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...
| Publicado en: | Psychological Review Vol. 124; no. 5; pp. 603 - 626 |
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| Autores principales: | , , |
| Formato: | Artículo |
| Publicado: |
American Psychological Association
Oct2017
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=125512879&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 125512879 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 0033295X PYV jtl: Psychological Review issn: 0033295X maglogo: N pubinfo: dt: Oct2017 vid: 124 iid: 5 pid: 34 pub: American Psychological Association artinfo: ui: 125512879 10.1037/rev0000072 ppf: 603 ppct: 23 formats: tig: atl: A Computational Model of Fraction Arithmetic. aug: 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 refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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