兒童在數位式數學實驗情境下的發現學習

Learning by Discovery: Children's Performance in a Computer-Based Geometry Lab

「發現」是知識創建的必經過程，在科技的支援下，學習者在獲得概念的同時也能透過數位虛擬情境體驗數學家發現的歷程。本研究以InduLab作為環境，探討四年級兒童在數位式數學實驗情境中變項操作經驗對幾何性質（內角和性質與外角性質）發現的影響，以及兒童在歷程中的實驗行為。受試者隨機分派到兩個可操作變項不同的InduLab版本進行學習。43位有效樣本的結果顯示，內角和性質的發現比外角性質困難，直接操作變項的經驗顯著提升內角和性質的發現率。在實驗行為上，受試者共產生四類實驗策略，性質的發現不受策略的影響，且以使用改變所有變項（change all variables）的策略為主，這顯示兒童的實驗行為仍缺乏系統性；而策略使用與正例間的顯著相關顯示正例可能影響策略的選擇。

Knowledge is constructed during the process of discovery. With the support of a computer-based environment, a learner can acquire concepts by imitating the ways in which mathematicians make discoveries. The purpose of this study is to investigate how the experience of manipulating variables affects children's discovery of two geometrical rules—the interior angle property (the interior angles of a triangle add up to 180 degrees) and the exterior angle property (an exterior angle of a triangle equals the sum of the two opposite interior angles). We are also interested in understanding what experimental strategies children use to discover the rules. Fifty-two fourth grade students participated in this study. They were randomly divided into two groups: "interior angle" and "exterior angle" groups. It was found to be harder for students to discover the interior angle property than the exterior angle property. Moreover, the experience of manipulating variables significantly affected the discovery of the interior angle property. We found that four strategies were used by the students and most students used at least one of them. The "change all variables" strategy was used frequently and the discovery process of these children was not very efficient. Furthermore, the strategy chosen by a student tended to depend on the positive reinforcement of coming up with positive instances, which led students to think that positive instances were the only useful kind of information in the discovery process.