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9 9 1 1 5 5 6 6 7 7 + 5 5 + 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 3-2+1=? Manipulatives and number sentences in computer aided arithmetic word problem solving 指導教授： Chen, Ming-puu 報 告 者： Jheng, Cian-you 報告日期： 2006/10/31 Stellingwerf, B.P., Ernest C.D.M.Van Lieshout.(1999). Manipulatives and number sentences in computer aided arithmetic word problem solving. Instructional Science, 27. 459-476.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Introduction Arithmetic word problem solving ： Jaspers and Van Lieshout (1994a, b) – Use of concrete external representations with manipulatives (MAN). – NUM ： open number sentences (a + ? = c and ? – a = b) closed number sentences (a + b= ? and a – b = ?) Ibarra (1982) argued that children have to learn to grasp the semantic relations hidden in the text before they are taught to write number sentences to the word problem.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Introduction Writing closed number sentences forces a direct translation from the text base to the formal mathematical solution model. It does not provide the children with the opportunity to build a more elaborate situation model. Using manipulatives or schematic drawings or rewording the problem may be beneficial in constructing an adequate situation model.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Purpose The purpose of the present study was to gather more information about instruction methods to improve word problem solving skills of children with learning problems.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Method 1. Pretest word problem test number sentence test Raven SPM nonverbal intelligence test Dutch reading test 140 children (mean age 11.3 years, SD = 2.1) →100 children mildly mentally retarded children MAN ONLY-treatment NUM ONLY-treatment COM-treatment ATC-treatment CNTL-group

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Method 2. Trainer guided instruction 3. Computer assisted training 4. Posttest The children had the opportunity to practice with the interface guided by the trainer. 12 individual sessions Maximum length of 30 minutes per session (1)The computer offered the 19 word problem types used to the children. number sentences or solution No feedback No concrete external representation (2) children were allowed to build a concrete external representation with manipulatives. (3) paper and pencil test

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Instructional treatment orientation representation solution

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Hypotheses The NUM and MAN component are both effective tools for children with learning problems. (MAN,NUM,or COM are expected to outperform children in the ATC- treatment.) MAN, NUM, and COM, the ATC contains some elements that may be advantageous (e.g., spoken text, feedback etc.) for learning to solve simple word problems. At least low performing children receiving a NUM- treatment will perform better on decontextualized open and closed number sentences than low performing children receiving a treatment without the use of number sentences.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 NUM COM Result

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 NUM ONLY-treatment and COM-treatment outperformed the children in the CNTL- group. – t(116) = 3.07, p < 0.05 and t(116) = 2.33, p < 0.05, respectively. Children in the MAN ONLY- and ATC- treatment did not perform better on the word problem posttest than children in the CNTL-group.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Result Easier for children to give the correct answer than to write down a correct number sentence. – a significant difference between the proportion of correct number sentences and the proportion of correct answers was found, F(1,116) = 15.22, p < 0.05.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 low competent children had the largest reduction on the “No answer” category and the “Only answer” category.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Discussion Children with learning deficits profit from computer aided instruction programs for solving simple arithmetic word problems. Writing number sentences is not a prerequisite for solving simple word problems. – For word problems with larger numbers a formal mathematical strategy may be more appropriate.

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Discussion Writing number sentences enables the child to use formal mathematical symbols as a symbolic representation of the word problem. Low competent children improved more in writing number sentences and providing correct answers than high competent children. →ceiling effect

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5 5 7 7 2 2 3 3 8 8 7 7 6 6 5 5 3 3 11 + 44 1 1 1 1 Discussion Instructional process: 1.Solved with the aid of manipulatives 2.Use of manipulatives is linked to using open or closed number sentences 3.Manipulatives can be safely omitted

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