Studien utgår från en kvalitativt inriktad analys och metod, där syftet är att undersöka vilka huvudräkningsstrategier som 3 svenska respektive 3 engelska lärare undervisar i, inom addition. Det empiriska materialet består av intervjuer som sedan har transkriberats och analyserats. Studien har låtit sig inspireras av ett hermeneutiskt perspektiv kombinerat med Grounded Theory. Hermeneutiskt perspektiv innebär att all data som finns i studien har tolkats och analyserats. Grounded Theory är ett vanligt sätt att analysera kvalitativ data och genom denna teori har kategorier skapats utifrån det resultat som framkommit. Resultatet av studien visar att de svenska lärarnas vanligaste val av strategier är: talsorter var för sig och algoritmer. De engelska lärarnas vanligaste val av strategier är: tiokamrater, additionstabellen och algoritmer. Av resultatet framkommer även de skillnader som finns mellan de intervjuade lärarnas val av strategier. / The study is based on a qualitatively directed method and the main aim is to investigate, and examine the mental arithmetic strategies of both Swedish and English teachers. In particular, the methods they use, to teach addition. The empirical data within this research is based on first hand interviews with six teachers; three from Sweden, and three from England. The study is inspired by a Hermeneutic Perspective in combination with Grounded Theory. The word hermeneutic, means that all of the data contained in the study has been interpreted and analyzed by the researcher. Grounded Theory is a common method used to analyze qualitative data. With this theory, categories have been created on the basis of the results obtained within this study. The results of the study show that Swedish teachers' most common choices of strategies are; partitioning method, and algorithms. In contrast, the English teachers’ strategies are the following; number bonds, the additiontable and algorithms. The results of this study also illustrate the differences between the Swedish and the English teachers’ choices of strategies.

Syftet med studien är att bidra till ökad förståelse av och fördjupad kunskap om taluppfattningens och skriftliga räknemetoders betydelse för hinder i elevers matematikutveckling, särskilt avseende addition och subtraktion, samt undersöka hur lärare arbetar med dessa områden för att förebygga och möta hinder för matematikutveckling. Elevers matematikkunskaper sjunker och på senare år har brister i taluppfattning uppmärksammats som en möjlig orsak. Denna studie med kvalitativ ansats har intervjuer och skriftliga dokument som datainsamlingsmetod. Hur uppfattar nio lärare som undervisar i år 1-6 nödvändiga kunskaper i taluppfattning för att hantera skriftliga räknemetoder i addition och subtraktion och vilka förklaringar till brister lyfter de. Vilka verktyg används för att få kännedom om elevers kunskaper i matematik vad gäller taluppfattning och skriftliga räknemetoder? Av resultatet av studien framkommer att det finns variationer i uppfattningar om nödvändiga kunskaper och undervisning om taluppfattning och skriftliga räknemetoder. Resultaten på Nationella prov vad gäller de båda studerade områdena visar på ett bättre resultat då det gäller taluppfattning jämfört med skriftliga räknemetoder. Detta kan bero på den komplexitet som det sociala samspelet mellan olika strukturer i samhället innebär.

Under den verksamhetsförlagda tiden väcktes intresset för huvudräkning hos mig, ef­tersom eleverna valde att använda sig av miniräknare trots att de hade kunskap om olika huvudräk­ningsstrategier. Enligt skolverket (2011b) skall eleverna vid huvudräkning ta del av olika strategier för att stärka självsäkerheten och tilltron till sin förmåga. Syftet med studien var att undersöka vilken eller vilka strategier som några elever i grundskolan föredrog vid huvudräk­ning inom addition och subtraktion. Undersökningen byggde på en kvalitativ metod och her­meneutiken som teoretisk forskningsansats. Urvalet bestod av ett målinriktat urval kombinerat med ett bekvämlighetsurval och resulterade i tre elever från vardera tre olika skolor och skol­områden. Huvudräkningsuppgifter samt intervjuer användes som datainsamlingsmetod. Data­bearbetningen av intervjuerna har utförts under inspiration av hermeneutiken som bygger på tolkningar. Resultatet av studien visade att inom addition är det strategin talsorter var för sig, algoritm och dubbla som elever föredrar helst. Inom subtraktion varierade eleverna mer vid valet av huvudräkningsstrategier, där de helst föredrar räkna uppåt, algoritm, jämföra, tals­orter var för sig, komplettera, lägga till och räkna neråt. Resultatet visade även att skillnaden mellan skolorna inte var så stor, dock fanns det en liten skillnad mellan skola II och skola III vad gäller strategin räkna uppåt. Skillnaden var att skola II föredrar flera olika strategier av­seende subtraktion. Det framgår tydligt att eleverna har en god kunskap om olika huvudräk­ningsstrategier vid addition och subtraktion. Enligt eleverna är det på grund av att lärarna i sin undervisning hade gått igenom olika strategier inom huvudräkning. / During my practical training periods I became interested in mental arithmetic because I expe­rienced that the students chose calculators despite their knowledge of mental arithmetic strat­egies. According to skolverket (2011b) students shall take part of different strategies to strengthen their selfconfidence and belief in their own ability. The purpose of this study was to identify which strategies some students in middle school choose when they are practising mental arithmetic in addition and subtraction. The study was based on a qualitative method and hermeneutic as a theoretical approach. The sample consisted of a targeted selection in combination with a convenience selection and resulted in three students from each of three different schools and school areas. Mental arithmetic tasks and interviews were used as data collection method. Data processing of the interviews has been processed using hermeneutics method and is based on interpretation. The result of the study showed that partitioning num­bers, algorithm and double was the most common mental arithmetic strategies in addition. When it comes to strategies in subtraction the students varied more and the most common was counting upwards, algorithm, compare, partitioning numbers, complementary addition and counting back from. The result also showed that there was no significant difference between the schools except school II and III when it comes to the strategy counting upwards. The dif­ference was that school II uses several different strategies when performing subtractions. It was rather clear that the students in this study had a good knowledge of various mental arithmetic strategies for addition and subtraction, and according to themselves it was a consequence of the various strategies in mental arithmetics, that their teachers had taught them.

Στόχος της παρούσας έρευνας ήταν να διερευνηθούν οι επιδόσεις και τα είδη των στρατηγικών που χρησιμοποιούν οι μαθητές της Δ΄ τάξης του δημοτικού σχολείου, με και χωρίς μαθησιακές δυσκολίες στα μαθηματικά (ΜΜΔ), όταν υπολογίζουν νοερά προσθέσεις και αφαιρέσεις διψήφιων αριθμών και να διαπιστωθεί αν υπάρχει αξιόλογη διαφορά στην επίδοση μεταξύ των μαθητών αυτών. Προηγούμενες μελέτες που αφορούν στις ΜΜΔ έχουν ασχοληθεί με τις απλές (π.χ. 3+5) και όχι με τις διψήφιες νοερές προσθέσεις και αφαιρέσεις. Στην παρούσα έρευνα συμμετείχαν 85 μαθητές (40 με ΜΜΔ και 45 κανονικής επίδοσης στα μαθηματικά-ΚΕ), όπως προέκυψε από την αξιολόγησή τους με σταθμισμένες και μη δοκιμασίες. Επιπλέον, στους μαθητές αυτούς χορηγήθηκε δοκιμασία στους νοερούς υπολογισμούς. Τα αποτελέσματα της έρευνας έδειξαν ότι οι μαθητές ΚΕ χρησιμοποιούν, κατά κύριο λόγο, στρατηγικές υψηλού επιπέδου (αυτές που συντελούν στην καλύτερη κατανόηση των αριθμών) τόσο στην πρόσθεση όσο και στην αφαίρεση. Παρόλα αυτά, η χρήση στρατηγικών υψηλού επιπέδου είναι πιο έντονη στην πρόσθεση συγκριτικά με την αφαίρεση, γεγονός που υποδηλώνει τη δυσκολία της αφαίρεσης ως πράξη. Επιπλέον, οι αφαιρέσεις με κρατούμενο είναι πιο δύσκολες από αυτές χωρίς κρατούμενο και για τις δύο ομάδες. Επίσης, τα αποτελέσματα έδειξαν ότι οι επιδόσεις των μαθητών με ΜΜΔ γενικά σε όλες τις πράξεις είναι χειρότερες από αυτές των μαθητών ΚΕ. Τέλος, οι μαθητές με ΜΜΔ υπέπεσαν σε περισσότερα λάθη σε σχέση με τους μαθητές ΚΕ, ανάλογα με το είδος της πράξης, αλλά και σε περισσότερα είδη λαθών. Τα περισσότερα λάθη των μαθητών εντοπίστηκαν κυρίως στις αφαιρέσεις με κρατούμενο, όπου είτε αφαιρούσαν τις μονάδες του μειωτέου από τις μονάδες του αφαιρετέου είτε έκαναν κάποιο λάθος στο δανεισμό. Περαιτέρω έρευνες είναι απαραίτητες προκειμένου να διαπιστωθούν οι διαφορές που εντοπίζονται στην επίδοση, τις στρατηγικές και τα λάθη μεταξύ των παραπάνω μαθητών στις διψήφιες νοερές προσθέσεις και αφαιρέσεις. / The purpose of the present study was to investigate the performance and the kinds of strategies that students, with and without mathematical learning disabilities (MLD), attending fourth grade of elementary school (9 years old) use when they add and subtract two-digit numbers mentally and to find out whether there is any notable difference in the performance between these groups. Previous studies related to MLD have dealt with simple mental additions and subtractions (eg 3+5) and not with two-digit calculations. Eighty five students participated in the present study (40 with MLD and 45 normally achieving students – NA). All students completed tests, which evaluated their mathematical skills. The results from these tests led to the selection of the students that would form each one of the two groups. Moreover, students of both groups were assessed on a mental calculation task. The results of the study indicated that NA students tend to use sophisticated strategies (those that contribute to a better understanding of numbers) both in addition and subtraction. However, the percentage of sophisticated strategies appeared to be higher in addition than in subtraction, a fact that implies there is a particular difficulty in subtractions. Moreover, this study found that subtractions, which involve regrouping procedures (such as “carrying” or “borrowing”), are more complex than others for both groups. Furthermore, the results showed that the performance of MLD students on mental calculation tasks was worse than NA students. Last but not least, MLD children made more errors than NA children depending on the type of operation and they made more types-categories of errors than NA children. Most errors were made in subtractions with carrying digit. There either they subtracted minuend’s units from subtrahend’s units or they made an error with the carrying digit. Further research is necessary in order to investigate the performance and the kinds of strategies that students, with and without mathematical learning disabilities when they add and subtract mentally two-digit numbers.

Made available in DSpace on 2014-12-17T15:04:59Z (GMT). No. of bitstreams: 1 FreudR_DISSERT.pdf: 1583176 bytes, checksum: edb85efc18144ffa5d56e32fae4d8c7c (MD5) Previous issue date: 2013-03-20 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / This paper describes a study on the possibilities of teaching Vedic Mathematics for teaching the four operations. For this various literature sources were consulted considering three main aspects. The first of a historical-cultural, in order to gather information about the Mathematics originated from Vedic civilization, which highlight (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida , 2009). This sought to emphasize relationships of the development of this culture with the math involved in the book Vedic Mathematics written by Tirthaji and published in 1965. In this respect the work brings notes on the history of mathematics on the development of mathematics in ancient India. The second aspect was related to teaching mathematics through research activities in the classroom, in this sense, I sought a bibliography to assist in the construction of a proposed activity to teach the four operations, based on the sutras of Vedic Mathematics, but within an investigative approach, assisting in the development of mental calculation strongly stimulated by the Vedic Mathematics Sutras. The authors were adopted (Mendes, 2006, 2009a, 2009b), Bridge (2003). The third aspect considered to search for books on teaching Vedic Mathematics, written by other authors, based on the book by Tirthaji. This revealed Vedic Mathematics textbooks adopted in schools and free courses in the UK, USA and India, all based on the book Vedic Mathematics of Tirthaji. From the bibliographical studies were prepared didactic guidelines and suggested activities for the teacher, to assist in teaching the four operations. The educational product, consisting of Chapters 4 and 5, is the body of the dissertation and consists of didactic guidelines and suggestions for activities that aim to contribute to the teachers who teach initial years of elementary school / Este trabalho descreve um estudo acerca das possibilidades did?ticas da Matem?tica V?dica para o ensino das quatro opera??es. Para isso foram consultadas v?rias fontes bibliogr?ficas considerando tr?s aspectos principais. O primeiro de car?ter hist?ricocultural, com a finalidade de reunir informa??es acerca da Matem?tica oriunda da civiliza??o v?dica, onde destaco (Plofker, 2009), (Joseph, 1996), (Bishop, 1999), (Katz, 1998), (Almeida, 2009). Este aspecto buscou evidenciar as rela??es do desenvolvimento desta cultura com a matem?tica implicada no livro V?dic Mathematics escrito por Tirthaji e publicado em 1965. Neste aspecto o trabalho traz apontamentos em Hist?ria da Matem?tica acerca do desenvolvimento da Matem?tica na ?ndia antiga. O segundo aspecto foi referente ao ensino de Matem?tica por meio de atividades de investiga??o em sala de aula, neste sentido, busquei uma bibliografia para auxiliar na constru??o de uma proposta de atividade para ensinar as quatro opera??es, partindo dos Sūtras da Matem?tica V?dica, mas dentro de um enfoque investigativo, auxiliando no desenvolvimento do c?lculo mental fortemente estimulado pelos Sūtras da Matem?tica V?dica. Os autores adotados foram (Mendes, 2006, 2009a, 2009b), Ponte (2003). O terceiro aspecto considerou a busca por livros sobre o ensino de Matem?tica V?dica, escritos por outros autores, baseados no livro de Tirthaji. Este aspecto revelou livros texto de Matem?tica V?dica adotados em escolas e cursos livres do Reino Unido, Estados Unidos e ?ndia, todos tendo como base o livro Vedic Mathematics de Tirthaji. A partir dos estudos bibliogr?ficos foram elaboradas orienta??es did?ticas e sugest?es de atividades para o professor, visando auxiliar no ensino das quatro opera??es. O produto educacional, composto pelos cap?tulos 4 e 5, encontra-se no corpo da disserta??o e consiste nas orienta??es did?ticas e sugest?es de atividades que visam contribuir com os professores que ensinam do Ensino Fundamental anos inicias

A pergunta principal de nossa pesquisa é: Qual o valor e o papel do cálculo mental nas séries iniciais do Ensino Fundamental? Esta pesquisa busca identificar quais as concepções de cálculo mental e a sua importância no contexto educacional da rede municipal de São Paulo, do 2º ao 5º ano do Ensino Fundamental. Buscamos compreender tal contexto junto aos professores da rede e também junto às propostas curriculares e aos cursos de formação. Para tanto, analisamos alguns documentos da rede municipal, questionários respondidos pelos professores e uma entrevista com uma formadora da rede. Consideramos cálculo mental como um conjunto de procedimentos de cálculo que podem ser analisados e articulados diferentemente por cada indivíduo para a obtenção mais adequada de resultados exatos ou aproximados, com ou sem o uso de lápis e papel. Os procedimentos de cálculo mental se apóiam nas propriedades do sistema de numeração decimal e nas propriedades das operações, e colocam em ação diferentes tipos de escrita numérica, assim como diferentes relações entre os números. O cálculo mental permite maior flexibilidade de calcular, bem como maior segurança e consciência na realização e confirmação dos resultados esperados, tornando-se relevante na capacidade de enfrentar problemas. Tal desenvolvimento de estratégias pessoais para se calcular vai ao encontro das tendências recentes da psicologia do desenvolvimento cognitivo, que nos apontam para a importância de uma aprendizagem com significado e do desenvolvimento da autonomia do aluno. Desse modo, paralelamente, outras perguntas foram sendo traçadas e surgiu a necessidade de buscarmos perceber quais as concepções de ensino-aprendizagem que estão por trás das estratégias de ensino de cálculo mental adotadas na rede. Portanto, também permeiam pela pesquisa, as discussões acerca da exploração e resolução de problemas, da relação professor-saber-aluno e da aprendizagem com compreensão, principalmente as suscitadas por Piaget, Kamii e Charnay. Percebemos que tanto por parte dos documentos quanto dos professores há o reconhecimento da importância do cálculo mental no ensino-aprendizagem de matemática, mas, na prática, é pouco usado em sala de aula e sua concepção gera diversas interpretações. Embora o cálculo mental venha recebendo destaque em diversos programas curriculares e em pesquisas acadêmicas, ainda há necessidade de se ampliar a discussão tanto em relação ao seu papel na construção dos conhecimentos matemáticos, quanto às formas ou metodologias envolvidas no seu desenvolvimento. Assim, esse trabalho procura contribuir para a reflexão da importância do cálculo mental para a construção dessa autonomia discente e traçar um olhar sobre o seu valor e papel no campo da educação matemática. / The main question of our research is: What is the value and role of mental calculation in the first grades of Elementary School? This research intends to identify what conceptions of mental calculation and its importance in the educational context of the municipal schools in São Paulo, from 2nd to 5th year of Elementary School. We wanted to understand this context with the teachers and also at the curriculum proposals and documents of courses for teachers. For this, we analyzed some of the municipal documents, questionnaires completed by teachers and an interview with a professional who provides courses to the teachers. We consider mental calculation as a group of calculation procedures that can be analyzed and articulated differently by each individual to achieve better accurate or approximate results, with or without the usage of pencil and paper. The procedures for mental calculation are based on the properties of the decimal system and the properties of operations, and put into action different types of writing numbers, as well as different relations between numbers. The mental calculation allows greater flexibility to calculate and it provides greater security and awareness in making and confirming expected results, becoming relevant in the ability to face problems. This development of personal strategies to calculate has similarities with the current trends in cognitive developmental psychology that point us to the importance of meaningful learning and the development of the learners autonomy. In such way, other questions have been outlined and the need to understand what concepts of teaching-learning underlie teaching strategies for mental calculation adopted by the municipal schools of São Paulo. Therefore, discussions about exploring and solving problems, the relation between teacher-knowledge-student and learning with understanding permeate the research as well, mainly those ones raised by Piaget, Kamii and Charnay. We realize that both documents and teachers recognize the importance of mental calculation in mathematics teaching-learning, but it is not very used in classrooms and its concept has different interpretations. Although the mental calculation has been receiving attention from various school curricula and academic researches, there is a need to broaden the discussion both in relation to its role in the construction of mathematical knowledge and to the forms or methodologies involved in its development. Thus, this study intends to contribute with the reflection of the importance of mental calculation in the construction of students autonomy and chart a look on its value and role in the field of mathematical education.

A pergunta principal de nossa pesquisa é: Qual o valor e o papel do cálculo mental nas séries iniciais do Ensino Fundamental? Esta pesquisa busca identificar quais as concepções de cálculo mental e a sua importância no contexto educacional da rede municipal de São Paulo, do 2º ao 5º ano do Ensino Fundamental. Buscamos compreender tal contexto junto aos professores da rede e também junto às propostas curriculares e aos cursos de formação. Para tanto, analisamos alguns documentos da rede municipal, questionários respondidos pelos professores e uma entrevista com uma formadora da rede. Consideramos cálculo mental como um conjunto de procedimentos de cálculo que podem ser analisados e articulados diferentemente por cada indivíduo para a obtenção mais adequada de resultados exatos ou aproximados, com ou sem o uso de lápis e papel. Os procedimentos de cálculo mental se apóiam nas propriedades do sistema de numeração decimal e nas propriedades das operações, e colocam em ação diferentes tipos de escrita numérica, assim como diferentes relações entre os números. O cálculo mental permite maior flexibilidade de calcular, bem como maior segurança e consciência na realização e confirmação dos resultados esperados, tornando-se relevante na capacidade de enfrentar problemas. Tal desenvolvimento de estratégias pessoais para se calcular vai ao encontro das tendências recentes da psicologia do desenvolvimento cognitivo, que nos apontam para a importância de uma aprendizagem com significado e do desenvolvimento da autonomia do aluno. Desse modo, paralelamente, outras perguntas foram sendo traçadas e surgiu a necessidade de buscarmos perceber quais as concepções de ensino-aprendizagem que estão por trás das estratégias de ensino de cálculo mental adotadas na rede. Portanto, também permeiam pela pesquisa, as discussões acerca da exploração e resolução de problemas, da relação professor-saber-aluno e da aprendizagem com compreensão, principalmente as suscitadas por Piaget, Kamii e Charnay. Percebemos que tanto por parte dos documentos quanto dos professores há o reconhecimento da importância do cálculo mental no ensino-aprendizagem de matemática, mas, na prática, é pouco usado em sala de aula e sua concepção gera diversas interpretações. Embora o cálculo mental venha recebendo destaque em diversos programas curriculares e em pesquisas acadêmicas, ainda há necessidade de se ampliar a discussão tanto em relação ao seu papel na construção dos conhecimentos matemáticos, quanto às formas ou metodologias envolvidas no seu desenvolvimento. Assim, esse trabalho procura contribuir para a reflexão da importância do cálculo mental para a construção dessa autonomia discente e traçar um olhar sobre o seu valor e papel no campo da educação matemática. / The main question of our research is: What is the value and role of mental calculation in the first grades of Elementary School? This research intends to identify what conceptions of mental calculation and its importance in the educational context of the municipal schools in São Paulo, from 2nd to 5th year of Elementary School. We wanted to understand this context with the teachers and also at the curriculum proposals and documents of courses for teachers. For this, we analyzed some of the municipal documents, questionnaires completed by teachers and an interview with a professional who provides courses to the teachers. We consider mental calculation as a group of calculation procedures that can be analyzed and articulated differently by each individual to achieve better accurate or approximate results, with or without the usage of pencil and paper. The procedures for mental calculation are based on the properties of the decimal system and the properties of operations, and put into action different types of writing numbers, as well as different relations between numbers. The mental calculation allows greater flexibility to calculate and it provides greater security and awareness in making and confirming expected results, becoming relevant in the ability to face problems. This development of personal strategies to calculate has similarities with the current trends in cognitive developmental psychology that point us to the importance of meaningful learning and the development of the learners autonomy. In such way, other questions have been outlined and the need to understand what concepts of teaching-learning underlie teaching strategies for mental calculation adopted by the municipal schools of São Paulo. Therefore, discussions about exploring and solving problems, the relation between teacher-knowledge-student and learning with understanding permeate the research as well, mainly those ones raised by Piaget, Kamii and Charnay. We realize that both documents and teachers recognize the importance of mental calculation in mathematics teaching-learning, but it is not very used in classrooms and its concept has different interpretations. Although the mental calculation has been receiving attention from various school curricula and academic researches, there is a need to broaden the discussion both in relation to its role in the construction of mathematical knowledge and to the forms or methodologies involved in its development. Thus, this study intends to contribute with the reflection of the importance of mental calculation in the construction of students autonomy and chart a look on its value and role in the field of mathematical education.

Made available in DSpace on 2015-09-25T12:18:15Z (GMT). No. of bitstreams: 1 Eliane Farias Ananias parte 1.pdf: 1950426 bytes, checksum: 53549b60d20134559e389bf0a27eddb3 (MD5) Previous issue date: 2010-12-13 / By carrying out a research work on the use of games in mathematical education under Piaget´s constructivist perspective, we realized that was from the XX Century which more relevant contributions appeared under teaching proposes that incorporated the use of pedagogical materials. The research work and studies of Piaget, Grando, Brenelli, Bittar and Freitas, Mendonça and Lellis, Piaget and Chomsky, Costa, Parra, Alves and Ramos based the research work in question. From this reality, the research aimed to investigate, to intervene and to analyze cognitive aspects on the construction and recall of mathematical concepts (addition, subtraction, multiplication and division) and the ability of mental calculus in the teaching and learning of Mathematics by using the Calendar and the Dominó game having the four operations as resources. The research work carried out is presented as a case study done in a public primary school in the city of Campina Grande Paraiba, with twenty five students between ten to eleven years old. The data collection was done in five moments by the classroom being the research environment. The data was analyzed by taking into account three categories which emerged from the five moments. Triangulation was the technique used in our analyses. As findings, the research work has initially shown that the students were not conscious that they were able to do mental calculus. The classroom environment itself showed to be good for knowledge construction, as the students showed interest and good during all the moments of the research. In this context, the Mental Calculus, within the developed activities with the use of the Calendar and the Dominó Game for the four operations, contributed for the students to be conducted gradually for constructed and recalled mathematical concepts within the Mathematical Operations. For seeking cognitive structures equilibration, the group work, which was not the focus of our research work, has shown to be important factor in the development of the students cognitive aspects. The research work also provoke the students teacher reflection on the use of Mental Calculus and of ludic activities in the classroom, mainly in the teaching concepts on Mathematical Operations, making her to realize improvement on the students learning process. / Ao realizar um estudo sobre o uso de jogos e a habilidade de cálculo mental na educação matemática, sob a perspectiva construtivista de Piaget, percebemos que foi a partir do século XX que apareceram as contribuições mais relevantes com propostas de ensino sobre os mesmos. Os estudos e pesquisas de Piaget, Grando, Brenelli, Bittar e Freitas, Mendonça e Lellis, Piaget e Chomsky, Costa, Parra, Alves e Ramos nortearam a pesquisa em questão. Diante desta realidade, essa pesquisa teve como objetivo investigar, intervir e analisar aspectos sobre construção e resgate de conceitos matemáticos (adição, subtração, multiplicação e divisão) e a habilidade de Cálculo Mental no ensino e aprendizagem da Matemática, utilizando o Calendário e o Jogo de Dominó com as Quatro Operações, como recursos. A pesquisa que realizamos se apresenta como um Estudo de Caso, realizado em uma escola primária da rede pública da cidade de Campina Grande - Paraíba, com vinte e cinco alunos, entre dez e onze anos. A coleta de dados se deu em Cinco Momentos, sendo o ambiente de pesquisa a própria sala de aula. Os dados foram analisados levando-se em consideração três categorias que emergiram dos Cinco Momentos. A técnica de triangulação foi utilizada em toda a análise. Como resultados, a pesquisa revelou inicialmente que os alunos não tinham consciência de que eram capazes de calcular mentalmente. O próprio ambiente sala de aula mostrou-se propício para a construção de conhecimento, uma vez que os alunos apresentaram interesse e gosto durante todos os momentos da pesquisa. Neste contexto, o Cálculo Mental, atrelado as Atividades desenvolvidas com o uso do Calendário e com o Jogo de Dominó com as Quatro Operações, contribuiu para que os alunos fossem conduzidos gradativamente a construírem e resgatarem conceitos matemáticos inerentes às Operações Matemáticas. Na busca pela equilibração das estruturas cognitivas, o trabalho em grupo, que não era foco de nossa pesquisa, mostrou ser um fator importante no desenvolvimento de aspectos cognitivos dos alunos. A pesquisa também proporcionou reflexão da professora da turma sobre a utilização do Cálculo Mental e de atividades lúdicas em sala de aula, principalmente no ensino de conceitos inerentes às Operações Matemáticas, fazendo-a perceber melhoria de aprendizagem dos alunos.

Made available in DSpace on 2015-09-25T12:22:02Z (GMT). No. of bitstreams: 1 PDF - Eliane Farias Ananias.pdf: 7392104 bytes, checksum: 261683bd406911e8bd044a35cf3dd3ab (MD5) Previous issue date: 2010-12-13 / By carrying out a research work on the use of games in mathematical education under Piaget´s constructivist perspective, we realized that was from the XX Century which more relevant contributions appeared under teaching proposes that incorporated the use of pedagogical materials. The research work and studies of Piaget, Grando, Brenelli, Bittar and Freitas, Mendonça and Lellis, Piaget and Chomsky, Costa, Parra, Alves and Ramos based the research work in question. From this reality, the research aimed to investigate, to intervene and to analyze cognitive aspects on the construction and recall of mathematical concepts (addition, subtraction, multiplication and division) and the ability of mental calculus in the teaching and learning of Mathematics by using the Calendar and the Dominó game having the four operations as resources. The research work carried out is presented as a case study done in a public primary school in the city of Campina Grande Paraiba, with twenty five students between ten to eleven years old. The data collection was done in five moments by the classroom being the research environment. The data was analyzed by taking into account three categories which emerged from the five moments. Triangulation was the technique used in our analyses. As findings, the research work has initially shown that the students were not conscious that they were able to do mental calculus. The classroom environment itself showed to be good for knowledge construction, as the students showed interest and good during all the moments of the research. In this context, the Mental Calculus, within the developed activities with the use of the Calendar and the Dominó Game for the four operations, contributed for the students to be conducted gradually for constructed and recalled mathematical concepts within the Mathematical Operations. For seeking cognitive structures equilibration, the group work, which was not the focus of our research work, has shown to be important factor in the development of the students cognitive aspects. The research work also provoke the students teacher reflection on the use of Mental Calculus and of ludic activities in the classroom, mainly in the teaching concepts on Mathematical Operations, making her to realize improvement on the students learning process. / Ao realizar um estudo sobre o uso de jogos e a habilidade de cálculo mental na educação matemática, sob a perspectiva construtivista de Piaget, percebemos que foi a partir do século XX que apareceram as contribuições mais relevantes com propostas de ensino sobre os mesmos. Os estudos e pesquisas de Piaget, Grando, Brenelli, Bittar e Freitas, Mendonça e Lellis, Piaget e Chomsky, Costa, Parra, Alves e Ramos nortearam a pesquisa em questão. Diante desta realidade, essa pesquisa teve como objetivo investigar, intervir e analisar aspectos sobre construção e resgate de conceitos matemáticos (adição, subtração, multiplicação e divisão) e a habilidade de Cálculo Mental no ensino e aprendizagem da Matemática, utilizando o Calendário e o Jogo de Dominó com as Quatro Operações, como recursos. A pesquisa que realizamos se apresenta como um Estudo de Caso, realizado em uma escola primária da rede pública da cidade de Campina Grande - Paraíba, com vinte e cinco alunos, entre dez e onze anos. A coleta de dados se deu em Cinco Momentos, sendo o ambiente de pesquisa a própria sala de aula. Os dados foram analisados levando-se em consideração três categorias que emergiram dos Cinco Momentos. A técnica de triangulação foi utilizada em toda a análise. Como resultados, a pesquisa revelou inicialmente que os alunos não tinham consciência de que eram capazes de calcular mentalmente. O próprio ambiente sala de aula mostrou-se propício para a construção de conhecimento, uma vez que os alunos apresentaram interesse e gosto durante todos os momentos da pesquisa. Neste contexto, o Cálculo Mental, atrelado as Atividades desenvolvidas com o uso do Calendário e com o Jogo de Dominó com as Quatro Operações, contribuiu para que os alunos fossem conduzidos gradativamente a construírem e resgatarem conceitos matemáticos inerentes às Operações Matemáticas. Na busca pela equilibração das estruturas cognitivas, o trabalho em grupo, que não era foco de nossa pesquisa, mostrou ser um fator importante no desenvolvimento de aspectos cognitivos dos alunos. A pesquisa também proporcionou reflexão da professora da turma sobre a utilização do Cálculo Mental e de atividades lúdicas em sala de aula, principalmente no ensino de conceitos inerentes às Operações Matemáticas, fazendo-a perceber melhoria de aprendizagem dos alunos.

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