國小學童計算能力之測量、發展軌跡與預測路徑

The Measurement and Developmental Trajectories of Arithmetic Competences and Prediction Routes of Arithmetic Competences in Elementary Students

國外研究指出，學童的計算能力發展從「數數」開始，逐步進展到「分解與重組」以及「數學事實提取」能力，最後再發展出成熟的「複雜計算」能力，而這些能力之間有其彼此影響的預測路徑。因此，本研究之目的乃以「基本數學核心能力測驗」作為研究工具，透過探索式因素分析和精熟分析的方法來探討臺灣國小一至六年級學童計算能力之發展軌跡，並以結構方程模式探討這些能力之間彼此的預測路徑。研究結果顯示：小一學童之個位數加法和減法事實提取能力尚未發展成熟，到了二年級則發展成熟，據此推論臺灣學童從數數進展到加減法事實提取能力發生在小一和小二之間，而乘法事實提取能力到小三也發展成熟；「分解與重組」能力在小一和小二尚未從「複雜計算」能力中分化出來，直到小三才分化出來形成獨立的因素。計算能力之間預測路徑的研究結果顯示，低年級學童的「數學事實提取」能力可以有效預測「複雜計算」能力，中年級學童的「數學事實提取」能力可以分別預測「分解與重組」和「複雜計算」能力，但「分解與重組」仍無法預測「複雜計算」能力，其到高年級才能進一步預測「複雜計算」能力。本研究結果與國外研究比較，對我國學童之計算能力發展提出建議。

The arithmetic competences were approved to develop from counting to decomposition and regrouping, math fact retrieval, and then complex calculation. Furthermore, math fact retrieval could predict the competence of decomposition and regrouping and complex calculation, respectively. And the decomposition and regrouping could predict the complex arithmetic competence. Two purposes of this study are: Firstly, to investigate the trajectories of 1st to 6th graded students' arithmetic competences in Taiwan; and secondly, to explore the predictive relation of these arithmetic competences of students of each grade. The results revealed that the trajectories of arithmetic competences from counting to math fact retrieval happened between grade one and grade two in Taiwan. However, the strategy of decomposition and regrouping had not been extracted from complex calculation in grade one and two. This was extracted as an independent calculation competence since grade three and after. The math fact retrieval could predict the complex calculation in grade one and two. At grades three and four, the math fact retrieval could predict complex calculation and decomposition and regrouping, respectively, but the competence of decomposition and regrouping could not predict the complex calculation. However, this predictive route would be significant statistically in grade five and six. The implication, limitation and suggestion of this study would be mentioned in these regards.