Studien undersöker hur matematiska begrepp etableras i diskursen i klassrummet och hur lärare planerar för, iscensätter och bearbetar matematiska begrepp. Studiens syfte är att studera hur lärare hanterar matematiska begrepp i undervisningen ur ett specialpedagogiskt perspektiv. Utifrån studiens ansats väljs två kvalitativa datainsamlingsmetoder. Till detta infogas Selander & Kress (2010) formellt inramad lärsekvens och Hallidays (2004) tre metafunktioner och en ny metafunktion, den institutionell funktion (Boistrup- Björklund, 2010).   Studien visar att procedurkunskap har en stor plats i undervisningen. Lärarna hanterar begrepp i förbifarten och funderar inte på vilken roll de språkliga uttrycken har. Det pågår först och främst två diskurser, den matematiska och den vardagliga. Diskurserna etableras utifrån olika sociala och sociomatematiska normer som styr undervisningen. Traditioner och förväntningar påverkar undervisningen och den påverkan verkar vara starkare än forskningsrön eller nya styrdokument. / The study examines how mathematical concepts established in the discourse in the classroom and how teachers plan for, implements and processes mathematical concepts. The study's purpose is to study how teachers deal with mathematical concepts in teaching from a special education perspective. Based on the study's approach chosen two qualitative data collection methods. To this inserts Selander & Kress´s (2010) formal learning design sequence and Halliday´s (2004), three meta-functions and an institutional function (Boistrup- Björklund, 2010).   The study shows that procedural knowledge has a big place in teaching.  Teachers deal with concepts in passing and not thinking about which part the linguistic expressions have. There are primarily two discourses ongoing, the mathematical and the everyday, the discourses are established based on various social and socio-mathematical norms that effects the teaching. Traditions and expectations affect the teaching and the effect seems to be stronger than research findings or new policy document.

<p>Denna studie syftar till att undersöka i vilka spontana lektyper inomhus, förskolebarn uttrycker matematiska begrepp. Bakgrunden till studien är att vi anser att matematikarbetet på förskolan ska utgå från barnens perspektiv och då har leken en viktig betydelse. Leken ses som en central del för matematiklärandet och begreppsbildningen och därför är förskolan en lämplig plats för denna studie. Om barnen redan på förskolan skapar ett intresse och börjar använda matematiska begrepp gynnar det även den begreppsanvändning som krävs i skolan. Med inspiration av ett etnografiskt förhållningssätt har det genomförts observationer på två förskoleavdelningar, vid sju tillfällen på varje avdelning. Avsikten har varit att observera barns matematiska begreppsanvändning i den spontana leken. Vid observationerna har ett särskilt framtaget observationsschema använts för att dokumentera vilka lektyper och matematiska begrepp som observerats. Resultatet visar att olika lektyper stimulerar olika begrepp och de begrepp som uttrycks mest är jämförelseord. De lektyper som framkom i resultatet är; rollek, bygglek, lego, spel, bilar, figurer, dockor och övrigt. Avslutningsvis diskuteras resultatet och metoden i förhållande till litteraturen och våra egna tankar. Tre teman är framtagna i resultatdiskussionen; språket, leken och miljön med utgångspunkt i barnens begreppsanvändning och lektyperna.</p> / <p>This study aims to examine in which spontaneous play indoors, children in preschool expresses mathematical concepts. The background to the study is our belief that the mathematics work in preschool should be assumed from the children's perspective and that play has an important role in that work. The spontaneous play are a central part of mathematics learning and conception and therefore is preschool an appropriate place for this study. If children in preschool at an early stage creates an interest and begin using mathematical concepts if also favors the concept of use, that required in school. Inspired by an ethnographic approach, there have been observations of two preschool departments, on seven occasions in each department. The intention has been to observe children's mathematical concepts used in the spontaneous play. At the observations, a designed observation chart has been used to record the play types and mathematical concepts observed. The result shows that different play types stimulate different concepts, and the concepts that are mostly expressed are comparison words. The play types that emerged in the result are; role play, construction play, lego, games, cars, figures, dolls and others. To sum up, we discuss the result and the method in relation to the literature and our own thoughts. Three themes are produced in the result discussion; language, play and the environment on the basis of children's concepts of use and play types.</p>

Denna kunskapsöversikt är skriven för att redogöra för vad forskning säger angående hur elevers matematiska språkutveckling påverkas av metoden kooperativt lärande. Den syftar också till redogörelse för hur den kooperativa undervisningsmetoden skiljer sig från den traditionella, det vill säga metoden som innebär att elever arbetar individuellt med uppgifter i en lärobok eller motsvarande.Arbetet är utfört med hjälp av publicerad forskning som behandlar ämnet. Resultatet beskriver den kooperativa lärandemetoden och jämför den med det traditionella sättet att lära sig på. Forskning redogör också för hur matematiken undervisas i klassrummet med hjälp avkommunikation och kooperativt lärande, samt hur användningen av det matematiska språketsker.Med hjälp av denna forskning har slutsatsen dragits att den kooperativa lärandemetoden harpositiv inverkan på den matematiska språkutvecklingen och att språkutvecklingen kan ske på ett enklare sätt med hjälp av kommunikation med de andra eleverna. Det matematiska språket kan utvecklas med hjälp av metoden kooperativt lärande då eleverna får större möjlighet att kommunicera och interagera med varandra på ett utvecklande sätt.

The problem of this study was an analysis of results obtained by a computer-assisted instructional approach and a lecture-demonstration instructional approach of teaching mathematical concepts in the area of office machines at the community college level. The purposes of this study were as follows: (1) to determine which method, the lecture-demonstration or computer assisted instruction, will produce the better mathematical skill in office machines; (2) to determine the effectiveness of computer-assisted instruction as compared to the lecture demonstration approach on the student’s attitude toward office machines, as measured by the Purdue attitude scale; (3) to compare the correlation between attitude and achievement for the computer-assisted instruction group and the lecture-demonstration group; and (4) to compare the correlation between attitude and achievement for high-ability students and low-ability students, based on scores obtained from the Otis-Lennon Mental Ability Test. The findings in this study indicate that there were no significant differences in mathematical achievement, attitude scores, or the correlation between attitude and achievement between students in the computer-assisted group and students in the lecture-demonstration group. The following conclusions were formulated from an analysis of this study. 1. Based on the mathematical achievement scores and the statistical analysis presented in this study, it is concluded that there are no demonstrated differences between the computer-assisted instructional approach and the lecture demonstration approach for teaching applied mathematical concepts to business machines students. 2. Based on the attitude scores presented in this study, students in both groups appear to have a favorable attitude toward the business machines course. Attitude scores for students in the computer-assisted group were not significantly different from scores for students in the lecture-demonstration group. 3. The integration of business machines and applied mathematics, in addition to developing speed and accuracy on electronic calculators and adding machines, produces increased achievement in mathematics.

Στην παρούσα έρευνα επιχειρείται να αναδειχθεί ο παιδαγωγικός ρόλος των δραστηριοτήτων στην οικειοποίηση από παιδιά της προσχολικής εκπαίδευσης μαθηματικών εννοιών, όπως η μέτρηση της χωρητικότητας δοχείων. Ερευνήθηκε η ηλικιακή επίδραση στο επίπεδο κατανόησης της έννοιας της μέτρησης της χωρητικότητας δοχείων. Τέλος προσπαθήσαμε να επαληθεύσουμε αποτελέσματα παρόμοιων ερευνών. Το δείγμα της έρευνας αποτέλεσαν 30 υποκείμενα ηλικιών 5–6 που φοιτούσαν το σχολικό έτος 2009-2010 σε δύο ελληνικά δημόσια νηπιαγωγεία και κοινωνικοοικονομικά ανήκαν στα μεσαία στρώματα. Η έρευνα διεξήχθη σε τρεις φάσεις: στο pre-test, τη διδασκαλία και το post-test. Στο pre-test, ελέγξαμε αν τα παιδιά μπορούν να πραγματοποιήσουν άμεσες (απευθείας μεταξύ δοχείων) και έμμεσες (με τη χρήση κάποιου κοινού μέτρου) συγκρίσεις της χωρητικότητας δοχείων. Στη διδακτική παρέμβαση προτάθηκαν δραστηριότητες, οι οποίες αποσκοπούσαν στη δημιουργία κατάλληλων frameworks σχετικά με τις άμεσες και έμμεσες συγκρίσεις. Ενώ περιελάμβανε και μια δραστηριότητα η οποία εισήγαγε τα παιδιά στην έννοια του μέτρου μέτρησης της χωρητικότητας δοχείων. Στο post-test, αξιολογήθηκε η επίδραση της teaching intervention στη βελτίωση της ικανότητας των παιδιών να χειρίζονται θέματα άμεσης και έμμεσης σύγκρισης χωρητικότητας δοχείων, καθώς και της χρήσης ενός αυθαίρετου οργάνου μέτρησης και μιας άτυπης μονάδας μέτρησης της χωρητικότητας. Τα ευρήματα ανέδειξαν το σημαντικό ρόλο που διαδραματίζει το επικοινωνιακό πλαίσιο στη διδασκαλία, που ενισχύει την αυτονομία των μαθητών και συνεισφέρει στην κατάκτηση της νέας γνώσης. / This research attempts to highlight the role of pedagogical activities in the ownership of pre-school children mathematical concepts such as measurement of container capacity. We investigated the age effect on the level of understanding of the concept of measuring the containes measurament. Finally we tried to verify results of similar investigations. The sample of the study consisted of 30 subjects aged 5–6, who attended the school year 2009-2010 in two Greek state kindergartens with the same social characteristics belonged to middle socioeconomic strata. The study was conducted in three phases: the pre-test, teaching intervention and post-test. In the pre-test, we examined whether children can perform direct (directly between containers) and indirect (using a common measure) comparisons of the containers capacity. The teaching intervention proposed activities, which aimed to create appropriate frameworks for the direct and indirect comparisons. While it included an activity which introduced children to the concept of measurement of containers capacity. In the post-test, evaluated the effect of teaching intervention to improve children’s ability to handle matters of direct and indirect comparison containers capasity, and the use of an arbitrary gauge and an informal unit of measurement of capacity. The findings highlighted the important role of communication within the teaching, enhancing the autonomy of pupils and contribute to the acquisition of new knowledge.

Essa tese tem como objetivo verificar se um programa de formação continuada de curta duração, para professores, melhora o desempenho dos alunos do 3º ano do Ensino Fundamental, em relações numéricas, quanto à composição aditiva, ao raciocínio aditivo e ao raciocínio multiplicativo, e se esse desempenho é significativo a ponto de se manter por seis meses. A fundamentação teórica revisou o processo de desenvolvimento das habilidades e dos conceitos matemáticos iniciais, e a discussão a respeito dos saberes docentes. O método compreendeu um estudo teórico e correlacional de caráter quali-quantitativo. Foi realizada, também, análise documental da Avaliação em Larga Escala e da legislação relacionada. A parte de campo envolveu dois grupos experimentais A e B, e um grupo controle, constituídos por alunos do 3º ano do Ensino Fundamental, e um programa de formação continuada para os professores regentes dos grupos experimentais. A amostra correspondeu a 248 alunos e 16 professores. No grupo experimental A, foram 93 alunos e seis professores, que participaram da formação por convocação obrigatória. Já no grupo experimental B, o estudo envolveu 121 alunos, com oito professores que buscavam aperfeiçoamento profissional. No grupo controle, foram envolvidos 34 alunos, sendo que os dois professores não participaram da formação. Partimos da coleta de informações sobre o nível conceitual dos alunos e, em função de tal nível, foi planejado o programa de formação continuada. Um bloco com dez questões foi aplicado aos alunos, em três momentos distintos: como pré-teste, antes da formação; como pós-teste 1, logo após o término da formação; e como pós-teste 2, seis meses depois. Para os professores dos grupos experimentais, foram aplicados dois questionários e uma ficha de autoavaliação. No programa de formação continuada, foram realizadas duas palestras e oito oficinas. Os resultados da ANOVA indicam diferença significativa do desempenho dos alunos. O grupo experimental B registrou maior impacto no desempenho dos alunos e maior percentual de utilização das estratégias econômicas, com uso de cálculos numéricos, na resolução das situações-problema. Os alunos do grupo controle utilizaram estratégias iniciais/simples em todos os blocos aplicados. A aprendizagem manteve-se, por seis meses, em ambos os grupos. Nas considerações finais, analisamos a formação continuada como uma oportunidade para os professores construírem saberes sobre os conceitos matemáticos iniciais, mas a eficácia depende diretamente da concepção dos professores sobre a formação continuada, do seu comprometimento com a aprendizagem e do trabalho a partir do nível conceitual dos alunos. / The primary aim of this thesis is to analyse whether a short-term continued education programme designed to qualify teachers helps to improve third graders’ performance regarding number relations: additive composition and reasoning, and multiplicative reasoning and if any such improvement is maintained after six months. The theoretical review includes the development of the early mathematical skills and concepts, the strategies used to solve problems, the concept of early evidence-based teaching, the project “Ensinar é Construir” (Teaching is Building – NUNES et al., 2009), the Brazilian legislation concerning the guidelines for continued education and teacher qualification. Based on the concept of evidence-based teaching, information regarding the conceptual level of learners was gathered and, from this starting point, the continued education programme was planned. The method contemplated a correlational study of a quantitative scope for both the experimental groups (A and B) and the control group, which were comprised of third graders, and a continued education programme for the teachers of the experimental groups. Pre- and post-tests were applied to the students. The participating teachers were interviewed and completed a selfassessment form. The test applied to the students comprised ten questions, one per page, as follows: two additive composition questions; six additive reasoning problems, two simple problems regarding the relationship between the parts and the whole, two inverted problems regarding the relationship part-whole, and two problems of comparison; and two multiplicative reasoning questions. The results in the pre-test, applied in the first quarter of 2011, were used as a guideline for the organization of the continued education programme. The same test was reapplied as a post-test 1 after the continued education programme, and as post-test 2 six months later. The 14 teachers who participated in the continued education programme were divided into two groups A and B. Group A was made up of teachers obliged to participate and group B by teachers seeking professional development. The sample consisted of 248 students allocated into three groups according to the status of the teacher, obliged or voluntary participation: 93 students in experimental group A and 121 in experimental group B. The control group consisted of 34 students whose teachers did not participate in the continued education programme. Most of the students improved the process of learning the early Mathematical concepts. During the meetings of the continued education programme, theoretical and practical activities were undertaken. ANOVA showed there was a significant improvement in the results achieved by the students in experimental group B who also showed the highest percentage of economic strategy use in the post-test. The control group used uneconomic strategies, such as counting, to solve both pre- and post-test problems. Learning remained the same in both the control and experimental groups for six months. The study concludes that the continued education programme had a statistically significant influence on the performance and in the progress of the strategies used in problemsolving situations with additive composition, additive and multiplicative reasoning in the experimental group B, whose teachers participated of the continued education programme in search of professional development.

Essa tese tem como objetivo verificar se um programa de formação continuada de curta duração, para professores, melhora o desempenho dos alunos do 3º ano do Ensino Fundamental, em relações numéricas, quanto à composição aditiva, ao raciocínio aditivo e ao raciocínio multiplicativo, e se esse desempenho é significativo a ponto de se manter por seis meses. A fundamentação teórica revisou o processo de desenvolvimento das habilidades e dos conceitos matemáticos iniciais, e a discussão a respeito dos saberes docentes. O método compreendeu um estudo teórico e correlacional de caráter quali-quantitativo. Foi realizada, também, análise documental da Avaliação em Larga Escala e da legislação relacionada. A parte de campo envolveu dois grupos experimentais A e B, e um grupo controle, constituídos por alunos do 3º ano do Ensino Fundamental, e um programa de formação continuada para os professores regentes dos grupos experimentais. A amostra correspondeu a 248 alunos e 16 professores. No grupo experimental A, foram 93 alunos e seis professores, que participaram da formação por convocação obrigatória. Já no grupo experimental B, o estudo envolveu 121 alunos, com oito professores que buscavam aperfeiçoamento profissional. No grupo controle, foram envolvidos 34 alunos, sendo que os dois professores não participaram da formação. Partimos da coleta de informações sobre o nível conceitual dos alunos e, em função de tal nível, foi planejado o programa de formação continuada. Um bloco com dez questões foi aplicado aos alunos, em três momentos distintos: como pré-teste, antes da formação; como pós-teste 1, logo após o término da formação; e como pós-teste 2, seis meses depois. Para os professores dos grupos experimentais, foram aplicados dois questionários e uma ficha de autoavaliação. No programa de formação continuada, foram realizadas duas palestras e oito oficinas. Os resultados da ANOVA indicam diferença significativa do desempenho dos alunos. O grupo experimental B registrou maior impacto no desempenho dos alunos e maior percentual de utilização das estratégias econômicas, com uso de cálculos numéricos, na resolução das situações-problema. Os alunos do grupo controle utilizaram estratégias iniciais/simples em todos os blocos aplicados. A aprendizagem manteve-se, por seis meses, em ambos os grupos. Nas considerações finais, analisamos a formação continuada como uma oportunidade para os professores construírem saberes sobre os conceitos matemáticos iniciais, mas a eficácia depende diretamente da concepção dos professores sobre a formação continuada, do seu comprometimento com a aprendizagem e do trabalho a partir do nível conceitual dos alunos. / The primary aim of this thesis is to analyse whether a short-term continued education programme designed to qualify teachers helps to improve third graders’ performance regarding number relations: additive composition and reasoning, and multiplicative reasoning and if any such improvement is maintained after six months. The theoretical review includes the development of the early mathematical skills and concepts, the strategies used to solve problems, the concept of early evidence-based teaching, the project “Ensinar é Construir” (Teaching is Building – NUNES et al., 2009), the Brazilian legislation concerning the guidelines for continued education and teacher qualification. Based on the concept of evidence-based teaching, information regarding the conceptual level of learners was gathered and, from this starting point, the continued education programme was planned. The method contemplated a correlational study of a quantitative scope for both the experimental groups (A and B) and the control group, which were comprised of third graders, and a continued education programme for the teachers of the experimental groups. Pre- and post-tests were applied to the students. The participating teachers were interviewed and completed a selfassessment form. The test applied to the students comprised ten questions, one per page, as follows: two additive composition questions; six additive reasoning problems, two simple problems regarding the relationship between the parts and the whole, two inverted problems regarding the relationship part-whole, and two problems of comparison; and two multiplicative reasoning questions. The results in the pre-test, applied in the first quarter of 2011, were used as a guideline for the organization of the continued education programme. The same test was reapplied as a post-test 1 after the continued education programme, and as post-test 2 six months later. The 14 teachers who participated in the continued education programme were divided into two groups A and B. Group A was made up of teachers obliged to participate and group B by teachers seeking professional development. The sample consisted of 248 students allocated into three groups according to the status of the teacher, obliged or voluntary participation: 93 students in experimental group A and 121 in experimental group B. The control group consisted of 34 students whose teachers did not participate in the continued education programme. Most of the students improved the process of learning the early Mathematical concepts. During the meetings of the continued education programme, theoretical and practical activities were undertaken. ANOVA showed there was a significant improvement in the results achieved by the students in experimental group B who also showed the highest percentage of economic strategy use in the post-test. The control group used uneconomic strategies, such as counting, to solve both pre- and post-test problems. Learning remained the same in both the control and experimental groups for six months. The study concludes that the continued education programme had a statistically significant influence on the performance and in the progress of the strategies used in problemsolving situations with additive composition, additive and multiplicative reasoning in the experimental group B, whose teachers participated of the continued education programme in search of professional development.

Essa tese tem como objetivo verificar se um programa de formação continuada de curta duração, para professores, melhora o desempenho dos alunos do 3º ano do Ensino Fundamental, em relações numéricas, quanto à composição aditiva, ao raciocínio aditivo e ao raciocínio multiplicativo, e se esse desempenho é significativo a ponto de se manter por seis meses. A fundamentação teórica revisou o processo de desenvolvimento das habilidades e dos conceitos matemáticos iniciais, e a discussão a respeito dos saberes docentes. O método compreendeu um estudo teórico e correlacional de caráter quali-quantitativo. Foi realizada, também, análise documental da Avaliação em Larga Escala e da legislação relacionada. A parte de campo envolveu dois grupos experimentais A e B, e um grupo controle, constituídos por alunos do 3º ano do Ensino Fundamental, e um programa de formação continuada para os professores regentes dos grupos experimentais. A amostra correspondeu a 248 alunos e 16 professores. No grupo experimental A, foram 93 alunos e seis professores, que participaram da formação por convocação obrigatória. Já no grupo experimental B, o estudo envolveu 121 alunos, com oito professores que buscavam aperfeiçoamento profissional. No grupo controle, foram envolvidos 34 alunos, sendo que os dois professores não participaram da formação. Partimos da coleta de informações sobre o nível conceitual dos alunos e, em função de tal nível, foi planejado o programa de formação continuada. Um bloco com dez questões foi aplicado aos alunos, em três momentos distintos: como pré-teste, antes da formação; como pós-teste 1, logo após o término da formação; e como pós-teste 2, seis meses depois. Para os professores dos grupos experimentais, foram aplicados dois questionários e uma ficha de autoavaliação. No programa de formação continuada, foram realizadas duas palestras e oito oficinas. Os resultados da ANOVA indicam diferença significativa do desempenho dos alunos. O grupo experimental B registrou maior impacto no desempenho dos alunos e maior percentual de utilização das estratégias econômicas, com uso de cálculos numéricos, na resolução das situações-problema. Os alunos do grupo controle utilizaram estratégias iniciais/simples em todos os blocos aplicados. A aprendizagem manteve-se, por seis meses, em ambos os grupos. Nas considerações finais, analisamos a formação continuada como uma oportunidade para os professores construírem saberes sobre os conceitos matemáticos iniciais, mas a eficácia depende diretamente da concepção dos professores sobre a formação continuada, do seu comprometimento com a aprendizagem e do trabalho a partir do nível conceitual dos alunos. / The primary aim of this thesis is to analyse whether a short-term continued education programme designed to qualify teachers helps to improve third graders’ performance regarding number relations: additive composition and reasoning, and multiplicative reasoning and if any such improvement is maintained after six months. The theoretical review includes the development of the early mathematical skills and concepts, the strategies used to solve problems, the concept of early evidence-based teaching, the project “Ensinar é Construir” (Teaching is Building – NUNES et al., 2009), the Brazilian legislation concerning the guidelines for continued education and teacher qualification. Based on the concept of evidence-based teaching, information regarding the conceptual level of learners was gathered and, from this starting point, the continued education programme was planned. The method contemplated a correlational study of a quantitative scope for both the experimental groups (A and B) and the control group, which were comprised of third graders, and a continued education programme for the teachers of the experimental groups. Pre- and post-tests were applied to the students. The participating teachers were interviewed and completed a selfassessment form. The test applied to the students comprised ten questions, one per page, as follows: two additive composition questions; six additive reasoning problems, two simple problems regarding the relationship between the parts and the whole, two inverted problems regarding the relationship part-whole, and two problems of comparison; and two multiplicative reasoning questions. The results in the pre-test, applied in the first quarter of 2011, were used as a guideline for the organization of the continued education programme. The same test was reapplied as a post-test 1 after the continued education programme, and as post-test 2 six months later. The 14 teachers who participated in the continued education programme were divided into two groups A and B. Group A was made up of teachers obliged to participate and group B by teachers seeking professional development. The sample consisted of 248 students allocated into three groups according to the status of the teacher, obliged or voluntary participation: 93 students in experimental group A and 121 in experimental group B. The control group consisted of 34 students whose teachers did not participate in the continued education programme. Most of the students improved the process of learning the early Mathematical concepts. During the meetings of the continued education programme, theoretical and practical activities were undertaken. ANOVA showed there was a significant improvement in the results achieved by the students in experimental group B who also showed the highest percentage of economic strategy use in the post-test. The control group used uneconomic strategies, such as counting, to solve both pre- and post-test problems. Learning remained the same in both the control and experimental groups for six months. The study concludes that the continued education programme had a statistically significant influence on the performance and in the progress of the strategies used in problemsolving situations with additive composition, additive and multiplicative reasoning in the experimental group B, whose teachers participated of the continued education programme in search of professional development.

The aim of the thesis is to describe the decision making process of students in the so-called simple categorization, i.e., decision whether a particular object is or is not an element of a category. This process is examined in the context of categories of mathematical objects. The theoretical part of the thesis presents arguments why the study of simple categorization of mathematical objects is important for mathematics education. These arguments are not only based on the available literature in mathematics education, but also partly draw on historical, mathematical and psychological literature. The practical chapters of the thesis describe the design and piloting of a research tool suitable for this research. The dominant elements of this tool are the measurement of the binary answers (yes / no) of the respondent and of his/her reaction time. This tool is then used in the Main study based on mixed, qualitative-quantitative methodology. It was found that with the help of the proposed tool, while adhering to appropriate methodological rules, it is possible to distinguish different approaches of respondents to categorization. In addition, the basic patterns in the decision-making process of the respondents were described. These are, for instance, differences in the categorization of examples and non-...

A presente tese teve como objetivo central investigar o processo de apropriação de conceitos matemáticos por professores do Ensino Fundamental em atividade de aprendizagem, em que se deu destaque ao conceito de medida. Foi desenvolvida na Faculdade de Educação da Universidade de São Paulo (FEUSP) e teve como campo empírico a formação continuada proporcionada pelo Projeto Observatório da Educação (OBEDUC) que, no nosso entender apresentou a estrutura funcional da \'atividade\' (LEONTIEV, 1978; 2010). Nessa formação, os sujeitos envolvidos, desenvolveram a prática do diálogo e a troca de informações em tarefas coletivas a partir de ações formativas propostas pelo referido projeto, sobretudo as Atividades Orientadoras de Ensino (AOE). O referido projeto teve o propósito de conscientizar seus integrantes, professores e alunos em geral, da necessidade de se ter um ensino organizado a partir do desenvolvimento de AOE. Essas atividades partem de situações desencadeadoras de aprendizagem, semelhantes às vivenciadas pelo homem no processo de criação dos conceitos matemáticos, a fim de que seja propiciado aos alunos a apropriação do conhecimento matemático historicamente acumulado como um instrumental para que esses sujeitos possam ter uma compreensão mais elaborada da realidade. Desse modo, esta investigação problematiza o fenômeno investigado neste estudo - a apropriação de conceitos matemáticos , a partir da seguinte questão central: O que revelam as ações proporcionadas pelo Projeto OBEDUC, no desenvolvimento coletivo de atividades de ensino, sobre a apropriação de conceitos matemáticos na aprendizagem da docência? Assim, como forma de apreensão do fenômeno, recorremos aos pressupostos do Materialismo Histórico e Dialético (MHD), preconizado por Karl Marx e, para a produção de dados, os instrumentos: videogravações dos encontros formativos; observações de campo realizadas durante os encontros formativos e seminários; Atividades Orientadoras de Ensino (AOE) desenvolvidas e aplicadas no espaço de aprendizagem criado pelo Projeto OBEDUC e sessão reflexiva. Com base no desenvolvimento das ações formadoras proporcionadas pelo mencionado projeto, mediadas pelos professores-pesquisadores, buscamos indícios reveladores da apropriação de conceitos matemáticos, ao se considerar o lógico histórico do conceito. Para atingir esse objetivo, ainda, aplicamos os procedimentos analíticos: a ideia de unidades de análise (VIGOTSKI, 2009) e de episódios de aprendizagem compostos por cenas (MOURA; LORENZATO, 2001; MOURA, 2013). De maneira conclusiva, a análise dos dados forneceu-nos indícios da manifestação de que as ações formativas propostas pelo Projeto OBEDUC, de modo particular as AOE, no desenvolvimento coletivo de atividades de ensino, mediadas pelo processo de reflexão, impactaram na organização do ensino em Matemática. Em decorrência disso, ao tomarem consciência da importância da teoria, os professores, sujeitos desta pesquisa, passaram a agir de forma intencional frente aos desafios postos pela atividade pedagógica, o que implicou na apropriação de conceitos matemáticos. / This thesis had as main objective to investigate the process of appropriation of mathematical concepts for elementary school teachers in learning activity, in which it was highlighted the concept of measurement, based on the theoretical principles of the Historical-Cultural Theory and activity Theory. It was developed at the Faculty of Education, University of São Paulo (FEUSP) and had as empirical field the continuing education provided by the Education Observatory Project (OBEDUC) which, in our view, presented the functional structure of the \'activity\' (LEONTIEV, 1978; 2010). For this training, the involved subjects developed the practice of dialogue and exchange of information on collective tasks from training actions proposed by this project, especially the Teaching Advisers Activities (AOE). This project aimed to educate its members, teachers and students in general, the need to have an organized education from the development of AOE. These activities start from triggering learning situations similar to those experienced by humans in the creation process of mathematical concepts, in order to afford the students the acquisition of mathematical knowledge, historically accumulated as an instrumental for these students to have a more elaborate understanding of reality. Thus, this research discusses the phenomenon investigated in this study - the appropriation of mathematical concepts - from the following central question: What the actions provided by OBEDUC Project reveal in collective development of teaching activities, on the appropriation of mathematical concepts in teacher learning? That said, as a way to arrest the phenomenon, we turned into the assumptions of Historical and Dialectical Materialism (MHD) favored by Karl Marx and, for data production, tools like: video recordings of the formation meetings; Field observations made during the formative meetings and seminars; Guiding activities of education (AOE) developed and applied in the learning space created by OBEDUC Design and reflective session. Based on the development of training actions provided by the project, mediated by researcher teachers, we seek for evidence of ownership of mathematical concepts when considering the historical logic of the concept. To achieve this goal, also, we applied analytical procedures: the view from units of analysis (VYGOTSKY, 2009) and episodes of learning composed by scenes (MOURA; LORENZATO, 2001; MOURA, 2013). Conclusively, the data analysis provided us with evidence from the manifestation of the training activities proposed by OBEDUC Project, particularly the AOE, the collective development of educational activities mediated by the reflection process, impacted on the organization of teaching in Mathematics. As a result, when they become aware of the importance of the theory, the teachers, subjects in this study, have to act intentionally forward to the challenges posed by pedagogical activity, which resulted in the appropriation of mathematical concepts.