<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0870-8231</journal-id>
<journal-title><![CDATA[Análise Psicológica]]></journal-title>
<abbrev-journal-title><![CDATA[Aná. Psicológica]]></abbrev-journal-title>
<issn>0870-8231</issn>
<publisher>
<publisher-name><![CDATA[ISPA-Instituto Universitário]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0870-82311997000400005</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Factores cognitivos do insucesso na matemática: Conhecimento do sistema de numeração e compreensão do valor de posição em crianças dos 4 aos 7 anos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martins-Mourão]]></surname>
<given-names><![CDATA[António]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,Universidade de Londres  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Reino Unido</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>1997</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>1997</year>
</pub-date>
<volume>15</volume>
<numero>4</numero>
<fpage>573</fpage>
<lpage>585</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_arttext&amp;pid=S0870-82311997000400005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_abstract&amp;pid=S0870-82311997000400005&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://scielo.pt/scielo.php?script=sci_pdf&amp;pid=S0870-82311997000400005&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Cento e sessenta e sete crianças inglesas de 4, 5 e 6 anos de idade foram avaliadas longitudinalmente ao longo de um ano escolar sobre (1) conhecimento da estrutura do sistema de numeração e (2) conhecimento de números escritos (e valor de posicão). O objectivo foi investigar se as crianças aprendem o valor de posição em função (a) da prática continua com a escrita de números multi-dígitos ou (b) através do conhecimento prévio da estrutura do sistema de numeração. Os resultados contradizem a tese de Luria (1969) sugerindo que a instrução de números escritos (e o valor de posição) é condição necessária para o conhecimento da estrutura do sistema de numeração. Pelo contrário, os resultados indicam que as crianças conhecedoras da estrutura do sistema de numeração apresentaram resultados significativamente superiores na utilização do valor de posição em números com 2, 3 e 4 dígitos. Estes resultados indentificam alguns facto-res cognitivos preditores do insucesso na matemática e sugerem a alteração dos programas educativos, os quais poderiam beneficiar da introdução do ensino sobre a estrutura do sistema de numeração a partir dos 5 anos de idade.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[The literature is not clear about children´s development of place value. A number of studies support the idea that children learn about place value from experience with written numbers. But there are also some data suggesting that children may benefit from their previous understanding of the structure of the numeration system, where no knowledge of written numbers is required, in order to succeed in place value. This study assessed 167 four, five and six year-olds longitudinally through one school year, with tasks on both achievements. The evidence presented here supports the second hypothesis.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Sistema numeração]]></kwd>
<kwd lng="pt"><![CDATA[decimal]]></kwd>
<kwd lng="pt"><![CDATA[valor posição]]></kwd>
<kwd lng="pt"><![CDATA[educação]]></kwd>
<kwd lng="en"><![CDATA[Numeration system]]></kwd>
<kwd lng="en"><![CDATA[decade]]></kwd>
<kwd lng="en"><![CDATA[place value]]></kwd>
<kwd lng="en"><![CDATA[mathematical cognition]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p><b>Factores cognitivos do insucesso na matem&aacute;tica: Conhecimento do sistema    de numera&ccedil;&atilde;o e compreens&atilde;o do valor de posi&ccedil;&atilde;o    em crian&ccedil;as dos 4 aos 7 anos (<a name="top1"></a><a href="#1">*</a>)</b></p>     <P>&nbsp;</P>     <P align="right">Ant&oacute;nio Martins-Mour&atilde;o (<a name="top2"></a><a href="#2">**</a>)  </P>     <P>&nbsp;</P>     <P>&nbsp;</P>     <P align="center">RESUMO<b> </b></P>     <P>Cento e sessenta e sete crian&ccedil;as inglesas de 4, 5 e 6  anos de idade foram avaliadas longitudinalmente ao longo de um ano escolar  sobre (1) conhecimento da estrutura do sistema de numera&ccedil;&atilde;o  e (2) conhecimento de n&uacute;meros escritos (e valor de posic&atilde;o).  O objectivo foi investigar se as crian&ccedil;as aprendem o valor de posi&ccedil;&atilde;o  em fun&ccedil;&atilde;o (a) da pr&aacute;tica continua com a escrita de n&uacute;meros  multi-d&iacute;gitos ou (b) atrav&eacute;s do conhecimento pr&eacute;vio da  estrutura do sistema de numera&ccedil;&atilde;o. Os resultados contradizem  a tese de Luria (1969) sugerindo que a instru&ccedil;&atilde;o de n&uacute;meros  escritos (e o valor de posi&ccedil;&atilde;o) &eacute; condi&ccedil;&atilde;o  necess&aacute;ria para o conhecimento da estrutura do sistema de numera&ccedil;&atilde;o.  Pelo contr&aacute;rio, os resultados indicam que as crian&ccedil;as conhecedoras  da estrutura do sistema de numera&ccedil;&atilde;o apresentaram resultados  significativamente superiores na utiliza&ccedil;&atilde;o do valor de posi&ccedil;&atilde;o  em n&uacute;meros com 2, 3 e 4 d&iacute;gitos. Estes resultados indentificam  alguns facto-res cognitivos preditores do insucesso na matem&aacute;tica e  sugerem a altera&ccedil;&atilde;o dos programas educativos, os quais poderiam  beneficiar da introdu&ccedil;&atilde;o do ensino sobre a estrutura do sistema  de numera&ccedil;&atilde;o a partir dos 5 anos de idade.</P>     <P><I>Palavras-chave</I>: Sistema numera&ccedil;&atilde;o, decimal,  valor posi&ccedil;&atilde;o, educa&ccedil;&atilde;o.</P>     <P>&nbsp;</P>     <P>&nbsp;</P>     ]]></body>
<body><![CDATA[<P align="center">ABSTRACT</P>     <P>The literature is not clear about children&acute;s development  of place value. A number of studies support the idea that children learn about  place value from experience with written numbers. But there are also some  data suggesting that children may benefit from their previous understanding  of the structure of the numeration system, where no knowledge of written numbers  is required, in order to succeed in place value. This study assessed 167 four,  five and six year-olds longitudinally through one school year, with tasks  on both achievements. The evidence presented here supports the second hypothesis. </P>     <P><I>Key words</I>: Numeration system, decade, place value, mathematical cognition.</P>     <P>&nbsp;</P>     <P>&nbsp;</P>     <P>Texto completo dispon&iacute;vel apenas em PDF.</P>     <p>Full text only available in PDF format.</p>     <P>&nbsp;</P>     <P align="center">&nbsp;</P>     <P align="center">REFER&Ecirc;NCIAS</P>     ]]></body>
<body><![CDATA[<!-- ref --><P>Baroody, A. J. (1990). How and when should place-value concepts and skills be taught? <I>Journal for Research in Mathematics Education, 22 </I>(4), 281-286. &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=000023&pid=S0870-8231199700040000500001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><P>Bednarz, N., & Janvier, B. (1982). The understanding of numeration in primary school. <I>Educational Studies in Mathematics, 13</I>, 33-57. </P>     <P>Bergeron, J. C., Herscovics, N. <I>et al. </I>(1990). Psychological aspects of learning early arithmetic. In P. Nesher, & J. Kilpatrick (Eds.), <I>Mathematics and cognition: A research synthesis by the international group for the psychology of mathematics education </I>(pp. 31-52). Cambridge: Cambridge University Press. </P>     <P>Brown, M. (1979). Place value and decimals. <I>Proceedings of the third international conference for the psychology of mathematics education</I>, Warwick. </P>     <P>Bryman, A., & Cramer, D. (1990). <I>Quantitative data analysis for social scientists. </I>London: Routledge. </P>     <P>Carraher, T. N. (1985). The decimal system. Understanding and notation. In L. Streefland (Ed.), <I>Proceedings of the Ninth International Conference for the Psychology of Mathematical Education </I>(Vol. 1: 288-303). Utrecht, Holland: University of Utrecht, Research Group on Mathematics Education and Computer Center. </P>     <P>Carraher, T. N., & Schliemann, A. D. (1990). Knowledge of the numeration system    among preschoolers. In L. Steffe, & T. Wood (Eds.), <I>Transforming children's    mathematics education - International perspectives </I>(pp. 135-141). Hillsdale,    NJ: Lawrence Erlbaum Associates, Publishers. </P>     <P>English, L., & Halford, G. (1995) <I>Mathematics education, models and processes</I>. New Jersey: LEA. </P>     <P>Fuson, K. (1990). Conceptual structures for multiunit numbers: Implications for learning and teaching multidigit addition, subtraction and place value. <I>Cognition and Instruction, 7 </I>(4), 343-403. </P>     <P>Ginsburg, H. P. (1977). <I>Children's Arithmetic</I>. New York: D. van Nostrand.  </P>     ]]></body>
<body><![CDATA[<P>Kamii, C. (1986). Place value: An explanation of its difficulties and educational implications for the primary grades. <I>Journal of Research in Childhood Education, 1 </I>(2), 75-85. </P>     <P>Kamii, C, & Joseph, L. (1988) Teaching place value and double column addition. <I>Arithmetic Teacher, 35 </I>(6), 48-52. </P>     <P>Luria, A. R. (1969). On the pathology of computational operations. In J. Kilpatrick, & I. Wirszup (Eds.), <I>Soviet studies in the psychology of learning and teaching mathematics. Vol. I: The learning of mathematical concepts </I>(pp. 37-74). Chicago: University of Chicago Press. </P>     <P>Nunes, T. N., & Bryant, P. (1996). <I>Children doing Mathematics</I>. Cambridge, MA: Blackwell. </P>     <P>Valente Pires, I. (1992). <I>Sistema de numera&ccedil;&atilde;o</I>. Set&uacute;bal: Escola Superior de Educa&ccedil;&atilde;o. </P>     <P>Ross, S. H. (1989) Parts, wholes and place value: A developmental view. <I>Arithmetic Teacher, 36 </I>(6), 47-51. </P>     <P>Resnick, L. B. (1986). The development of mathematical intuition. In M. Perlumutter (Ed), <I>Perspectives on intellectual development: Minnesota Symposia on Child Psychology </I>(Vol. 19: 159-194). Hillsdale, NJ: Erlbaum. </P>     <P>Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), <I>The development of mathematical thinking </I>(pp. 109-151). New York: Academic Press. </P>     <P>Raven, J. C. (1965). <I>Guide to using the Coloured Progressive Matrices</I>. London: HK Lewis. </P>     <P>Saxe, G. B. (1988). Candy selling and mathematics learning. <I>Educational Researcher, 17 </I>(6), 14-21. </P>     ]]></body>
<body><![CDATA[<P>Sinclair, A., & Scheuer, N. (1993). Understanding the written number system: 6 year-olds in Argentina and Switzerland. <I>Educational Studies in Mathematics, 24</I>, 199-221. </P>     <P>Sinclair, A., Garin, A., & Tieche-Christinat, C. (1992). Constructing and understanding of place value in numerical notation. <I>European Journal of Psychology of Education, 7 </I>(3), 191-207. </P>     <P>VanLehn, K. (1990). <I>Mind bugs: The origins of pro</I><I>cedural misconceptions</I>.    Cambridge, MA: MIT Press. </P>     <P>&nbsp;</P>     <P>(<a name="1"></a><a href="#top1">*</a>) O manuscrito &eacute; baseado numa    comunica&ccedil;&atilde;o apresentada no IV Simp&oacute;sio Nacional de Investiga&ccedil;&atilde;o    em Psicologia, Lisboa, Novembro de 1996. O autor &eacute; doutorando em psicologia    cognitiva no Institute of Education da Universidade de Londres. Este projecto    foi apoiado pelo programa Praxis XXI da Junta Nacional de Investiga&ccedil;&atilde;o    Ci&ecirc;ncia e Tecnologia. A correspondencia relacionada com este artigo dever&aacute;    ser enviada para: Institute of Education, Department of Child Development and    Learning, 20 Bedford Way, London, WC1H OAL, UK; e-mail: <a href="mailto:a.mourao@ioe.ac.uk">a.mourao@ioe.ac.uk    </a></P>     <P>(<a name="2"></a><a href="#top2">**</a>) Universidade de Londres, Reino Unido.  </P>      ]]></body><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baroody]]></surname>
<given-names><![CDATA[A. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[How and when should place-value concepts and skills be taught?]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1990</year>
<volume>22</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>281-286</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
