本研究旨在探討幼童數量推理能力的發展，並分析不同族群幼童，在數量判斷上的表現。本研究的樣本取自美國夏威夷州小學附設幼稚園二十名及台灣國小附設幼稚園及私立幼稚園各二十名幼童，男女各半，平均年齡5.5歲。研究方法採用評量、觀察與訪談。爲瞭解幼童數量推理能力的表現，本研究發展出兩種實物評量對不同族群的幼童施測。幼童在進行兩組數量的比較時，以不經計算，用目測估算解題，比較兩數量的大小。研究結果顯示在具體實物（如玩具動物）評量中，幼童答對75%以上，符合具體認知發展模式，且沒有群族差異；再以半抽象的物件測，如動物貼紙測幼童，發現幼童在判斷2:3比例的量數上，表現佳，然而在比較5:6的數量時，表現較差，因爲幼童會受到物件大小及排列面積的影響。此外，台灣的幼童答對率在一些數量推理上高於夏威夷的幼童。最後，根據研究結果提供幼童教學建議：1.幼童數學教學應從數量概念學習著手，才進入數數的練習，以幫助幼童建立正確數的概念；2.結合幼童的生活經驗，讓幼童有具體操作、評估、比較與預測的機會，爲幼童奠下良好數學基礎。

The purpose of this research was to explore the development of quantitative reasoning in young children, and also to analyze the numerosity discrimination of children from different groups. The results will be applied to early childhood mathematical pedagogy. The research subjects came from three kindergartens in elementary schools in Hawaii and Taiwan. Each research group has twenty children. In addition, twenty children were sampled from a private kindergarten in Taiwan. Each school had twenty children who were equal in gender and were an average of. years old. Research methods used assessment, observation and interview. There were two objective scales to evaluate the children's quantitative reasoning. During the process of the research, the researcher gave opportunities to children who operated objects and named objects, and practiced a small aggregate amount before the formal test. At the same time, the researcher asked the children, without actually counting, but with a quick look with their eyes to estimate two aggregate amounts, then, solved problems. The result showed that the children had a 75% success rate to discriminate numerosity in real objects that fit the developmental model of cognition, but without the cultural difference. Furthermore, when using the scale of half obstacle objects (sticker) to test the children, the result revealed that children performed the 2:3 ratios to discriminate numerosity better than 5:6 ratios. However, Taiwanese children had correct answer scores that were higher than those of Hawaiian children on some problem items. Moreover, to apply the research results to early childhood instruction: 1. To start the concept of quantity learning, then to practice counting to help children have good number concepts. 2. To combine the children's life experiences to give them opportunities of operation, estimation, comparison and prediction so that those children can have a good mathematics foundation.