A Computational Model of Fraction Arithmetic.

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model o...

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Detalles Bibliográficos
Publicado en:Psychological Review Vol. 124; no. 5; pp. 603 - 626
Autores principales: Braithwaite, David W., Pyke, Aryn A., Siegler, Robert S.
Formato: Artículo
Publicado: American Psychological Association Oct2017
Materias:
Acceso en línea:Ver este registro en EBSCOhost
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      dt: Oct2017
      vid: 124
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      pub: American Psychological Association
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        au:
          Braithwaite, David W.
          Pyke, Aryn A.
          Siegler, Robert S.
        affil:
          Carnegie Mellon University
          Beijing Normal University
      su:
        Learning
        Arithmetic
      sug:
        subj:
          Learning
          Arithmetic
      keyword:
        fraction arithmetic
        fractions
        numerical cognition
        production systems
        textbook analysis
        fraction arithmetic
        fractions
        numerical cognition
        production systems
        textbook analysis
      ab: Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it with the problems from a widely used textbook series. The simulation generated many phenomena of children's fraction arithmetic performance through a small number of common learning mechanisms operating on a biased input set. The biases were not unique to this textbook series--they were present in 2 other textbook series as well--nor were the phenomena unique to a particular sample of children--they were present in another sample as well. Among other phenomena. the model predicted the high difficulty of fraction division, variable strategy use by individual children and on individual problems, relative frequencies of different types of strategy errors on different types of problems, and variable effects of denominator equality on the four arithmetic operations. The model also generated nonintuitive predictions regarding the relative difficulties of several types of problems and the potential effectiveness of a novel instructional approach. Perhaps the most general lesson of the findings is that the statistical distribution of problems that learners encounter can influence mathematics learning in powerful and nonintuitive ways.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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