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Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study Reimer, K., & Moyer, P. S. (2005). Third-graders learn about fractions using virtual manipulatives: a classroom study. The Journal of Computers in Mathematics and Science Teaching, 24(1), 5-25. 指導教授： Chen, Ming-puu 報 告 者： Jheng, Cian-you 報告日期： 2006/09/01

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What are Virtual Manipulatives? Virtual nanipulatives are essentially replicas of physical manipulatives placed on the World Wide Web in the form of computer applets with additional advantageous features. Using virtual manipulatives does not insure learning. One feature that makes virtual manipulative applets advantageous for mathematics instruction is their capability to connect dynamic visual images with abstract symbols - one limitation of physical manipulatives.

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Limited Research on Virtual Manipulatives Teachers wish to use virtual manipulatives for instruction? Teachers must have an understanding of how to use representations for mathematics instruction. Teachers must be prepared for situations where computers may not be reliable. Internet connections are not working properly.

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Computer-based manipulatives have produced inconclusive results Due to a variety of design and sampling characteristics that may affect student achievement results. A varietyof studies in which "computer manipulative programs" were examined for their ability to support student learning in mathematics confirmed positive results in student achievement and attitudes (Char, 1989; Clements & Battista,1989; Kieran & Hillel, 1990; Thompson, 1992).

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Research questions (1)What impact do virtual fraction manipulatives have on students' conceptual and procedural understanding of fractions? (2)What are students' attitudes about using virtual fraction manipulatives during the learning of fractions?

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Purpose The project serves as an impetus for teachers and researchers to use virtual manipulatives in teaching mathematics in other classroom projects.

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Method-Participant 19 third-grade students. A diverse student population. Caucasian, Hispanic, African-American, Asian, and Middle-Eastern.

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Method-Procedure Pretest conceptual knowledge of fractions procedural computation skills with fractions Introduced to the virtual manipulative applets. - Base 10 blocks applet. - familiar with computer applets. - they would not be practicing fraction skills using this applet. The teacher taught a unit on fractions in the computer lab. - A one-hour lesson on each day(4 days). - An introduction to the virtual manipulative applet → Several mathematical tasks for the students. (Students worked independently on the activities.) Pretest ─ conceptual and procedural knowledge Interviews Attitude Survey First week second week

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Method-Procedure Second Week National Library of Virtual Manipulatives Day 1 Fractions - Parts of a WholeFractions - Parts of a Whole Day 2 Pattern BlocksPattern Blocks Day 3 Equivalent FractionsEquivalent Fractions Day 4 Comparing FractionsComparing Fractions

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Method-Data Sources The pre and posttests of conceptual knowledge. four questions and students were asked to explain their thinking using writings and drawings. For example, one question on this assessment asked students to draw a picture representation of the fraction one-fourth and explain their drawing. incorrect(0), partially correct(1), and entirely correct(2) This gave a total of 16 points for the pretest and posttest on conceptual knowledge.

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Method-Data Sources The pre and posttests of procedural knowledge. These questions required students to demonstrate fraction knowledge using computation and symbols only. For example, questions on this assessment asked students to compare fractions such as 4/8 and 1/4 or to name a fraction equivalent to 1/2. This test were either correct(1) or incorrect(0). Total of 14 points on the test.

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Method-Interviews Students were asked the following questions: 1.Tell me what you're doing? 2.Can you explain to me how you are using the virtual manipulative? 3.How is this applet helping you learn about fractions?

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Method-Attitude Survey a happy face for yes (which represented a positive response). a straight face for maybe (which represented a neutral response). a sad face for no (which represented a negative response). The questionnaire was administered in the classroom three days after students used the virtual manipulatives for the fraction unit. anonymous

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Results- Conceptual Knowledge Assessment The virtual fraction manipulatives would impact students’ conceptual knowledge. - 10 out of 19 (53%) students improved their scores. - 5 of 19 (26%) students’ scores decreased. - 4 of 19 (21%) students had scores that stayed the same. significant

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Results- Procedural Knowledge Assessment Because the pretest scores on this assessment were so high, this allowed very little room for improvement in students' scores. No significant - 7 out of 19 (37%) students improved their scores. - 5 of 19 (26%) students' scores decreased. - 7 of 19 (37%) students had scores that stayed the same.

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Results- Student Attitudes Questionnaire 59% positive responses, 23% neutral, and 18% negative.

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Results- Interaction Interviews The virtual manipulatives were helping students learn about fractions. "It's like a computer game that helps me learn" (Student #18). The students liked the immediate feedback they received on the virtual manipulative applets. "If I was wrong, it [the virtual manipulatives applet] would tell me the information. Like if the denominator was wrong, then I would switch that" (Student #1); The virtual manipulatives were easier and faster to use than paper-and-pencil. "It's easier on the computer because it's harder to draw them [fractions] on paper" (Student#5). Students had a positive experience while working with the virtual manipulative. "Cool! This is fun!" (Student #4).

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Results- Interaction Interviews Students indicated that the virtual manipulatives were helping them learn, they were easy to use, they gave specific feedback, and they were enjoyable to use.

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Discussion Practicing with the visual computer images could have enhanced students' abilities to explain and represent their thinking using pictorial models. These specific instances of feedback in written form on the computer may have served the function of correcting or highlighting students' errors, making students more aware of their own misconceptions.

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