年齡和學校教育，對臺灣兒童數學發展的影響

Effects of Age and Schooling on Taiwanese Children's Development of Basic Mathematics Skills

兒童的數概念發展主要受到年齡與學校教育影響，過去研究（Bisanz et al., 1995）發現數量保留概念受到年齡影響比較大，心智運算（Mental arithmetic, Bisanz et al., 1995）與加法計算策略（Miura & Naito, 2001）受到學校教育影響比較大。本研究採入學截斷設計（cutoff design, Bisanz et al., 1995）探討年齡和學校教育如何影響臺灣兒童在加減法可逆、數量估計、數感、工作記憶的發展，並以改編自Naito與Miura（2001）提出的年齡與學校教育因素影響模式來分析。本研究受試者包含年長的大班幼兒（Old Kindergarteners: OK組）、年幼的一年級兒童（Young 1st graders: Y1組）與年長的一年級兒童（Old 1st graders: O1組），其中OK與Y1年齡相同但學校教育不同，Y1與O1學校教育相同但年齡不同，所有的受試者在學期初（T1）與學期末（T2）接受一次測驗。研究發現，加減法可逆、數量估計的發展是受到年齡影響，O1組表現優於Y1組與OK組，Y1組與OK組有相似的表現；數感、工作記憶是受到學校教育影響，O1組與Y1組的成長幅度大於OK組。

Young children's math learning can be influenced by either age (e.g., number conservation, Bisanz et a., 1995) or schooling (e.g., mental arithmetic, Bisanz et al). This study thus adopted a cutoff design (Bisanz et al., Miura & Naito, 2001) to separate the schooling factor from the age factor on children's development of the addition-subtraction inverse principle (ASIP), numerosity estimation, number sense, and working memory. Three groups of children were investigated, in which older kindergarteners and younger 1st graders differed in schooling, while younger 1st graders and older 1st graders differed in age. Results showed that development of ASIP and numerosity estimation improved as a function of age, while children's development of number sense and working memory improved as a function of schooling. The findings suggest that age as well as schooling are important factors in developing children's mathematical concepts.