手勢融入範例對低能力學生運算與幾何學習的影響

The Effects of Gesture on Low-Ability Students' Learning of Arithmetic and Geometry Using Worked Examples

體現認知的研究發現，學生在幾何學習時以手勢配合描摹幾何圖，比起限制手勢所獲得的學習 效果好，但在非幾何的材料上卻不一定有此體現效果。本研究以整數加減運算與平行線截角性 質為材料，並經測驗篩出整數加減運算尚不純熟的七年級生進行實驗。在 18 位受試者的前導實 驗以改善範例、練習，和程序之後，正式實驗的 52 位學生被隨機分派到使用手勢的實驗組與無 手勢的控制組，進行範例學習與後測。三至四個月之後進行延宕測驗與訪談。結果顯示，兩組 在整數加減的學習時間、答對率，以及認知負荷皆無顯著差異，但在延宕測驗答對率中有四種 題型顯現組間顯著差異。平行線截角性質的實驗組後測遠遷移題答對率比控制組高，此一效果 未出現在延宕測驗。綜合實驗一和二，在已學過的整數加減運算上未見手勢的效果，而在未學 過的幾何教材上，描摹具有即時效果，但未具保留效果。體現認知效果在數學教育的實徵研究 與實務應用上，尚有廣大的發展空間。

Research on embodied cognition has found that students who use gestures to trace geometric figures while learning geometry perform better than students who restrict their use of gestures. However, this effect may not appear in non-geometric learning. This study investigates this through the tasks of adding and subtracting integers and angle relationships involving parallel lines. The participants were lowability seventh graders unable to master integer addition and subtraction on a screening test. A pilot study was conducted with 18 seventh graders, and the results were used to improve the worked examples, practices, and procedures. In formal experiments, 52 students were randomly assigned to experimental and control groups, where they studied worked examples either with or without gestures. A delayed test and interview were conducted three to four months after the experiment. The results showed that the experimental group did not differ from the control group in learning time, cognitive load, and accuracy in Experiment 1, but the accuracy of the two groups for the four question types was different in the delayed test. In Experiment 2, the accuracy of the experimental group was higher than that of the control group on the post-test far transfer problems. However, this effect was not observed in the delayed test. In summary, the present study found good gesture design combined with examples that participants have learned, enhance student learning. Also, for geometric materials that participants have not learned, gestures led by principles in textbooks can greatly enhance learning. Both the research and practice of mathematics education has considerable potential to explore the effect of embodied cognition.