以微觀發展論設計與情境式動畫探究5歲幼兒加減法可逆原則的認知發展

A Microgenetic Study with Animations on 5-Year-Old Preschoolers’ Development of the Addition-Subtraction Inverse Principle

「加減法可逆原則」意指加減同一數量，並不會改變原本的量，是幼兒理解算術的關鍵。隨著數位技術成熟，許多教師使用情境式動畫輔助學生學習，動畫能提高學習興趣與專注度，進而提升數學理解。本研究目的在使用情境式動畫探索5歲幼兒在加減法可逆原則的表現，並以微觀發展論設計，檢視5歲幼兒在加減法可逆原則的習得歷程。34位5歲幼兒參與本研究，將幼兒分為助長組（全可逆題，a+b-b）和一般組（一半可逆題與標準題，a+b-c），接受四個練習與兩個學習成效檢視階段。本研究以學習經驗的影響、策略選擇的改變、學習速率的改變與策略多樣化的改變檢視幼兒的認知發展，編製七個加減法情境動畫，並使用Superlab呈現動畫與記錄幼兒的答題反應與時間。研究發現，以學習經驗而言，助長組幼兒比一般組幼兒更快發現加減法可逆原則；以策略選擇而言，助長組幼兒比一般組幼兒更常使用成熟策略；以學習速率而言，助長組幼兒習得成熟策略後會更穩定持續使用；以策略多樣化而言，助長組幼兒使用策略種類的數量多於一般組幼兒。此外，即使幼兒已習得成熟策略，他們仍然會使用不成熟策略，呼應R. S. Siegler的重疊波浪模式理論，幼兒會同時使用成熟與不成熟的策略解題。

Addition-subtraction inverse principle (ASIP) plays an important role in children’s mathematics learning. Animations have been widely used to facilitate learning because previous studies have repeatedly supported that animations could successfully attract attention and increase understanding. We examined children’s development of ASIP using the microgenetic design with 3 test sessions and 4 training sessions. Using trial-by-trial analyses, we could clearly unveil children’s understanding of the ASIP. Thirty four children participated, half of them being assigned to the facilitative group (inverse problems only: a + b – b) and the other half to the nonfacilitative group (half inverse problems and half standard problems: a + b – c). Children’s developments of strategy change, rate change, and variability of change were examined. In order to attract these preschoolers’ attention, we created 7 animations controlled by Superlab, in which we recorded children’s answers and reaction time. Results showed that children in the facilitative group improved significantly more than those in the nonfacilitative group, with the former adopting more mature strategies than the latter, and the former starting to adopt the mature strategies sooner than the latter. Children in the facilitative group adopted more numbers of strategies than those in the nonfacilitative group after the training. Surprisingly, some children still used the computation strategy even after they already discovered the shortcut strategy, which might be explained by the overlapping wave model and the fact that persistent use of the well-established strategies is a fundamental characteristic of human cognition.