Um estudo sobre as relações entre o desenvolvimento do pensamento algébrico, as crenças de autoeficácia, as atitudes e o conhecimento especializado de professores pre-service e in-service
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Data
2019-07-29
Autores
Santana, Roseli Regina Fernandes
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Universidade Estadual Paulista (Unesp)
Resumo
Esta pesquisa se desenvolveu na perspectiva da Psicologia da Educação Matemática e buscou investigar o desenvolvimento do pensamento algébrico face às crenças de autoeficácia, as atitudes em relação à Matemática e ao conhecimento matemático especializado para o seu ensino nos anos iniciais do Ensino Fundamental. Buscou, também, analisar possíveis relações e influências de aspectos afetivos na solução de problemas algébricos, com foco na capacidade de generalização, cerne do desenvolvimento do pensamento algébrico. A investigação foi ancorada numa abordagem mista, quanti-qualitativa, fundamentada nos estudos de Creswell e Park (2013). Os participantes da pesquisa foram 128 estudantes do curso de Pedagogia (pre-service) de instituições privadas e 119 professores (in-service) dos anos iniciais, da rede pública de ensino. Para tanto, os instrumentos utilizados para essa investigação contaram em sua primeira etapa com um questionário para caracterização dos participantes, sendo um para os pre-service e outro para os in-service; uma Escala de Atitudes traduzida e validada por Brito (1996); um questionário estruturado em duas subescalas do tipo likert, uma sobre as crenças de autoeficácia dos participantes em relação ao conhecimento especializado para o desenvolvimento do pensamento algébrico e a outra para o ensino desse pensamento matemático nos anos iniciais. Na segunda etapa da pesquisa, foram selecionados três pre-service e três in-service considerando suas pontuações nas escalas (abaixo, mediano e acima do ponto central) para uma entrevista semiestruturada e solução de problemas algébricos formulados de acordo com algumas habilidades requeridas para a unidade temática Álgebra nos anos iniciais, propostos na Base Nacional Comum Curricular (BRASIL, 2017) e da Série X, de Krutetskii (1976), contemplando a generalização e a composição de equações usando os termos de um problema. A análise das transcrições de gravações de áudio foi realizada pelo método “Pensar em voz alta”, de Brito (2002). Os participantes foram convidados a relatar o que pensavam enquanto resolviam os problemas algébricos, a fim de analisarmos a influência das atitudes e crenças de autoeficácia no julgamento de suas capacidades na persistência, empenho, conhecimento especializado e predisposição para o ensino. A análise dos dados, em suas diferentes etapas, evidenciou que: 1) os pre-service apresentaram ter atitudes negativas em relação à Matemática, enquanto os in-service, positivas; 2) quanto às crenças de autoeficácia para o conhecimento especializado e ensino do desenvolvimento do pensamento algébrico mostraram-se positivas nos dois grupos, apesar dos in-service serem crenças mais positivas; 3) os participantes se sentiram menos seguros para o ensino do pensamento algébrico do que quanto ao conhecimento de conteúdo curricular, embora revelassem conhecer pouco a respeito de elementos conceituais e pedagógicos, bem como os caracterizadores desse pensamento matemático. Além disso, alguns fatores identificados influenciaram tais atitudes e crenças, tais como: idade, tempo de magistério, reprovação, julgamento do seu desempenho nas aulas de Matemática, formação inicial, possuir pós-graduação, entre outros que destacamos no estudo. Esperamos que essa pesquisa de mestrado contribua para a desconstrução de práticas da formação inicial e continuada de professores e futuros professores dos anos iniciais, ressignificando o ensino para o desenvolvimento do pensamento matemático, em especial o algébrico, sob o viés de aspectos cognitivos e afetivos inerentes ao professor e alunos, dando voz e vez à Matemática que se deseja ser ensinada para todos nas escolas públicas do país e assim caminharmos para o ensino de Matemática significativo e consciente, garantindo de fato os direitos de aprendizagens dos estudantes.
This research developed from the perspective of the Mathematics Education psychology and sought to investigate the algebraic thinking development in relation to the self-efficacy beliefs, attitudes towards Mathematics and specialized mathematical knowledge for its teaching in the early years of Elementary School. It also sought to analyze possible relationships and influences of affective aspects in solving algebraic problems, focusing on the generalization capacity, the core of the algebraic thinking development. The research was anchored in a mixed, quanti-qualitative approach based on the studies of Creswell and Park (2013). The participants of the study were 128 students from the pre-service pedagogy course, from private institutions and 119 teachers (in-service) from the early years of the public school system. To do so, the instruments used for this research had in their first stage a questionnaire to characterize the participants, one for pre-service and the other for in-service; a Scale of Attitudes translated and validated by Brito (1996); a questionnaire structured in two likert type subscales, one on the participants' self-efficacy beliefs regarding the specialized knowledge for the algebraic thought development and the other for the teaching of this mathematical thought in the early years. In the second stage of the research, three pre-service and three in-service were selected considering their scores on the scales (below, median and above the central point) for a semistructured interview and solution of algebraic problems formulated according to some skills required for thematic unit Algebra in the early years, proposed in the National Curricular Common Base (BRAZIL, 2017) and the X Series, of Krutetskii (1976), contemplating the generalization and composition of equations using the terms of a problem. The analysis of the áudio transcriptions recordings was performed by the "Thinking in a loud voice" method, by Brito (2002). Participants were invited to report their thoughts while solving algebraic problems in order to analyze the influence of attitudes and beliefs of self-efficacy in judging their abilities in persistence, commitment, specialized knowledge and predisposition to teaching. The analysis of the data, in its different stages, showed that: 1) pre-services present negative attitudes towards Mathematics, while in-service, positive; 2) as to the self-efficacy beliefs for the specialized knowledge and teaching of the algebraic thought development were positive in both groups, although in-service beliefs were more positive; 3) the participants feel less secure in the teaching of algebraic thinking than in the knowledge of curricular content, although they know little about conceptual and pedagogical elements, as well as the characterizers of this mathematical thought. In addition, some identified factors influence such attitudes and beliefs, such as: age, teaching time, reproof, judgment of their performance in Mathematics classes, initial formation, post graduation, among others we highlighted in the study. We hope this master's research contributes to the deconstruction of the initial and continuing teachers and future ones of the early years’ practices, resignifying the teaching for the mathematical thinking development, especially the algebraic one, under the bias of inherent cognitive and affective aspects to the teacher and students, giving voice to Mathematics that one wishes to be taught to all in the public schools of the country and thus to move towards meaningful and concious Mathematics teaching , ensuring indeed the rights of students' learning.
This research developed from the perspective of the Mathematics Education psychology and sought to investigate the algebraic thinking development in relation to the self-efficacy beliefs, attitudes towards Mathematics and specialized mathematical knowledge for its teaching in the early years of Elementary School. It also sought to analyze possible relationships and influences of affective aspects in solving algebraic problems, focusing on the generalization capacity, the core of the algebraic thinking development. The research was anchored in a mixed, quanti-qualitative approach based on the studies of Creswell and Park (2013). The participants of the study were 128 students from the pre-service pedagogy course, from private institutions and 119 teachers (in-service) from the early years of the public school system. To do so, the instruments used for this research had in their first stage a questionnaire to characterize the participants, one for pre-service and the other for in-service; a Scale of Attitudes translated and validated by Brito (1996); a questionnaire structured in two likert type subscales, one on the participants' self-efficacy beliefs regarding the specialized knowledge for the algebraic thought development and the other for the teaching of this mathematical thought in the early years. In the second stage of the research, three pre-service and three in-service were selected considering their scores on the scales (below, median and above the central point) for a semistructured interview and solution of algebraic problems formulated according to some skills required for thematic unit Algebra in the early years, proposed in the National Curricular Common Base (BRAZIL, 2017) and the X Series, of Krutetskii (1976), contemplating the generalization and composition of equations using the terms of a problem. The analysis of the áudio transcriptions recordings was performed by the "Thinking in a loud voice" method, by Brito (2002). Participants were invited to report their thoughts while solving algebraic problems in order to analyze the influence of attitudes and beliefs of self-efficacy in judging their abilities in persistence, commitment, specialized knowledge and predisposition to teaching. The analysis of the data, in its different stages, showed that: 1) pre-services present negative attitudes towards Mathematics, while in-service, positive; 2) as to the self-efficacy beliefs for the specialized knowledge and teaching of the algebraic thought development were positive in both groups, although in-service beliefs were more positive; 3) the participants feel less secure in the teaching of algebraic thinking than in the knowledge of curricular content, although they know little about conceptual and pedagogical elements, as well as the characterizers of this mathematical thought. In addition, some identified factors influence such attitudes and beliefs, such as: age, teaching time, reproof, judgment of their performance in Mathematics classes, initial formation, post graduation, among others we highlighted in the study. We hope this master's research contributes to the deconstruction of the initial and continuing teachers and future ones of the early years’ practices, resignifying the teaching for the mathematical thinking development, especially the algebraic one, under the bias of inherent cognitive and affective aspects to the teacher and students, giving voice to Mathematics that one wishes to be taught to all in the public schools of the country and thus to move towards meaningful and concious Mathematics teaching , ensuring indeed the rights of students' learning.
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Palavras-chave
Pensamento algébrico, Anos iniciais, Crenças de autoeficácia, Atitudes em relação à Matemática, Conhecimento matemático especializado do professor para o ensino, Algebraic thinking, Early years, Beliefs of self-efficacy, Attitudes towards Mathematics, Teacher’s specialized mathematical knowledge for teaching