The teaching of mathematics to young children using a problem solving approach

1980 ◽  
Vol 11 (1) ◽  
pp. 43-58 ◽  
Author(s):  
Leone Burton
Author(s):  
Ana Queli Reis ◽  
Cátia Maria Nehring

Resumo Este artigo objetiva apresentar um panorama sobre a contextualização através de uma meta análise de pesquisas que tratam deste conceito. Consideramos pesquisas que abordam a contextualização a partir de sua proposição pelas políticas públicas, através de documentos, livros didáticos e avaliações, bem como as concepções e práticas desenvolvidas por professores e pesquisadores da educação matemática. As análises evidenciam um distanciamento entre o que é compreendido epistemologicamente e a prática em sala de aula. A fragilidade de entendimentos sobre o que é contextualização tem limitado o ensino à resolução de problemas e aplicação, simplificando conceitos no processo de ensino e aprendizagem por não enfatizarem o processo de abstração decorrente da contextualização. Abstract This paper aims to present an overview of the contextualization through a meta-analysis of researches, which deal with this concept. We consider researches that address the contextualization from its proposition by public policies through documents, textbooks and assessments, as well as the conceptions and practices developed by teachers and researchers of mathematics education. The analyses have shown a gap between what is epistemologically understood and practice in the classroom. The weakness in understanding what is contextualization has limited teaching to problem solving and application, simplifying concepts in the process of teaching and learning due to not emphasizing the abstraction process arising from the contextualization.


2018 ◽  
Vol 24 (esp.) ◽  
pp. 89
Author(s):  
Luciana Figueiredo Lacanallo Arrais ◽  
Lucinéia Maria Lazaretti ◽  
Paula Tamyris Moya ◽  
Silvia Pereira Gonzaga de Moraes

  No cenário da educação infantil, principalmente na prática pedagógica com bebês, ainda persistem desafios em torno da organização do ensino para esse período de vida. Diante disso, este texto tem o objetivo de discutir as possibilidades educativas para os primeiros anos de vida da criança em relação à aprendizagem da matemática por meio de uma atividade de ensino, considerando a singularidade do desenvolvimento infantil. Ancoradas na Teoria Histórico-Cultural, estruturamos essa discussão em dois momentos: a) a especificidade do desenvolvimento da criança pequena e a organização do ensino de matemática na educação infantil; b) a análise de uma atividade de ensino para crianças do berçário. Esperamos que o texto possa auxiliar o trabalho educativo com a matemática na educação infantil, pois um ensino sistemático e dirigido, desde os primeiros anos, é condição fundamental para a aprendizagem e para as transformações qualitativas no desenvolvimento psíquico das crianças.Palavras-chave: Educação Infantil. Ensino de Matemática. Primeira Infância.TEACHING MATHEMATICS TO YOUNG CHILDREN: attraction, discovery and exploration in relationships between magnitudes ABSTRACT: Several challenges exist on teaching organization within early childhood, mainly with regard to the pedagogical practice with young children. Owing to the uniqueness of children´s development, the educational possibilities on the teaching of Mathematics, through activities, in their early life period, are discussed. Based on the Cultural and Historical Theory, current discussion underscores two factors: a) the specificity of children´s development and the organization of the teaching of Mathematics in early education; b) the analysis of a teaching activity for kindergarten children. The authors expect that current analysis will aid the teaching of Mathematics in young children´s education. In fact, systematic and monitored teaching during the early years of life is a crucial condition for learning and for qualitative transformations in children´s psychic development.Keywords: Early Childhood Education; the teaching of Mathematics; Early childhood.ENSEÑANDO MATEMÁTICA A LOS BEBÉS: encantos, descubrimientos y exploración de las relaciones entre grandezas RESUMEN: En el escenario de la educación inicial, principalmente en la práctica pedagógica con bebés, aún persisten desafíos en torno a la organización de la enseñanza para ese período de vida. Este texto tiene por objetivo discutir las posibilidades educativas de los primeros años de vida del niño en relación al aprendizaje de las matemáticas considerando la singularidad del desarrollo infantil, a través de una actividad educativa. Ancladas en la Teoría Histórico-Cultural, estructuramos esta discusión en dos momentos: a) la especificidad del desarrollo del niño y la organización de la enseñanza de las matemáticas en la educación inicial; b) el análisis de una actividad de enseñanza para bebés. Esperamos que el texto pueda auxiliar el trabajo educativo con las matemáticas en la educación inicial, pues una enseñanza sistemática y dirigida desde los primeros años es condición fundamental para el aprendizaje y las transformaciones cualitativas en el desarrollo psíquico de los niños.Palabras clave: Educación inicial; Enseñanza de la Matemática; Primera infancia. 


Author(s):  
Kaique Nascimento Martins ◽  
Jamille Vilas Bôas

ResumoO presente estudo é uma pesquisa bibliográfica inspirada no Estado do Conhecimento, tendo como objetivo compreender focos temáticos nas produções acadêmicas que utilizam/abordam o ensino de matemática através da resolução de problemas. Para tanto, realizou-se um mapeamento das produções acadêmicas publicadas nos periódicos: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista e Educação Matemática Pesquisa, entre janeiro de 2011 e junho de 2019. De um modo geral, percebemos uma variedade de estudos contendo diferentes perspectivas discutidas e abordadas tanto na educação básica quanto no ensino superior.  A partir deste trabalho, é possível ampliar o entendimento sobre a temática, fortalecendo a ideia de que esta pode potencializar o processo de ensino e aprendizagem de matemática.Palavras-chave: Resolução de problemas, Mapeamento, Educação matemática.AbstractThe present study is a bibliographic research inspired by the state of knowledge, aiming to understand thematic focuses on academic productions that use/approach teaching mathematics through problem-solving. For this purpose, we mapped the academic productions published in journals: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista, and Educação Matemática Pesquisa, published between January 2011 and June 2019. We noticed a variety of studies containing different perspectives discussed and addressed both in basic and university education. From this work, it is possible to broaden the understanding of the theme, strengthening the idea that it can enhance the mathematics teaching and learning process.Keywords: Problem solving, Mapping, Mathematics education. ResumenEl presente estudio es una investigación bibliográfica inspirada en el estado del conocimiento, con el objetivo de comprender enfoques temáticos sobre producciones académicas que utilizan/abordan la enseñanza de las matemáticas a través de la resolución de problemas. Para ello, mapeamos las producciones académicas publicadas en las revistas: BOLEMA, Boletim GEPEM, Zetetiké, Educação Matemática em Revista y Educação Matemática Pesquisa, publicadas entre enero de 2011 y junio de 2019. Notamos una variedad de estudios que contienen diferentes perspectivas discutidas y abordadas tanto en educación básica como en educación universitaria. A partir de este trabajo, es posible ampliar la comprensión del tema, fortaleciendo la idea de que puede potenciar el proceso de enseñanza y aprendizaje de las matemáticas.Palabras clave: Resolución de problemas, Mapeo, Educación matemática.


Author(s):  
David Tzuriel

Dynamic assessment (DA) is guided by theoretical conceptualization about the nature of cognitive modifiability and needs to construct diagnostic measures for children who do not reveal their learning potential in conventional static tests. The development of DA was stirred by inadequacy of conventional testing to provide precise answers for individual differences in learning ability, learning processes, cognitive functions, and non-intellective factors that are responsible for cognitive modifiability. The rationale for developing DA for preschool children is that early identification of children’s learning potential and deficient cognitive functions would facilitate development of mediation strategies to overcome their learning difficulties and actualize their learning potential. DA is defined as an assessment, by an active teaching process, of a child’s perception, learning, thinking, and problem solving. DA is aimed at modifying an individual’s cognitive functioning and observing subsequent changes in learning and problem-solving patterns within the testing situation. Development of DA was driven by criticism of standardized testing: (a) bias toward minority groups and children with special needs, (b) selective administration procedures of children with high-risk for being labled as intellectualy disabled, (c) lack of consideration of motivational and emotional factors, (d) lack of information on learning and metacognitive processes, and (e) inadequate recommendations on specific intervention strategies and prescriptive teaching. The main goals of DA are to assess learning potential, deficient cognitive functions, amount and nature of mediation required for change, and transfer of learning. The main mediation strategies used in DA are establishing prerequired thinking behaviors, self-regulation of behavior, enhancement of reflective and analytic processes, teaching task-specific concepts, feedback on success/failure in learning processes, and development of basic communication skills. DA of preschool children is more challenging than that of older children because executive functions and communication skills of young children are less developed. The best known DA approaches for young children are those of Lidz and Tzuriel; both are based on the theories of Vygotsky and Feuerstein. Lidz’s approach is focused on objectives that reflect curriculum demands of educational settings. Her Application of the Cognitive Functions Scale indicates the degree of mastery on cognitive tasks, responsiveness to intervention, and non-intellective factors. Tzuriel’s approach is characterized by innovations of instruments, assessment procedures adapted for developmental stages, mediation strategies, behavior checklists, and a recording and scoring for clinical and measurement versions. Tzuriel’s approach is characterized by 10 aspects: Adaptation of test materials to child’s developmental level, “bridging” of concrete operations to abstract operations, communication aspects, clinical and measurement versions, preliminary phase component of DA, scoring methods for the measurement version, transfer problems, comparison of modifiability across task dimensions, assessment of non-intellective factors, and creativity in construction of problems. A growing body of theory and research on DA supports the crucial role of the DA in: (a) reflecting better the learning potential of children than standardized testing, (b) confirming that the quality of mediation within the family, school, and peers systems is a strong determinant of cognitive modifiability, and (c) demonstrating DA as a powerful approach in revealing the implicit effects of intervention cognitive programs on cognitive development.


1988 ◽  
Vol 36 (4) ◽  
pp. 6-9
Author(s):  
James S. Cangelosi

Developing students' abilities to rcason with mathematics and apply mathematics to the solution of problems occurring in the real world hould be a primary focus of school mathematics (National Council of Teachers of Mathematics 1980). However, most mathemati cal curricula seem to place more emphasis on memorization of fact and algorithm than on reasoning and problem solving (Romberg and Carpenter 1986). The mathematics education literature abound with ideas for reversing the emphasis on memorization and for guiding the teaching of mathematics so that it has real-life meaning for children. Included among the idea are the following:


1982 ◽  
Vol 30 (3) ◽  
pp. 2

“Children can demonstrate some good problem solving if given a chance,” according to Moser and Carpenter. In “Young Children Are Good Problem Solvers” (p. 24). they report on a study of problem solving done by young children. One of the authors' concluding statements is, “lf you want good performance, you have to work at it and include a strong dose of problem solving in your teaching.”


1984 ◽  
Vol 15 (1) ◽  
pp. 73-75
Author(s):  
John G. Harvey

Unlike most books reviewed in the journal for Research in Mathematics Education, Problem Solving in the Mathematics Curriculum (PSMC) does not report research. Instead, it seems designed to (a) recommend that problem solving be consistently included in collegiate mathematics instruction, (b) describe some considerations in and ways of teaching problem solving, (c) present an extensive bibliography chosen to help those initiating or teaching problem-solving courses or problem-solving sequences within courses, and (d) give the results of a survey conducted by the Committee on the Teaching of Mathematics of the Mathematical Association of America; the survey provided the impetus for PSMC. Accordingly, the book is divided into four parts. The short first part describes the evolution of PSMC and the recommendations of the Committee on the Teaching of Mathematics. The second part, a more-or-less personal essay by Alan Schoenfeld, gives suggestions for teaching problem solving. The third and most extensive part is an annotated bibliography of journals, books, and articles that might be used to develop in struction in problem solving or to find appropriate problems for such instruction. The last part presents both the survey instrument and the results of the survey.


1983 ◽  
Vol 14 (3) ◽  
pp. 210-213
Author(s):  
Leslie P. Steffe ◽  
Rick N. Blake

Mathematics educators have for some time been interested in psychological bases for the teaching of mathematics in the schools (Buswell, 1951). They have naturally turned to cognitive theorists in their quest to understand such terms as knowledge, meaning, concepts, mental operations, problem solving, and insight. Gagné's (1983) paper is bur one example of this historical collaboration. His purpose is to “relate what is known about learning, … from the kind of theory [he has] described, to the problem of improving mathematics learning” (p. 10).


2004 ◽  
Vol 10 (6) ◽  
pp. 302-309
Author(s):  
Larry Buschman

Teachers face many challenges when attempting to teach problem solving to young children. This article examines these challenges from a classroom teacher's perspective and suggests ways to facilitate reform in mathematics instruction.


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