國小二年級學生在古氏積木、錢幣、櫻桃表徵問題下的位值概念研究

本研究以桃園市與新北市四所國小之481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（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，本研究以試題反應理論（IRT）分析題目難度與學生能力值，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不同表徵問題表現的差異，本研究獲致以下結論：一、七成的二年級學生已達層次三「理解期」，代表已建構二位數位值概念，並清楚十位與個位的分別。二、二年級學生在測驗中的錢幣問題上有最好的表現，古氏積木與櫻桃問題則沒有分別。若單純看十位題目的表現，則學生在錢幣問題的表現優於古氏積木問題，且古氏積木問題的表現優於櫻桃問題。三、無十單位結構的教具，如櫻桃表徵，因不容易連結十個為一個的單位，所以學生在進行位值的判別時，表現較不好。本研究根據以上研究結果提出建議，作為教師、教科書編輯者及未來研究者的參考。

關鍵字

表徵問題；位值概念；古氏積木；試題反應理論

並列摘要

The participants of this study were 481 second-year students from four elementary schools in Taoyuan and New Taipei City. The aim was to examine students’ development levels and performance of place value with questions in three representations: base-ten blocks, coins, and cherries. The research tool was a self-developed test consisting of 18 questions both on units and tens places. Based on the students’ test results, item response theory (IRT) was used to analyze the questions’ difficulty level and the students’ abilities. The questions were sorted according to difficulty level, with the passing criterion being four-fifths of the questions on units and tens places. The students’ place value development was divided into three levels: (i) confused period, (ii) establishment period, and (iii) understanding period. Next, variance analysis was used to analyze the differences in performance for problems with different representations. The conclusions of this study were as follows: i. Among the participants, 70% had achieved Level 3 (understanding period), meaning that they had established the concept of two-digit place value and were clear about the tens and units places. ii. In the test, the students performed the best on problems represented by coins. However, there was no difference in performance between problems represented by base-ten blocks and cherries. Looking solely at the questions on tens place, the students performed better on problems represented by coins than by base-ten blocks and better on those by base-ten blocks than by cherries. iii. Teaching aids without a tens place structure (such as cherries) made it more difficult for students to link ten units into one tens, which explained their poorer performance when determining place value. Recommendations are proposed based on the aforementioned research findings, which can serve as a reference for teacher, textbook compilation, and future researcher.