二至三歲幼兒的數量表徵發展

Development of Quantity Representations for 2-3-Year-Old Toddlers

過去研究發現幼兒的數量表徵能力與未來的數學表現具有高相關性，學齡前階段能使用符號來表示數量的幼兒，在未來學習數學時較不易產生障礙。學齡前幼兒如何習得數字符號一直受到認知發展學者的注意，本研究探究二至三歲幼兒在數量表徵類型的發展，以及檢視幼兒的數能力（唱數與點數）與數量表徵發展的關係。本研究的對象為46位二歲與三歲幼兒（二歲20位，三歲26位），利用個別晤談，請受試幼兒畫下看到的數量。研究發現多數幼兒使用三種數量表徵方式，分別為特異表徵、圖畫表徵與形象表徵；幼兒在較小的數量（數量1、數量2）傾向使用形象表徵，而在較大的數量（數量4、數量5）則使用特異表徵，幼兒在不同大小數量表徵有水平落差的現象（horizontal ‘decalage）。此外，多數二歲幼兒使用特異表徵，而多數三歲幼兒傾向使用形象表徵與圖畫表徵，幾乎沒有二歲與三歲幼兒使用符號表徵。此外，幼兒的數量表徵發展與數能力（與點數）有正相關，數能力表現較好的幼兒傾向使用較成熟的數量表徵。

The aim of current research was to investigate 2–3-year-old toddlers’ development of quantity representations and examined how their numerical competencies (e.g., oral counting and enumeration) influence their quantity representations. Twenty 2 year olds (31 months) and twenty-six 3 year olds (42 months) toddlers from three private preschools representing high SES participated in this study. Firstly, the pictures of apples in number sequence of one, two, four, and five apples were presented to the participants who were then asked to put something on the papers to show how many apples were on the papers. Results showed that four types of responses, idiosyncratic responses, pictographic responses, iconic responses, and symbolic responses were observed hierarchically. Toddlers tended to represent smaller quantities in a more sophisticated way than larger quantities, as décalage effect was suggested. Three-year-old toddlers represented quantities using more mature responses (e.g., pictographic responses and iconic responses) than their 2-year-old counterparts who typically responded idiosyncratically. Only a few participants used symbolic responses. Furthermore, toddlers’ quantity representation was highly correlated to their numerical competencies.