五歲與六歲幼兒加減法可逆概念的理解

Comprehension of Addition-Subtraction Inverse Principle in 5- and 6-year-old Children

加減法可逆概念係指一個起始量在加減相同數量之後，不會改變原本的數量，即a+b−b = a，為加減運算邏輯中相當重要的概念（Baroody & Lai, 2007）。過去研究大多使用單一工具探究幼兒在加減法可逆原則的理解程度，然而單一工具有其限制，故本研究同時採用兩種任務作為測驗工具，客觀地釐清五歲與六歲幼兒在加減法可逆概念的理解情形與差異。研究對象為五歲與六歲幼兒各20名，材料為代數推理（森林小鳥、池塘青蛙）與運算捷徑任務（籃子蘋果、水草小魚），四種情境皆含「可逆題」（a+b−b）與「標準題」（a+b−c），測驗題目以情境式動畫呈現。研究發現，五歲與六歲幼兒的加減法可逆概念理解程度在代數推理及運算捷徑任務之間表現類似，已經達到基礎理解程度，而且在年齡之間並無表現差異。

Addition-Subtraction Inverse Principle (ASIP), understanding that adding and subtracting the same number will leave the original amount unchanged, plays an important role in children’s arithmetic development (Baroody & Lai, 2007). Previous studies on ASIP mostly adopted either computational shortcut tasks or algebraic-reasoning tasks, in which the former was targeted on procedural knowledge and might overestimate children’s ASIP and the latter on conceptual knowledge and might underestimate children’s ASIP. In this study, we examined children’s comprehensive understanding of ASIP using both computational shortcut tasks and algebraic-reasoning tasks, which were presented through 4 animations designed to attract these preschoolers’attention. By doing so, we could clearly reveal children’s unbiased understanding of the ASIP. Twenty 5-year-old and 6-year-old children (N = 40) from central Taiwan participated. Instruments included algebraic-reasoning tasks (e.g., forests and birds) and computational shortcut tasks (e.g., baskets and apples), in which 6 inversion trials and 6 standard trials were created for each scenario. The results showed that Taiwanese 5-year-old and 6-year-old children’s understanding of ASIP was similar on both tasks and these participants already exhibited marginal competence on ASIP. Interestingly, participants performed better on the inversion trials than on the standard trials in the computational shortcut tasks while performing similarly on both trials in the algebraic-reasoning tasks. Finally, educational implications and future research questions are provided.