本研究探討國小二年級兒童數量概念的發展與數量的推理能力，在研究設計中，以兩個階段的評量對兒童這些表現加以施測，第一階段以實物施測，經三個月之後，再以半具體的物件施測。為進一步瞭解兒童解決問題的歷程，施測過程中觀察兒童推理的策略，並在施測後對兒童進行訪談。 研究樣本取自台灣國小二年級及美國夏威夷州小學二年級學生，各地取二十名，另外，為瞭解二年級學生對辨識數量的策略是否與成人的方式相似，樣本還包含二十名成人。研究結果顯示，台灣和夏威夷兒童在實物評量的表現上，當兩個數量比例相近時，兒童的答對比率達到90%，反而在判斷半具體物件的數量時，兒童正確率降低，尤其當兒童比較兩組數量比例相近(5：6)時，兒童答對率低於65%。至於兒童在解題策略方面，發現二年級兒童答對百分之百的學生與答對百分之分成人的解題策略是相似的，他們不受物件間距效應影響，而答對90%學生，在辨識數量時，不受物件大小影響，卻受到間距效應的影響。

The purpose of the research is to explore the second graders’ concept of numerosity development and quantitative reasoning. For this purpose, there are two stages of trials for the children. The first trial is concrete objects. After three months, the children accepted the second trial of half concrete objects. However, to understand how the process of solving problems of children is necessary, the researcher observed how children used strategies to discriminate numerosity. After that the researcher interviewed students. The research sample came from second graders of Taiwanese and Hawaii Elementary schools. Each place had 20 students. In addition, in order to understand whether numerosity discrimination strategy in children was the same as adult’s or not? The sample included 20 adults. The result of the research showed that Taiwanese and Hawaiian children reached up to a 90% rate of correct answer in the trial of real objects. But in the trial of half concrete objects, the rate of correct answers was down to 65%, especially when children compared two quantities of 5:6 ratio. As for strategy, the strategies of the children who completed correct answers were the same as the adult who did whole correct answers. Because their discrimination was not influenced by distance effect, they could judge the numerosity correctly. However, the children who got 90% correction were impacted by distance effect but not influenced by the size of the object.