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 one-by-one representations.
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Second Graders’ Concepts of Place Value Represented by Problems Involving Cuisenaire Rods, Coins, and Cherries
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