國小二年級學生在古氏積木、錢幣、櫻桃表徵物問題下的位值概念研究

Second Graders' Concepts of Place Value Represented by Problems Involving Cuisenaire Rods, Coins, and Cherries

本研究以桃園市與新北市四所國小之 431 位二年級學生為研究對象，並以自編的位值概念測驗 （個位問題 18 題，十位問題 18 題）為研究工具，探討二年級學生在三種表徵物（古氏積木、 錢幣與櫻桃）問題下的位值概念發展及表現。根據學生的測驗結果，本研究將題目依難易度排 序後，以通過個位、十位題目之五分之四為判斷通過的標準，將學生的位值發展分為三個層次： （一）渾沌期；（二）建構期；（三）理解期，接著以變異數分析考驗學生在不同表徵物問題表現 的差異。本研究的主要發現為：（一）63.6%的國小二年級學生已建構二位數位值概念，達層次 三「理解期」，24.6%的學生在「建構期」，而 11.8%的學生還在層次一「渾沌期」；（二）學生在 三種表徵物的個位問題並未出現表現差異，但在十位問題上，錢幣表徵問題的表現優於古氏積 木表徵，且古氏積木表徵優於櫻桃表徵；（三）學生在非例行性十進位及一個一個數的十位問題 表現不如例行性十進位問題。

The objective of this study was to examine students' developmental levels and performance in relation to the topic of place value. Accordingly, questions featuring three mathematical representations were used: cuisenaire rods, coins, and cherries. A total of 431 second-grade students were enrolled from four elementary schools in Taoyuan and New Taipei City. The research tool was a self-developed test with 18 questions on place value for units and tens. On the basis of the students' test results, questions were sorted according to difficulty, and four-fifths of the questions on ones and tens were used as the criteria to create three levels for classifying students' development in relation to place value: chaos level, construction level, and understanding level. The main findings of this study are outlined as follows: (1) 64.6% of the second-year elementary school students constructed a two-digit place value concept and reached the "understanding level," 24.6% were at the "construction level," and 11.8% remained at the "chaotic level." (2) No differences existed in students' performance in the three representations of the problems involving units. However, on the problems involving tens, students performed better in the coin representation problem than they did in the cuisenaire rods representation and better in the cuisenaire rods representation than they did in the cherry representation. (3) For problems involving tens, students performed better in problems represented in routine manners than in non-routine and oneby-one representations.