This report recognizes the common mistakes students make solving single variable equations and attempts to connect these errors to varying levels of developmental readiness. Striving to meet the needs of all students, this report offers an alternative to lecture based mathematics lessons by exploring the benefits of a unit based curriculum. The unit poses an overarching problem for the students to investigate and answer, while the students still receive the instruction on solving algebraic equations. The goal is to move beyond traditional procedures when solving equations to help students become more familiar with symbol manipulation involved in solving real world story problems. / text

It is our purpose here to investigate the method of solving equations for real roots by Newton's Method and to indicate a generalization arising from this method.

The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without manipulatives. Further, the researcher wanted to investigate unique benefits and drawbacks associated with each manipulative. Qualitative research methods such as observation, teacher interviews, and student focus group interviews were employed. Quantitative data analysis techniques were used to analyze pretest and posttest data of middle school students (n=76). ANCOVA, analysis of covariance, uncovered statistically significant differences in favor of the control group. Differences in posttest scores, triangulated with qualitative data, suggested that concrete and virtual manipulatives require more classroom time because of administrative issues and because of time needed to learn how to operate the manipulative in addition to necessary time to learn mathematics content. Teachers must allow students enough time to develop conceptual understanding linking the manipulatives to the mathematics represented. Additionally, a discussion of unique benefits and drawbacks of each manipulative sheds light on the use of manipulatives in middle school mathematics.

Submitted by Franciele Moreira (francielemoreyra@gmail.com) on 2017-12-27T12:13:05Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Adão Gomes de Souza - 2017.pdf: 2241174 bytes, checksum: f485f691848f41537c07408e1c5b96ad (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-12-28T09:30:56Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Adão Gomes de Souza - 2017.pdf: 2241174 bytes, checksum: f485f691848f41537c07408e1c5b96ad (MD5) / Made available in DSpace on 2017-12-28T09:30:56Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Adão Gomes de Souza - 2017.pdf: 2241174 bytes, checksum: f485f691848f41537c07408e1c5b96ad (MD5) Previous issue date: 2017-11-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The main objective of this work is to discuss in a conceptual way the historical process and evolution of the resolution of algebraic equations. The justification for choosing the theme hovers about its contemporaneity, besides the expectation of contributing to the academic scope. The research method followed is qualitative, with a basic research approach, exploratory nature and information collection through bibliographic research. Among the main findings, it was possible to conclude that algebraic equations arise in the midst of ancient human civilizations, in the man's attempt to measure quantities and solve everyday problems of life. Therefore, it is noted that, unlike the stigma that hangs over the content of mathematics, the science it involves is not far from reality and human experience, but rather a part of it that seeks answers to the common problems of life. What makes math as a whole and the algebraic equations common problems of life that need to be learned and solved. / O presente trabalho tem como objetivo central debater de maneira conceitual sobre o processo e evolução histórica da resolução das equações algébricas. A justificativa para a escolha do tema paira sobre sua contemporaneidade, além da expectativa de contribuir para o âmbito acadêmico. O método de pesquisa empreendido segue natureza qualitativa, com abordagem de pesquisa básica, de natureza exploratória e coleta de informações por meio de pesquisa bibliográfica. Dentre os principais achados, foi possível concluir que as equações algébricas surgem em meio a civilizações humanas antigas, na tentativa do homem de mensurar quantidades e resolver problemas cotidianos da vida. Portanto, nota-se que, diferente do estigma que paira sobre o conteúdo da matemática, a ciência que envolve não é distante da realidade e da experiência humana, mas sim, uma parte dela que busca respostas aos problemas comuns da vida. O que faz da matemática como um todo e das equações algébricas, problemáticas comuns da vida e que precisam ser aprendidos e solucionados.