Os números na História da Matemática
Autor: Jeober Marinho da Silva | Publicado: 2011-10-05T16:07:00-07:00

Autores: Jeober Marinho da Silva, Maria de Lourdes, Jorge Ricardo Cruz, José Pereira, André José Costa

1.&nbsp;&nbsp;&nbsp; BREVE HISTÓRICO:   ASSIM NASCE A CIÊNCIA DOS NÚMEROS  Um, dois e muitos – CONTAR: Promoção do progresso da humanidade  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A vida ensinou os primitivos, através de suas necessidades, a desenvolverem a ideia de reconhecer e comparar quantidades: rebanho de animais, passagem de luas, habitantes de uma tribo. Desse modo, o homem primitivo adquiriu a ideia de quantidade e a habilidade de contar.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Os números não existiam tal como os conhecemos hoje, nem mesmo a ideia de sua existência.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; O conceito de número é abstrato e seu desenvolvimento deu-se através de um processo bastante lento e complexo, envolvendo diversas civilizações e muitos milhares de anos.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Os entalhes em ossos era uma estratégia que o homem primitivo desenvolveu para poder comparar quantidades, mas não conseguia distinguir uma grande quantidade de marcas. Com o tempo, desenvolveu a técnica do agrupamento, que gerou a necessidade de criar símbolos para os grupos.  2.&nbsp;&nbsp;&nbsp; PANORAMA NO CURRÍCULO:   Atualmente, os números estão presentes em diversas situações do cotidiano: indicando quantidades, sendo usados como códigos. São de vários tipos e expressam diversas situações. São organizados em sistemas.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; No currículo de Matemática o estudo dos números segue um processo evolutivo:  ·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; nas séries iniciais do Ensino Fundamental – estudo da representação de pequenas quantidades, conhecimento do sistema decimal de numeração (unidades, dezenas, centenas...), comparação e ordenação, operações, conhecendo os conjuntos numéricos: os naturais, racionais e resolução de problemas.  ·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; nas séries finais do Ensino Fundamental: ampliação dos conjuntos numéricos, leitura e escrita de números, os diferentes sistemas numéricos, representações diferentes de um mesmo número (decimal, fração e porcentagem) um pouco da história dos números e sua evolução, operações, resolução de problemas.   ·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; no ensino Médio: ampliação dos campos numéricos, funções, resolução de problemas.  3.&nbsp;&nbsp;&nbsp; PANORAMA ATUAL:   Há alguns anos o ensino de números era totalmente enfatizado nos cálculos, na resolução de grandes expressões numéricas sem nenhum contexto, na memorização de propriedades numéricas. Os números eram introduzidos sem significado. Com a chegada dos PCNs, essa história começou a tomar outro rumo, porque percebeu-se que o ensino precisava de diretrizes inovadoras, pois a Matemática tradicional estava se tornando obsoleta ante os progressos sociais. Então, o ensino de Números atualmente deve estar voltado para o contexto social, onde, por exemplo os números racionais tenham real aplicabilidade e se apresente com total significado.   Por que ensinar Matemática tem sido tarefa difícil atualmente? Vários pensadores já discorreram acerca desta questão apontando como causa do problema um ensino descontextualizado, gerando desmotivação, desinteresse por parte do alunado.  Ensinar matemática tem sido tarefa difícil. Às dificuldades intrínsecas somam-se aos problemas causados por uma visão distorcida da matéria, estabelecida desde os primeiros contatos. Um desses problemas é exatamente a descontextualização, o que leva os professores a se defrontarem com perguntas do tipo: “Quem inventou isso não tinha nada para fazer.”;” Para que estudar isso?”. É justamente pelo fato do estudo da matemática ter se tornado uma chatice, uma mesmice, decoreba que nossos alunos jovens e adolescentes não se sentem motivados a aprendê-la e a estudá-la.http://educacaomatematica.vilabol.uol.com.br/histmat/texto1.htm  &nbsp;4.&nbsp;&nbsp;&nbsp; FUNDAMENTAÇÃO TEÓRICA:   O ensino da História da Matemática, em particular, dos Números tem sua aplicabilidade prática justamente na necessidade de se entender como a Matemática se desenvolveu até os dias de hoje.Saber como pouco a pouco foram sendo construídos os conceitos e as notações matemáticas, serve também para compreender melhor certos erros dos nossos alunos e poder pôr em prática situações didáticas mais adequadas para uma apropriação progressiva de certos conceitos.http://educacaomatematica.vilabol.uol.com.br/histmat/texto1.htm  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Segundo Milies (2003), o conhecimento da História da Matemática possibilita perceber que as teorias que hoje aparecem acabadas e elegantes resultaram de desafios que os matemáticos enfrentaram e que foram desenvolvidas com grande esforço (até os símbolos indo arábicos que hoje utilizamos levaram bastante tempo para serem aperfeiçoados, a inclusão do zero possibilitou o desenvolvimento dos sistemas de numeração), quase sempre, numa ordem bem diferente daquela em que são apresentadas após o processo de formalização. Isso é confirmado por Nobre (1996), ao constatar que muitos conhecimentos matemáticos são transmitidos como se fossem obtidos de forma natural e apresentados como desprovidos de erros e dificuldades. Nesse sentido, o autor, destaca a necessidade de o professor observar que a forma acabada na qual hoje se encontra o conceito matemático esconde modificações sofridas ao longo de sua história e que isso deve ser levado em conta na elaboração de atividades para aprendizagem, já que a forma como um assunto é tratado influencia a sua compreensão. Para D’Ambrosio (1999), em Matemática é impossível discutir práticas educativas que se fundam na cultura, em estilos de aprendizagem e nas tradições sem recorrer à História, que compreende o registro desses fundamentos: “Desvincular a Matemática das outras atividades humanas é um dos maiores erros que se pratica particularmente na Educação Matemática” (p. 97). Propõe ele que se recupere a presença de ideias matemáticas em todas as ações humanas. Para isso, em afinidade com o pensamento de Paulo Freire, argumenta ser necessário recorrer à História no processo de ensinoaprendizagem da Matemática.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   5.&nbsp;&nbsp;&nbsp; REVISÃO DE LITERATURA:   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Os atuais livros didáticos de Matemática já apontam um ensino voltado para uma discussão do contexto social, de um ensino baseado na resolução de problemas, enfocando o processo histórico de desenvolvimento da Matemática.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Nas obras Matemática (Imenes e Lellis - 2009) – coleção de livros didáticos para as séries finais do Ensino Fundamental, especialmente o livro do 7º ano, em seu capítulo inicial, há uma aborda bem interessante da história da matemática e o desenvolvimento dos sistemas numéricos e no final da cada capítulo há um resgate do processo histórico do conteúdo estudado.  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Em seu livro intitulado O ensino da Matemática hoje: enfoque, sentidos e desafios, Patrícia Sadovsky entende que o ensino da Matemática hoje deve se manifestar através da INTERAÇÃO: professor-aluno, aluno-aluno. Tudo num constante participar, onde todos são autores da construção do saber matemático. Ela observa e nos alerta para a necessidade urgente de avaliar, questionar e repensar os métodos de ensino da disciplina, diante das dificuldades e condições adversas do meio escolar. Ressalta a importância dos jogos e da modelagem no ensino da Matemática.  6.&nbsp;&nbsp;&nbsp; PROPOSTA DE USO DO RECURSO HISTÓRIA DA MATEMÁTICA NO ENSINO:   Diante do exposto, nosso grupo elaborou a seguinte proposta para o ensino de Números utilizando a História da Matemática:  Tema: Sistemas de numeração  ·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; A escrita dos números no passado;  ·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Nosso sistema de numeração  Público alvo: alunos do 7º ano do Ensino Fundamental   Objetivo: Analisar, discutir, através de imagens e argumentações, a escrita dos números pela civilização egípcia e romana e compará-las com o nosso sistema de numeração para perceber suas diferenças em relação ao nosso e então entender a necessidade da criação de um sistema que seja “universal”, prático.  Desenvolvimento:    Inicia-se a aula solicitando aos alunos a leitura de um texto sobre a escrita dos números no passado. 
Em seguida, abre espaço para um diálogo sobre as informações trazidas pelo texto, dando destaque à questão apresentada na letra f.

  Deste ponto em diante, espera-se que o aluno já tenha percebido que os dois sistemas apresentados no texto possuem limitações: de ordem, excesso de símbolos para representar um valor grande. Fazendo comparações entre os sistemas de numeração egípcio e romano com o sistema numérico indo-arábico, é possível perceber a sua simplificação deste último na representação de valores grandes e o quanto a criação do zero permitiu o desenvolvimento desse sistema.                                                 <v:shape id="Imagem_x0020_5" o:gfxdata="UEsDBBQABgAIAAAAIQDI4TOSFQEAAFICAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbKSSTW7DIBCF
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" o:spid="_x0000_s1026" style="height: 362.4pt; margin-left: 221.25pt; margin-top: 42.15pt; mso-height-percent: 0; mso-height-relative: page; mso-position-horizontal-relative: text; mso-position-horizontal: absolute; mso-position-vertical-relative: text; mso-position-vertical: absolute; mso-width-percent: 0; mso-width-relative: page; mso-wrap-distance-bottom: 0; mso-wrap-distance-left: 9pt; mso-wrap-distance-right: 9pt; mso-wrap-distance-top: 0; position: absolute; visibility: visible; width: 226.1pt; z-index: -251653120;" type="#_x0000_t75">     Depois, segue mais uma leitura e discussão para finalizar a estratégia: