為解題者是否具有適切的問題基模，是解題成功的重要因素，而透過範例教學（worked example instruction），有助於學生獲得有效的問題基模，進而提升學生的解題能力。\r本研究以兩班國小五年級學生為研究對象，實驗組與控制組的學生皆為34位。實驗組接受範例教學法，控制組接受傳統教學法。以實驗組與控制組的教學法為自變項，數學成就測驗前測為共變量，數學成就測驗後測為依變項，所進行的共變數分析研究結果顯示，實驗組調整後的數學成績（M’=84.93）顯著高於控制組調整後的數學成績（M’=71.98）。

Advocators of the Cognitive Load Theory claimed that human cognitive resources were limited. That is to say， if the cognitive resources required for learning activities outran those which learners were able to make use of， it would cause burden on learners’ cognitive load and therefore would lead to failure in learning. The Cognitive Load theorists believed that whether a problem solver has optimal problem schemas was crucial and contributed to the success of problem-solving. Accordingly， through the worked example instruction， learners would acquire effective problem schemas and thus improve their problem solving ability.This study was involved with 68 fifth grade students， who were divided into the experiment group and the control group. The experiment group learned mathematics through the worked example instruction and the control group through the traditional instruction. The results showed that the students who received the worked example instruction gained significantly higher grades (M’=84.93) than those who received the traditional instruction (M’=71.98) in a posttest for mathematical achievement.