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| 篇名： | 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 byProblems Involving Cuisenaire Rods, Coins, and Cherries |
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| 作者： | 蔡曉回、袁媛Hsiao-Hui Tsai, Yuan Yuan |
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| 刊名： | 臺灣數學教育期刊/Taiwan Journal of Mathematics Education |
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| 出版者： | 台灣數學教育學會、國立臺灣師範大學數學系共同發行Department of Mathematics, National Taiwan Normal UniversityTaiwan Association for Mathematics Education |
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| 中文摘要： | 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。 |
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| 英文摘要： | The objective of this study was to examine students’ developmental levels and performance in relationto the topic of place value. Accordingly, questions featuring three mathematical representations wereused: cuisenaire rods, coins, and cherries. A total of 431 second-grade students were enrolled from fourelementary schools in Taoyuan and New Taipei City. The research tool was a self-developed test with18 questions on place value for units and tens. On the basis of the students’ test results, questions weresorted according to difficulty, and four-fifths of the questions on ones and tens were used as the criteriato 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 andreached 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 theproblems involving units. However, on the problems involving tens, students performed better in thecoin representation problem than they did in the cuisenaire rods representation and better in thecuisenaire rods representation than they did in the cherry representation. (3) For problems involvingtens, students performed better in problems represented in routine manners than in non-routine and oneby-one representations. |
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| 關鍵詞： | 古氏積木、位值概念、表徵、例行性十進位Cuisenaire rods, Place value, Representation, Canonical base 10 |
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| DOI： | 10.6278/tjme.202010_7(2).002 |
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