國小低年級學生在不同表徵物問題的位值概念研究

Study of First and Second Graders’ Concept of Place Value in Problems of Different Representation Objects

本研究以桃園市兩個國小之一年級學生326人及二年級學生340人為研究樣本，並以位值概念測驗收集研究資料，其中位值概念測驗的題型是依表徵數值物的不同區分為雞蛋問題、錢幣問題及古氏積木問題，主要的研究目的在瞭解低年級學生於不同表徵物問題下的位值概念表現。研究結果發現：一年級學生的位值概念多處於只認識數字而不知其意義的階段，而半數的二年級學生則已建構二位數系統的位值概念；低年級學生在雞蛋與錢幣問題的位值概念表現並無差異，但在古氏積木問題的表現則較差。不論是一年級學生或二年級學生，在問十位數數碼表示的意義時，答對率最高的都是錢幣問題，因此錢幣應是比古氏積木更能幫助學生建構十位數位值概念的有效輔具。

The purposes of this study were to investigate the development of the first and second graders’ concepts of place value. The subjects were students selected from 326 first and 340 second graders of two elementary schools in Taoyuan City. The study used the place value concept test as the examining tool. Questions in the place value concept test were divides into three representation objects: Cuisenaire， coin， and egg. Research results were: (1)The first graders knew number symbol， but almost didn’t understand the meaning of number representation. However， about 50% of the second graders already constructed place value concept of the two-digit number system. (2)Significant performance differences were found among questions with the three representation objects for the first and second graders. In fact， no performance differences were found between questions with coin representation and egg representation. It was more difficult to understand questions in Cuisenaire representation for the first and second graders. To help lower graders’ understanding a number’s place value of tens， coin representation might be more efficient than Cuisenaire representation.