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The diploma thesis is focused on mathematical knowledge of pupils at the beginning of primary school. The theoretical part deals with characteristics of a preschool child and of a child at the beginning of a primary school, and especially with the specifics in their cognitive functions. Further the theses includes a chapter with an overview of several surveys about mathematical skills of Czech pupils. Finally, there is a chapter about building mathematical ideas at school and in a family. The practical part of the theses presents the results of the quantitative research in the field of mathematical ideas of a primary school child.

A presente tese teve por objetivo investigar e desenvolver formas alternativas de abordagem dos conteúdos matemáticos de Cálculo I, através de sua integração com conteúdos da disciplina de Física I, com vistas à aprendizagem significativa em física básica universitária. A investigação foi de caráter qualitativo, descritivo e interpretativo, fundamentada em estudos etnográficos. Para tanto, as intervenções da pesquisa ocorreram em turmas de Física Geral I A, disciplina ofertada para os discentes de Física da Universidade Federal do Rio Grande do Sul – UFRGS. Na primeira fase de pesquisa, de caráter exploratório, concluiu-se que os conceitos matemáticos centrais do Cálculo I – derivadas e integrais – ora são contornados enquanto desenvolvido o conteúdo da Mecânica, ora são apresentados antecipadamente, com linguagem e notações distintas daquelas veiculadas no Cálculo I. A significação de tais conceitos, porém, não é estritamente necessária à resolução das situações-problemas propostas na disciplina. Na segunda fase de pesquisa, houve o desenvolvimento de material instrucional do Cálculo I para a disciplina de Física Geral I A. O referido material foi embasado na integração entre aquelas áreas, sendo distribuído nos seguintes módulos: vetores e trigonometria, noções de Cálculo Diferencial, e noções de Cálculo Integral. Constatou-se que o significado lógico do material dependia fortemente do modo com que era introduzido aos discentes: se trabalhado articuladamente ao longo do desenvolvimento do campo conceitual da Mecânica, e não de forma compartimentalizada, é que seria bem sucedido. Ainda na segunda etapa, vislumbrou-se a necessidade de criar estratégias de ensino que favorecessem a troca de significados entre os sujeitos participantes da pesquisa. Já na terceira etapa realizou-se, finalmente, a investigação da aprendizagem assentada na proposta integrada de ensino, a partir da visão de um professor de Cálculo. Sendo assim, no decorrer das atividades colaborativas, foi percebida a correlacionabilidade entre os conteúdos do Cálculo e os da Física. As atividades individuais, por sua vez, demonstraram que muitos discentes careciam de subsunçores básicos necessários à aprendizagem significativa em Mecânica e, dentre os que possuíam os subsunçores, poucos externalizavam a correlação entre Cálculo e Física. Tal fato demonstra a existência de uma estrutura cognitiva compartimentada mesmo se tratando de conhecimentos correlacionados. Discutem-se, pois, as implicações deste estudo para o ensino do Cálculo direcionado aos discentes da Física. / This thesis aims to investigate and develop alternative ways of addressing the mathematical content of Calculus I, through its integration with content of Physics I, with a view to meaningful learning basic physics university. The research was qualitative, descriptive and interpretive, based on ethnographic studies. Therefore, the interventions occurred in the research groups of General Physics IA, discipline offered to the students of Physics, Federal University of Rio Grande do Sul - UFRGS. In the first phase of research, exploratory, it was concluded that the central mathematical concepts of Calculus I - derivatives and integrals - why are contoured as content developed of mechanics, are now presented in advance, with language and notation different from those conveyed in Calculation I. The significance of these concepts, however, is not strictly necessary to the resolution of problem situations in the proposed discipline. In the second phase of research was the development of instructional material from Calculus I for the introductory physics course I A. Such material was based on the integration between these areas, being distributed in the following modules: vectors and trigonometry, notions of differential calculus, integral calculus and basic. It was found that the logical meaning of the material relied heavily on the manner in which it was introduced to the students: it worked articulately throughout the development of the conceptual field of mechanics, not so compartmentalized, that would be successful. Still in the second stage, saw the need to create teaching strategies that would promote the exchange of meanings between subjects participating in the research. In the third step was conducted, finally, the investigation of learning grounded in the proposed integrated education, from the perspective of a teacher of Calculus. Thus, in the course of collaborative activities were perceived correlations between the contents of Calculus and Physics. Individual activities, in turn, demonstrated that many students lacked basic subsumers necessary for meaningful learning in mechanics and, among those who had the subsumers, few perceived correlations between calculation and Physics. This fact demonstrates the existence of a cognitive structure compartmentalized knowledge despite being correlated. We discuss therefore the implications of this study for teaching Calculus directed to students of physics.

A presente tese teve por objetivo investigar e desenvolver formas alternativas de abordagem dos conteúdos matemáticos de Cálculo I, através de sua integração com conteúdos da disciplina de Física I, com vistas à aprendizagem significativa em física básica universitária. A investigação foi de caráter qualitativo, descritivo e interpretativo, fundamentada em estudos etnográficos. Para tanto, as intervenções da pesquisa ocorreram em turmas de Física Geral I A, disciplina ofertada para os discentes de Física da Universidade Federal do Rio Grande do Sul – UFRGS. Na primeira fase de pesquisa, de caráter exploratório, concluiu-se que os conceitos matemáticos centrais do Cálculo I – derivadas e integrais – ora são contornados enquanto desenvolvido o conteúdo da Mecânica, ora são apresentados antecipadamente, com linguagem e notações distintas daquelas veiculadas no Cálculo I. A significação de tais conceitos, porém, não é estritamente necessária à resolução das situações-problemas propostas na disciplina. Na segunda fase de pesquisa, houve o desenvolvimento de material instrucional do Cálculo I para a disciplina de Física Geral I A. O referido material foi embasado na integração entre aquelas áreas, sendo distribuído nos seguintes módulos: vetores e trigonometria, noções de Cálculo Diferencial, e noções de Cálculo Integral. Constatou-se que o significado lógico do material dependia fortemente do modo com que era introduzido aos discentes: se trabalhado articuladamente ao longo do desenvolvimento do campo conceitual da Mecânica, e não de forma compartimentalizada, é que seria bem sucedido. Ainda na segunda etapa, vislumbrou-se a necessidade de criar estratégias de ensino que favorecessem a troca de significados entre os sujeitos participantes da pesquisa. Já na terceira etapa realizou-se, finalmente, a investigação da aprendizagem assentada na proposta integrada de ensino, a partir da visão de um professor de Cálculo. Sendo assim, no decorrer das atividades colaborativas, foi percebida a correlacionabilidade entre os conteúdos do Cálculo e os da Física. As atividades individuais, por sua vez, demonstraram que muitos discentes careciam de subsunçores básicos necessários à aprendizagem significativa em Mecânica e, dentre os que possuíam os subsunçores, poucos externalizavam a correlação entre Cálculo e Física. Tal fato demonstra a existência de uma estrutura cognitiva compartimentada mesmo se tratando de conhecimentos correlacionados. Discutem-se, pois, as implicações deste estudo para o ensino do Cálculo direcionado aos discentes da Física. / This thesis aims to investigate and develop alternative ways of addressing the mathematical content of Calculus I, through its integration with content of Physics I, with a view to meaningful learning basic physics university. The research was qualitative, descriptive and interpretive, based on ethnographic studies. Therefore, the interventions occurred in the research groups of General Physics IA, discipline offered to the students of Physics, Federal University of Rio Grande do Sul - UFRGS. In the first phase of research, exploratory, it was concluded that the central mathematical concepts of Calculus I - derivatives and integrals - why are contoured as content developed of mechanics, are now presented in advance, with language and notation different from those conveyed in Calculation I. The significance of these concepts, however, is not strictly necessary to the resolution of problem situations in the proposed discipline. In the second phase of research was the development of instructional material from Calculus I for the introductory physics course I A. Such material was based on the integration between these areas, being distributed in the following modules: vectors and trigonometry, notions of differential calculus, integral calculus and basic. It was found that the logical meaning of the material relied heavily on the manner in which it was introduced to the students: it worked articulately throughout the development of the conceptual field of mechanics, not so compartmentalized, that would be successful. Still in the second stage, saw the need to create teaching strategies that would promote the exchange of meanings between subjects participating in the research. In the third step was conducted, finally, the investigation of learning grounded in the proposed integrated education, from the perspective of a teacher of Calculus. Thus, in the course of collaborative activities were perceived correlations between the contents of Calculus and Physics. Individual activities, in turn, demonstrated that many students lacked basic subsumers necessary for meaningful learning in mechanics and, among those who had the subsumers, few perceived correlations between calculation and Physics. This fact demonstrates the existence of a cognitive structure compartmentalized knowledge despite being correlated. We discuss therefore the implications of this study for teaching Calculus directed to students of physics.

A presente tese teve por objetivo investigar e desenvolver formas alternativas de abordagem dos conteúdos matemáticos de Cálculo I, através de sua integração com conteúdos da disciplina de Física I, com vistas à aprendizagem significativa em física básica universitária. A investigação foi de caráter qualitativo, descritivo e interpretativo, fundamentada em estudos etnográficos. Para tanto, as intervenções da pesquisa ocorreram em turmas de Física Geral I A, disciplina ofertada para os discentes de Física da Universidade Federal do Rio Grande do Sul – UFRGS. Na primeira fase de pesquisa, de caráter exploratório, concluiu-se que os conceitos matemáticos centrais do Cálculo I – derivadas e integrais – ora são contornados enquanto desenvolvido o conteúdo da Mecânica, ora são apresentados antecipadamente, com linguagem e notações distintas daquelas veiculadas no Cálculo I. A significação de tais conceitos, porém, não é estritamente necessária à resolução das situações-problemas propostas na disciplina. Na segunda fase de pesquisa, houve o desenvolvimento de material instrucional do Cálculo I para a disciplina de Física Geral I A. O referido material foi embasado na integração entre aquelas áreas, sendo distribuído nos seguintes módulos: vetores e trigonometria, noções de Cálculo Diferencial, e noções de Cálculo Integral. Constatou-se que o significado lógico do material dependia fortemente do modo com que era introduzido aos discentes: se trabalhado articuladamente ao longo do desenvolvimento do campo conceitual da Mecânica, e não de forma compartimentalizada, é que seria bem sucedido. Ainda na segunda etapa, vislumbrou-se a necessidade de criar estratégias de ensino que favorecessem a troca de significados entre os sujeitos participantes da pesquisa. Já na terceira etapa realizou-se, finalmente, a investigação da aprendizagem assentada na proposta integrada de ensino, a partir da visão de um professor de Cálculo. Sendo assim, no decorrer das atividades colaborativas, foi percebida a correlacionabilidade entre os conteúdos do Cálculo e os da Física. As atividades individuais, por sua vez, demonstraram que muitos discentes careciam de subsunçores básicos necessários à aprendizagem significativa em Mecânica e, dentre os que possuíam os subsunçores, poucos externalizavam a correlação entre Cálculo e Física. Tal fato demonstra a existência de uma estrutura cognitiva compartimentada mesmo se tratando de conhecimentos correlacionados. Discutem-se, pois, as implicações deste estudo para o ensino do Cálculo direcionado aos discentes da Física. / This thesis aims to investigate and develop alternative ways of addressing the mathematical content of Calculus I, through its integration with content of Physics I, with a view to meaningful learning basic physics university. The research was qualitative, descriptive and interpretive, based on ethnographic studies. Therefore, the interventions occurred in the research groups of General Physics IA, discipline offered to the students of Physics, Federal University of Rio Grande do Sul - UFRGS. In the first phase of research, exploratory, it was concluded that the central mathematical concepts of Calculus I - derivatives and integrals - why are contoured as content developed of mechanics, are now presented in advance, with language and notation different from those conveyed in Calculation I. The significance of these concepts, however, is not strictly necessary to the resolution of problem situations in the proposed discipline. In the second phase of research was the development of instructional material from Calculus I for the introductory physics course I A. Such material was based on the integration between these areas, being distributed in the following modules: vectors and trigonometry, notions of differential calculus, integral calculus and basic. It was found that the logical meaning of the material relied heavily on the manner in which it was introduced to the students: it worked articulately throughout the development of the conceptual field of mechanics, not so compartmentalized, that would be successful. Still in the second stage, saw the need to create teaching strategies that would promote the exchange of meanings between subjects participating in the research. In the third step was conducted, finally, the investigation of learning grounded in the proposed integrated education, from the perspective of a teacher of Calculus. Thus, in the course of collaborative activities were perceived correlations between the contents of Calculus and Physics. Individual activities, in turn, demonstrated that many students lacked basic subsumers necessary for meaningful learning in mechanics and, among those who had the subsumers, few perceived correlations between calculation and Physics. This fact demonstrates the existence of a cognitive structure compartmentalized knowledge despite being correlated. We discuss therefore the implications of this study for teaching Calculus directed to students of physics.

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.

In this research it was followed the conception that situation-problem is a main point to start learning mathematical concepts, as suggested by PCN, and not a mere acquired content s application. It was actively investigated, aiming at an approximation of practical and school knowledge in order to improve learning through situation-problems. The methodological proceedings used were based on a qualitative approach, through an investigation-action cycle in the problematizing-dialogic perspective, in which the school practices were carried out to answer the following question: analyzing practical and school knowledge, through situation-problems, contributes to the learning of mathematical concepts? During the situation-problems solution, the students acted in the context they live, simulating, weighing and measuring lengths, becoming more active and motivated due to these proceedings. Through dialogues, they have expressed the new relation they were doing with what they have learned day by day during the situation-problems solving. The students noticed themselves differently facing the lived experiences because they have observed information around them and related to what was studied in class. From these declarations, it was possible to notice that there is possibility in relating practical and school knowledge through situation-problems in the mathematical school practices. Considering that teaching through situation-problems emphasizes interaction among mathematical concepts, action, observation and analyzes, minimizing operatory process of mechanical form, can develop a more integrated theoretical and practical knowledge, and turn school practices more motivating and dynamic. / Seguiu-se, nesta pesquisa, a concepção sugerida pelos PCN de que situaçãoproblema é ponto de partida para a aprendizagem de conceitos matemáticos e não uma mera aplicação de conteúdos já adquiridos. Investigou-se ativamente, visualizando uma aproximação entre os conhecimentos prático e escolar de modo a favorecer a aprendizagem através de situações-problema. Os procedimentos metodológicos utilizados estão circunscritos na abordagem qualitativa, onde, através da dinâmica dos ciclos de investigação-ação na perspectiva dialógico-problematizadora, as práticas escolares foram realizadas para responder a seguinte pergunta: aproximar os conhecimentos prático e escolar, através de situações-problema, contribui com a aprendizagem de conceitos matemáticos? Durante a resolução das situações-problema, os alunos agiram no meio em que vivem, simulando, pesando e medindo, tornando-se, frente a esses procedimentos, mais ativos e motivados. Eles expressaram, através do diálogo, as novas relações que estavam fazendo no dia-a-dia com o que aprenderam durante a resolução das situações-problema. Os alunos perceberam-se diferentes diante de experiências vividas ao observarem as informações que estão ao seu redor com o que foi tratado em aula. Dessas declarações, pode-se perceber que há possibilidade, nas práticas escolares de matemática, de fazer um ajuste entre o conhecimento escolar e o prático através de situações-problema, visando uma aproximação. Tendo-se como proposição que o ensino através de situações-problema enfatiza a interação entre conceitos matemáticos, ação, observação e análise, minimizando os processos operatórios de forma mecânica, este poderá desenvolver um conhecimento teórico e prático mais integrado, e tornarem as práticas escolares de matemática mais motivadoras e dinâmicas.

Denna uppsats belyser några av förskoleklassens läromedel i matematikämnet. Vi har undersökt specifikt i vilken utsträckning leken tar plats i läromedel, samt vilket stöd läraren får att genomföra lek som kan bidra till elevernas begrepps och/eller resonemangsförmåga. Förskoleklassen har nyligen blivit obligatorisk och ska fungera som en bro mellan förskolan och skolan. Den förväntas ta över förskolans lekpedagogik samtidigt som den ska introducera skolans rutiner och undervisningsmetoder. Vi har använt innehållsanalys som metod för att undersöka läromedel både kvantitativt och kvalitativt. Studiens resultat visar att lek som bidrar till elevernas begrepps- och/eller resonemangsförmåga finns i lärarhandledningar. Det finns även olika typer av stöd för läraren att genomföra lekbaserad undervisning som bidrar till elevernas begrepps- och/eller resonemangsförmåga. Det kan bidra till att eleverna utvecklar och befäster sina kunskaper om matematiska begrepp och/eller resonemang via leken. Studien visar också att lek i läromedlets elevböcker i stort sett saknas. Vilket kan innebära att eleverna går miste om lek i matematikundervisningen om läraren väljer att endast använda elevboken. / This master thesis focuses on mathematics textbooks for preschool class. We have studied to what extent play is found in the textbooks and what kind of the support for implementation is offered to the teacher. We have focused on play which can contribute to the pupils’ concept and/or reasoning ability.  Preschool class is now a compulsory school form. Preschool class is a class between preschool and primary school and is expected to function as a bridge between these two. There are many expectations for preschool class: implementing preschool pedagogy while introducing the primary school’s routines and teaching methods. We have used content analysis as a method in this study. The method has been used in both a quantitative and a qualitative way.  The results show that teacher guides offer play contributing to conceptual and/or reasoning. The results also show that the teacher gets support for implementing such play in the classroom. This offers opportunities for pupils to consolidate and develop their knowledge of mathematical concepts as well as their reasoning. Further, the study shows that play in the pupils’ textbook largely is lacking. If the teacher chooses to only use the pupil’s textbooks, the consequence can be that the pupils are missing out on play in mathematical education.

Denna uppsats belyser några av förskoleklassens läromedel i matematikämnet. Vi har undersökt specifikt i vilken utsträckning leken tar plats i läromedel, samt vilket stöd läraren får att genomföra lek som kan bidra till elevernas begrepps och/eller resonemangsförmåga. Förskoleklassen har nyligen blivit obligatorisk och ska fungera som en bro mellan förskolan och skolan. Den förväntas ta över förskolans lekpedagogik samtidigt som den ska introducera skolans rutiner och undervisningsmetoder. Vi har använt innehållsanalys som metod för att undersöka läromedel både kvantitativt och kvalitativt. Studiens resultat visar att lek som bidrar till elevernas begrepps- och/eller resonemangsförmåga finns i lärarhandledningar. Det finns även olika typer av stöd för läraren att genomföra lekbaserad undervisning som bidrar till elevernas begrepps- och/eller resonemangsförmåga. Det kan bidra till att eleverna utvecklar och befäster sina kunskaper om matematiska begrepp och/eller resonemang via leken. Studien visar också att lek i läromedlets elevböcker i stort sett saknas. Vilket kan innebära att eleverna går miste om lek i matematikundervisningen om läraren väljer att endast använda elevboken. / This master thesis focuses on mathematics textbooks for preschool class. We have studied to what extent play is found in the textbooks and what kind of the support for implementation is offered to the teacher. We have focused on play which can contribute to the pupils’ concept and/or reasoning ability.  Preschool class is now a compulsory school form. Preschool class is a class between preschool and primary school and is expected to function as a bridge between these two. There are many expectations for preschool class: implementing preschool pedagogy while introducing the primary school’s routines and teaching methods. We have used content analysis as a method in this study. The method has been used in both a quantitative and a qualitative way.  The results show that teacher guides offer play contributing to conceptual and/or reasoning. The results also show that the teacher gets support for implementing such play in the classroom. This offers opportunities for pupils to consolidate and develop their knowledge of mathematical concepts as well as their reasoning. Further, the study shows that play in the pupils’ textbook largely is lacking. If the teacher chooses to only use the pupil’s textbooks, the consequence can be that the pupils are missing out on play in mathematical education.

The purpose of the dissertation is to study, describe and analyses which comparative measurement activities preschool children construct and use, and how they solve problems and communicate when they use the comparative measurement activities whilst playing with Lego (“the Lego play”). The measurement activities chosen are length/height, quantity and time. The empirical material is based on data from two preschool classes with children aged 2 – 5 year, It was collected through participant observation (video captures) of the children’s Lego play. The theoretical starting points in this study are grounded in childhood sociology and the sociocultural perspective. The study assumes the childhood sociology perspective by viewing the children as competent and active in creating meaning as well as controlling and influencing their own and others’ social environment. The sociocultural perspective gives prominence to development and learning, and its related tools and concepts are used to analyses the results of the study. That is, the Lego play is studied in a social context from the child’s perspective, and the sociocultural perspective describes and analyses the child’s use of mathematics and the acquisition of knowledge in the Lego play in a sociocultural context. The results show that children measuring length/height and quantity explored a store of measurement tools in order to make comparisons, and adapted these to the context in question. These were own body, other body, artefacts, numbers and counting. The measurements were used individually and with others, and the solving of the own or shared problems constituted a large share of the time spent constructing models during Lego play. By contrast, the time concept was used mainly as a tool when the children played with their finished Lego models. Thus, a time perspective was added to the child’s finished model, which inspired thoughts and reflections about time used in the Lego play. The children used the time concepts of the present, the past and the future, and also considered the concept of velocity in the context of the timescale. The children’s communication had a large impact on the Lego play, and they expressed their ideas verbally, physically and through action. The children’s use of mathematics was prominent and meaningful during the Lego play.