幼兒數學認知診斷評量工具初探

A Preliminary Study on Mathematic Cognitive Diagnostic Assessment for Kindergarten Children

本研究主要的目的在發展一份適合幼兒園大班幼兒之數學認知診斷評量工具，藉以分析個別幼兒之數學認知屬性。「大班幼兒數學認知診斷評量工具」主要是測量大班幼兒20以內之非正式數學能力，內容包含計數、比較、加法、和減法等四個學習面向，試題涵蓋其體表徵、圖像表徵、數字表徵、十的合成與分解、和十進位等五種數學認知屬性。本研究採取便利取樣法，以桃園縣兩所私立幼兒園大班之65位幼兒進行預試，試題項目分析顯示本評量項目之難度偏易，但符合幼兒診斷性評量的目的；Cronbachα係數為.713，顯示內部一致性良好；Spearman等級相關顯示，本測驗與外在效標「教師評定」之間其有顯著之中度正相關；在單因子變異數分析中，不同「教師評定分組」之幼兒在「總分」及若干變項上有顯著差異，顯示本測驗具有良好之效標關聯效度。綜言之，「大班幼兒數學認知診斷評量工具」具有良好之信度與效度，且操作簡便，具有認知診斷功能，可提供認知診斷資訊給幼兒園教師與父母參考。

The purpose of this study is to develop a Mathematic Cognitive Diagnostic Assessment for kindergarten children (MCDA-KC) and to analyze the mathematic cognitive attributes of the individuals. The MCDA-KC focuses on children's informal mathematic abilities on positive integers less than 20, and it includes four learning aspects-counting, comparison, addition, and subtraction, and contains five cognitive attributes-concrete representation, iconic representation, number representation, composition and decomposition of 10, and base ten number concept. The convenience sampling had been used in this study. Sixty-five kindergarten children from two private preschools in Taoyuan County had taken the test. According to the item analysis, the MCDA-KC is tend to be easy for kindergarten children, but is suitable for the purpose of the cognitive diagnostic assessment. Cronbach α is .713 which indicates good internal consistency reliability of the MCDA-KC. Spearman's rank correlation shows that there is a moderate, positive correlation between the test and teacher's rating, and the scores of children within different teacher's rating groups were significantly different in one-way ANOVA. These results reveal that the test has evidences of good criterion-related validity. In summary, the MCDA-KC has good reliability and validity and is easy to use and has diagnostic function, and it can provide cognitive diagnostic information for kindergarten teachers and parents.