Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração
Autor(a) principal: | |
---|---|
Data de Publicação: | 2012 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/6036 |
Resumo: | Research has shown that some properties of the additive problem may cause difficulties to solve it. The most important are: the problems presentation form, the semantic structure and the position of the unknown. Two experiments were conducted with some methodological differences, but both with the aim of investigating if the formation of an equivalence class between different problems presentation forms could reduce difficulties in solving problems. Eight students from the 2nd to the 5th year of elementary school with difficulties in solving problems of the pretest analysis participated in Experiment 1. It was applied a procedure for teaching conditional discriminations between different forms of presentation of addition problems (numeralproblem, word-problem, collection-problem and balance-problem), followed by Posttest 1. There was an increase in the percentage of accuracy for all types of problems, but five participants had difficulties with the balance-problems. It was also assessed if an additional procedure for teaching algorithmic for problem solving additives with unknowns at positions a and b could produce even greater increase in the percentage of correct answers. There were two sessions for teaching the addition algorithm, followed by post-test 2, and two sessions for teaching subtraction algorithm, succeeded by Posttest 3 and generalization test. Four participants showed an increase in the percentage of correct responses at post-test 2 and six at Post-test 3. This result, although positive, suggests that procedural changes are necessary so that all may be benefited by learning algorithms. Participants achieved 100% correct responses at generalization test. In Experiment 2, three forms of presentation (numeral-problem, word-problem and balance-problem) were used. The goal was to produce the formation of two sets of equivalence classes, one of addition and one of subtraction, and evaluate its effect on problem solving performances. In order to reduce difficulties with balance, two sessions were designed to teach participants about their operation. Eight students in the 2nd to 5th year that presented difficulties in the pre-test problem solving participated. After the formation of classes, it was found in Post-test 1 that all participants increased the percentage of correct answers. It was then assessed whether a practice in solving balance-problems could further improve this performance, which was confirmed. In Generalization Test 1, all participants reached percentages above 75% accuracy. We evaluated whether it would be possible to improve the teaching of algorithms phase of Experiment 1. We performed a single session for teaching together addition and subtraction algorithms, which was followed by post-test 3, in which there was an increase in the percentage of correct responses. Then the generalization test was reapplied, in which all achieved 100% accuracy. In Experiment 2, at each post-test, there was improvement in performance. It was demonstrated that the teaching procedures adopted are important to reduce learning difficulties in problem solving. |
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Henklain, Marcelo Henrique OliveiraCarmo, João dos Santoshttp://lattes.cnpq.br/1263046410329694http://lattes.cnpq.br/3486276032268863a62394c1-63b8-4a36-80df-e6978a860e572016-06-02T20:30:54Z2012-12-212016-06-02T20:30:54Z2012-12-14https://repositorio.ufscar.br/handle/ufscar/6036Research has shown that some properties of the additive problem may cause difficulties to solve it. The most important are: the problems presentation form, the semantic structure and the position of the unknown. Two experiments were conducted with some methodological differences, but both with the aim of investigating if the formation of an equivalence class between different problems presentation forms could reduce difficulties in solving problems. Eight students from the 2nd to the 5th year of elementary school with difficulties in solving problems of the pretest analysis participated in Experiment 1. It was applied a procedure for teaching conditional discriminations between different forms of presentation of addition problems (numeralproblem, word-problem, collection-problem and balance-problem), followed by Posttest 1. There was an increase in the percentage of accuracy for all types of problems, but five participants had difficulties with the balance-problems. It was also assessed if an additional procedure for teaching algorithmic for problem solving additives with unknowns at positions a and b could produce even greater increase in the percentage of correct answers. There were two sessions for teaching the addition algorithm, followed by post-test 2, and two sessions for teaching subtraction algorithm, succeeded by Posttest 3 and generalization test. Four participants showed an increase in the percentage of correct responses at post-test 2 and six at Post-test 3. This result, although positive, suggests that procedural changes are necessary so that all may be benefited by learning algorithms. Participants achieved 100% correct responses at generalization test. In Experiment 2, three forms of presentation (numeral-problem, word-problem and balance-problem) were used. The goal was to produce the formation of two sets of equivalence classes, one of addition and one of subtraction, and evaluate its effect on problem solving performances. In order to reduce difficulties with balance, two sessions were designed to teach participants about their operation. Eight students in the 2nd to 5th year that presented difficulties in the pre-test problem solving participated. After the formation of classes, it was found in Post-test 1 that all participants increased the percentage of correct answers. It was then assessed whether a practice in solving balance-problems could further improve this performance, which was confirmed. In Generalization Test 1, all participants reached percentages above 75% accuracy. We evaluated whether it would be possible to improve the teaching of algorithms phase of Experiment 1. We performed a single session for teaching together addition and subtraction algorithms, which was followed by post-test 3, in which there was an increase in the percentage of correct responses. Then the generalization test was reapplied, in which all achieved 100% accuracy. In Experiment 2, at each post-test, there was improvement in performance. It was demonstrated that the teaching procedures adopted are important to reduce learning difficulties in problem solving.Pesquisas demonstraram que algumas propriedades do problema aditivo podem gerar dificuldades para solucioná-lo, como: a forma de apresentação do problema, a estrutura semântica e a posição da incógnita. Foram realizados dois experimentos com algumas diferenças metodológicas, porém ambos com o objetivo de investigar se a formação de uma classe de equivalência entre diferentes formas de apresentação de problemas pode reduzir dificuldades na resolução de problemas. Participaram do Experimento 1 oito estudantes do 2° ao 5° ano do Ensino Fundamental com dificuldades, verificadas no pré-teste, na resolução de problemas. Aplicou-se procedimento para ensino de discriminações condicionais entre diferentes formas de apresentação de problemas de adição (operação com algarismo, problema escrito, coleção e balança), seguido pelo Pós-teste 1. Houve aumento na porcentagem de acertos em todos os tipos de problemas, porém cinco participantes tiveram dificuldades com os problemas na forma de balança. Foi avaliado em seguida se um procedimento adicional de ensino de algoritmo para resolução de problemas aditivos com incógnitas nas posições a e b poderia produzir aumento ainda maior na porcentagem de acertos dos participantes. Foram realizadas duas sessões para ensino do algoritmo de adição, seguida pelo Pós-teste 2, e duas sessões para o ensino do algoritmo de subtração, sucedida pelo Pós-teste 3 e teste de generalização. Quatro participantes apresentaram aumento da porcentagem de acertos no Pós-teste 2 e seis no Pós-teste 3. Esse resultado, embora positivo, sugere que mudanças de procedimento são necessárias de modo que todos possam ser beneficiados pelo ensino de algoritmos. Os participantes acertaram todos os problemas do teste de generalização. No Experimento 2, foram utilizadas três formas de apresentação (algarismos, escrito e balança). O objetivo foi produzir a formação de dois conjuntos de classes de equivalência, uma de adição e outra de subtração, e avaliar o seu efeito sobre o desempenho na solução de problemas. Com o intuito de reduzir dificuldades com a balança, foram planejadas duas sessões para ensinar os participantes sobre o seu funcionamento. Participaram oito estudantes do 2º ao 5º ano que apresentaram dificuldades no pré-teste na solução de problemas. Após a formação das classes, verificou-se no Pós-teste 1 que todos os participantes aumentaram a porcentagem de acertos. Foi avaliado então se um treino de resolução de problemas sob a forma de balança poderia melhorar ainda mais esse desempenho, o que foi confirmado. No Teste de Generalização 1, todos os participantes alcançaram porcentagens de acerto acima de 75%. Foi avaliado também se seria possível aprimorar a fase de ensino de algoritmos do Experimento 1. Realizou-se uma única sessão para ensino conjunto dos algoritmos de adição e subtração, que foi seguida pelo Pós-teste 3, no qual verificou-se aumento na porcentagem de acertos. Em seguida foi reaplicado o teste de generalização, no qual todos alcançaram 100% de acerto. No Experimento 2, a cada pós-teste, observou-se melhora de desempenho. Foi demonstrado que os procedimentos de ensino adotados constituem aprendizagens importantes para reduzir dificuldades na resolução de problemas.Universidade Federal de Minas Geraisapplication/pdfporUniversidade Federal de São CarlosPrograma de Pós-Graduação em Psicologia - PPGPsiUFSCarBRPsicologia do comportamento e cogniçãoEquivalência de estímulosMatemáticaResolução de problemasMatemática Adição e subtraçãoEstudantes de ensino fundamentalStimulus equivalenceMathematicsProblem solvingAddition and subtractionElementary School StudentsCIENCIAS HUMANAS::PSICOLOGIAEfeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtraçãoSome effects of equivalence class formation over the solution of addition and subtraction problemsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesis-1-1549c4715-88e5-452b-a95c-99dee222f747info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINAL4767.pdfapplication/pdf2897312https://repositorio.ufscar.br/bitstream/ufscar/6036/1/4767.pdf90bb4e18d1a2983784bf8df4c4c7b625MD51TEXT4767.pdf.txt4767.pdf.txtExtracted texttext/plain0https://repositorio.ufscar.br/bitstream/ufscar/6036/2/4767.pdf.txtd41d8cd98f00b204e9800998ecf8427eMD52THUMBNAIL4767.pdf.jpg4767.pdf.jpgIM Thumbnailimage/jpeg6460https://repositorio.ufscar.br/bitstream/ufscar/6036/3/4767.pdf.jpg2a9cafaab9633caef407f73e5756b193MD53ufscar/60362023-09-18 18:31:37.592oai:repositorio.ufscar.br:ufscar/6036Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:37Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
dc.title.alternative.eng.fl_str_mv |
Some effects of equivalence class formation over the solution of addition and subtraction problems |
title |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
spellingShingle |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração Henklain, Marcelo Henrique Oliveira Psicologia do comportamento e cognição Equivalência de estímulos Matemática Resolução de problemas Matemática Adição e subtração Estudantes de ensino fundamental Stimulus equivalence Mathematics Problem solving Addition and subtraction Elementary School Students CIENCIAS HUMANAS::PSICOLOGIA |
title_short |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
title_full |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
title_fullStr |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
title_full_unstemmed |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
title_sort |
Efeitos da formação de classes de equivalência sobre a solução de problemas de adição e subtração |
author |
Henklain, Marcelo Henrique Oliveira |
author_facet |
Henklain, Marcelo Henrique Oliveira |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/3486276032268863 |
dc.contributor.author.fl_str_mv |
Henklain, Marcelo Henrique Oliveira |
dc.contributor.advisor1.fl_str_mv |
Carmo, João dos Santos |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1263046410329694 |
dc.contributor.authorID.fl_str_mv |
a62394c1-63b8-4a36-80df-e6978a860e57 |
contributor_str_mv |
Carmo, João dos Santos |
dc.subject.por.fl_str_mv |
Psicologia do comportamento e cognição Equivalência de estímulos Matemática Resolução de problemas Matemática Adição e subtração Estudantes de ensino fundamental |
topic |
Psicologia do comportamento e cognição Equivalência de estímulos Matemática Resolução de problemas Matemática Adição e subtração Estudantes de ensino fundamental Stimulus equivalence Mathematics Problem solving Addition and subtraction Elementary School Students CIENCIAS HUMANAS::PSICOLOGIA |
dc.subject.eng.fl_str_mv |
Stimulus equivalence Mathematics Problem solving Addition and subtraction Elementary School Students |
dc.subject.cnpq.fl_str_mv |
CIENCIAS HUMANAS::PSICOLOGIA |
description |
Research has shown that some properties of the additive problem may cause difficulties to solve it. The most important are: the problems presentation form, the semantic structure and the position of the unknown. Two experiments were conducted with some methodological differences, but both with the aim of investigating if the formation of an equivalence class between different problems presentation forms could reduce difficulties in solving problems. Eight students from the 2nd to the 5th year of elementary school with difficulties in solving problems of the pretest analysis participated in Experiment 1. It was applied a procedure for teaching conditional discriminations between different forms of presentation of addition problems (numeralproblem, word-problem, collection-problem and balance-problem), followed by Posttest 1. There was an increase in the percentage of accuracy for all types of problems, but five participants had difficulties with the balance-problems. It was also assessed if an additional procedure for teaching algorithmic for problem solving additives with unknowns at positions a and b could produce even greater increase in the percentage of correct answers. There were two sessions for teaching the addition algorithm, followed by post-test 2, and two sessions for teaching subtraction algorithm, succeeded by Posttest 3 and generalization test. Four participants showed an increase in the percentage of correct responses at post-test 2 and six at Post-test 3. This result, although positive, suggests that procedural changes are necessary so that all may be benefited by learning algorithms. Participants achieved 100% correct responses at generalization test. In Experiment 2, three forms of presentation (numeral-problem, word-problem and balance-problem) were used. The goal was to produce the formation of two sets of equivalence classes, one of addition and one of subtraction, and evaluate its effect on problem solving performances. In order to reduce difficulties with balance, two sessions were designed to teach participants about their operation. Eight students in the 2nd to 5th year that presented difficulties in the pre-test problem solving participated. After the formation of classes, it was found in Post-test 1 that all participants increased the percentage of correct answers. It was then assessed whether a practice in solving balance-problems could further improve this performance, which was confirmed. In Generalization Test 1, all participants reached percentages above 75% accuracy. We evaluated whether it would be possible to improve the teaching of algorithms phase of Experiment 1. We performed a single session for teaching together addition and subtraction algorithms, which was followed by post-test 3, in which there was an increase in the percentage of correct responses. Then the generalization test was reapplied, in which all achieved 100% accuracy. In Experiment 2, at each post-test, there was improvement in performance. It was demonstrated that the teaching procedures adopted are important to reduce learning difficulties in problem solving. |
publishDate |
2012 |
dc.date.available.fl_str_mv |
2012-12-21 2016-06-02T20:30:54Z |
dc.date.issued.fl_str_mv |
2012-12-14 |
dc.date.accessioned.fl_str_mv |
2016-06-02T20:30:54Z |
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masterThesis |
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