This thesis deals with the possible way to use the Theory of didactic situations in the second level of Czech primary schools. The main topic of the experiment is the introduction of functions in the 9th grade of primary schools. The entire work is divided into two parts - theoretical and experimental. The theoretical part is focused on introduction of the Theory of didactic situations and processing the topic in the educational materials used in the Czech Republic. It also deals with the historical development of the topic of functions in the Czech curricula. In this context, the author conducted a survey, the purpose of which was primarily the view of a primary school mathematics teacher on teaching of functions and on changes that recently accompany the Czech school system. In the experimental part, the author presents detailed information about the educational block processed and implemented according to the principles of the Theory of didactic situations. The aim of the experiment was to watch the reaction of students to the concept of teaching according to the Theory of didactic situations and to evaluate their success in relation to the desired outcomes of the topic. The thesis describes the preparation, progress and evaluation of the prepared educational unit.

Τα σημερινά δεδομένα για την ανάγκη ενσωμάτωσης των ψηφιακών τεχνολογιών σχετικά με τα μαθήματα των Μαθηματικών της Δευτεροβάθμιας Ελληνικής Εκπαίδευσης είναι συνδεδεμένη με την ανάπτυξη των αναγκαίων υποδομών στα σχολεία, αλλά και με το επίπεδο δεξιοτήτων που έχουν αναπτύξει οι εκπαιδευτικοί που διδάσκουν Μαθηματικά στην σχολική εκπαίδευση. Η συγκεκριμένη έρευνα θέτει ερωτήματα που αφορούν στην χρήση των ψηφιακών τεχνολογιών και ιδιαίτερα στην παιδαγωγική αξιοποίηση τους, με βάσιμη υπόθεση ότι οι εκπαιδευτικοί που νοιώθουν αρκετά ικανοί ή θεωρούν ότι το εκπαιδευτικό τους έργο είναι διαφορετικό και κυρίως προς όφελος του μαθητή δεν διστάζουν να το δημοσιοποιήσουν μέσω του Διαδικτύου. Κατά τεκμήριο ο πληθυσμός αυτός αποτελεί ένα «ασφαλές» δείγμα από το στρώμα των περισσότερο απασχολούμενων με τις Τεχνολογίες της Πληροφορίας και των Επικοινωνιών (ΤΠΕ) εκπαιδευτικών. Επίσης γίνεται προσπάθεια διερεύνησης των παραγόντων εκείνων που επηρεάζουν την ενσωμάτωση των ΤΠΕ στην εκπαιδευτική διαδικασία. Στο εμπειρικό σκέλος το εκπαιδευτικό υλικό διαχωρίζεται και αξιολογείται σε σχέση με την αξιοποίηση των ΤΠΕ, την πληρότητα και την χρήση του μέσω μιας σειράς παραμέτρων όπως η προστιθέμενη αξία, η ευχρηστία, η πρωτοτυπία και η καταλληλότητα για την τάξη, καθώς και η προτεινόμενη οργάνωση της τάξης ή/και οι οδηγίες προς τους μαθητές. Εξετάζεται αν χρησιμοποιείται εκπαιδευτικό λογισμικό, η κατηγορία στην οποία ανήκει, το είδος του και με ποιο τρόπο εμπλέκει τους μαθητές στην εκπαιδευτική διαδικασία, αν δημοσιεύεται το ψηφιακό υλικό, η ποιότητα του καθώς και η ακολουθούμενη μέθοδος διδασκαλίας. Τα κυριότερα ευρήματα αφορούν στη διαπίστωση της σχέσης που υπάρχει μεταξύ της δημοσιοποίησης του εκπαιδευτικού υλικού με το προσδοκώμενο αποτέλεσμα. Οι παράγοντες που επηρεάζουν αυτή την σχέση είναι καθοριστικοί για την παρεχόμενη ποιότητα στην μαθηματική εκπαίδευση, την ανάπτυξη κριτικής σκέψης εκ μέρους των μαθητών, της αλλαγής του μοντέλου διδασκαλίας στην τάξη και της στάσης του εκπαιδευτικού απέναντι στη χρήση τεχνολογίας. Κυρίαρχο ρόλο κατέχει η ανάδειξη της απαιτούμενης επιμόρφωσης των εκπαιδευτικών στην παιδαγωγική αξιοποίηση των ΤΠΕ, ώστε η ένταξη και χρήση τους στα μαθήματα της τάξης να αποδίδει καλύτερα αποτελέσματα προς όφελος των μαθητών. / --

Made available in DSpace on 2014-06-11T19:31:40Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-03-25Bitstream added on 2014-06-13T21:03:02Z : No. of bitstreams: 1 cardia_em_dr_bauru.pdf: 6450245 bytes, checksum: 981f1254d937d381bc4026a41146b00d (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / A pesquisa teve como objetivo geral o ensaio de uma Didática da Matemática, embasada na Pedagogia Histórico-Crítica, utilizando a Seguridade Social como tema político-social estruturador. O método de abordagem adotado foi o da Dialética Materialista Histórica e a pesquisa desenvolveu-se com a participação de professores e alunos de escolas públicas na aplicacao da proposta que enfocou conteúdos matemáticos selecionados para compreensão dos conteúdos político-sociais relacionados a Seguridade Social. O reconhecimento da Previdencia Social como componente da Seguridade Social e desta como Direito Humano e importante para todos os cidadãos mas o conhecimento que se tem desses temas ou da Matemática neles contidas é, muitas vezes, insuficiente e pouco científico. Para interessar aos estudantes, é necessário abordá-lo de forma adequada, apoiando-se nos fundamentos da Psicologia Sócio-Histórica. A proteção social, da forma como foi desenvolvida pelos homens, tem sua sustentabilidade econômico-financeira dependente de inúmeros fatores como envelhecimento da população, níveis de emprego, níveis de faixas salariais e outros. Os conhecimentos matemáticos e atuariais desenvolvidos até nossos dias permitem que os sistemas existentes nos diversos países sejam constantemente avaliados de modo a se determinar, de tempos em tempos, se as regras sociais acordadas estão adequadas ou se há necessidade de reformá-las, no todo ou em parte. Mas, o imenso volume de dinheiro movimentado pela Seguridade Social, um dos maiores do planeta, desperta outros interesses nas reformas, nem sempre compromissados com a proteção social. A Matemática pode ajudar-nos a compreender as intenções explícitas e implícitas de cada uma das reformas ocorridas ou a ocorrer e os resultados da pesquisa mostram que é possível levar esse conhecimento para a Educação Básica. / The general purpose of this research was essay of Mathematics’ didactics based on historical-critical pedagogy focusing the Social Security as structural sociopolitical theme. The Historical-materialist dialectic approach method was applied and the research was developed by the public schools´ teachers and students participation in the proposal´s application that focused selected mathematical contents for understanding the sociopolitical contents relating to Social Security. The recognition of the social welfare and Social Security as Human Right is important for all the citizens but their knowledge on these subjects or about the Mathematics they contain is many times insufficient and poorly scientific. To the students’ interest, it is necessary to approach it adequately, supporting itself in the grounds of Social-Historical Psychology. The social protection, the manner by which it was developed by the humanity has its economic-financial sustainability dependent of several factors as population aging, level of employment, income strata and others. The mathematical and actuarial knowledge developed so far allows that the existing systems in the several countries be constantly evaluated in order to determine between times if the dealt social rules are appropriate or there is need to remodel them, in whole or in part. However, the huge quantity of money moved up by the Social Security, one of the greater of the planet, stimulate other interests toward to restructures, not always compromised with the social protection. The Mathematics can help us to understand the explicit and implicit intentions of each one of the implemented or to implement changes and research´s results they shows that it is possible bring this knowledge for the Elementary Education.

Dans notre recherche nous nous intéressons à la gestion de l’hétérogénéité des apprentissages des élèves d’une même classe ainsi que sur la différenciation dans l’enseignement dans le domaine du calcul algébrique, en fin de scolarité obligatoire en France. Ces questions ont fait l’objet de plusieurs recherches notamment dans le domaine de la sociologie (Bourdieu, 1966), les sciences de l’éducation (Perrenoud, 1989, 1991 ; Przesmycki, 1991 ; Caron, 2003 ; Sarrazy, 2007) ainsi que dans le domaine de la didactique des mathématiques (Charnay, 1995 ; Grugeon, 1997 ; Castela, 2007 ; Pilet, 2012). Ils constituent depuis quelques années deux thèmes d’actualité dans l’enseignement secondaire français. Les différentes recherches soulignent le fait que les enseignants se trouvent démunis face à leur difficulté à faire progresser les élèves. Deux raisons nous amènent à nous intéresser à ces thèmes. D’une part, le constat du désarroi des enseignants dans la gestion des difficultés croissantes des élèves (dont nous même, en tant qu’enseignante dans un collège classé REP, sommes confrontée) et, d’autre part, les résultats du système scolaire français en termes de connaissances et compétences des élèves aux évaluations nationales et internationales, notamment dans le domaine mathématique. L’enjeu de notre recherche est d’étudier les évolutions des pratiques de différenciation dans l’enseignement en calcul algébrique, à l’aide de ressources dont la pertinence cognitive et épistémologique a été soulignée dans les recherches de Pilet (2012) et d’un travail collaboratif entre enseignants et chercheurs dans le cadre d’un groupe IREM intitulé « Différenciation dans l’enseignement de l’algèbre ». / In our research, we are interesting in the management of the heterogeneity of students learning of the same class, and in the differentiation of teaching in the field of algebraic calculations,in the end of compulsory schooling in France. These questions have been the subject of several studies especially in the field of sociology (Bourdieu 1966), Science Education (Perrenoud, 1989, 1991; Przesmycki, 1991; Caron, 2003; Sarrazy, 2007) and in the field of mathematics education (Charnay, 1995; Grugeon, 1997; Castela , 2007; Pilet, 2012). Since recent years, they constitute two news topics in French secondary education. The different research highlights the fact that teachers are in difficulty to advance students. Two reasons lead us to focus on these themes. On one hand, the finding of confusion for teachers in managing the growing difficulties of students, and, on the other hand, the results of the French school system in terms of knowledge of students in national and international evaluations, particularly in the mathematical field. The aim of our research is to study the evolution of differentiation practices in teaching algebra, using resources whose cognitive and epistemological relevance has been highlighted in Pilet’s researches (2012) and a collaborative work between teachers and researchers as part of IREM group entitled « Differentiation in teaching algebra »

Η παρούσα διδακτορική διατριβή εστιάζεται στο πρόβλημα της “μετάβασης” από την δευτεροβάθμια εκπαίδευση στην τριτοβάθμια προτείνοντας την σύνδεση των Στοιχειωδών με τα Ανώτερα Μαθηματικά. Η σύνδεση αυτή επιχειρείται να γίνει μέσω κατάλληλα επιλεγμένων θεμάτων και οι μη-Ευκλείδειες Γεωμετρίες αποτελούν ένα ελκυστικό αντικείμενο για έρευνα στο παραπάνω πλαίσιο. Η διατριβή αυτή, αφορά τις μη Ευκλείδειες Γεωμετρίες και τα μοντέλα τους και ιδιαίτερα την Ελλειπτική Γεωμετρία: καθώς αυτή μοντελοποιείται πάνω στη σφαίρα, θα μπορούσε να αποτελέσει τη “γέφυρα” για το πέρασμα από την Ευκλείδεια στις μη-Ευκλείδειες Γεωμετρίες. Γίνεται μια σύντομη ιστορική αναδρομή από την ανακάλυψη των μη Ευκλείδειων Γεωμετριών μέχρι την αξιωματική θεμελίωση του Hilbert. Περισσότερη έμφαση δίνεται στα μοντέλα των μη Ευκλειδείων και προτείνεται μια κατηγοριοποίηση αυτών για παιδαγωγικούς σκοπούς καθώς και ένα μοντέλο της Ελλειπτικής Γεωμετρίας για πιθανή διδακτική χρήση. Επίσης αναλύεται ένα νέο θεωρητικό πλαίσιο έρευνας για την διδακτική της γεωμετρίας και στην συνέχεια θα περιγραφεί η ερευνητική μεθοδολογία και το κυρίως διδακτικό πείραμα. Στο διδακτικό πείραμα, στο οποίο βασίζεται η διατριβή αυτή, συμμετείχαν φοιτητές του Μαθηματικού Τμήματος του Πανεπιστημίου Πατρών οι οποίοι ασχολήθηκαν, μεταξύ άλλων, με ζητήματα όπως: η συντομότερη διαδρομή μεταξύ δύο σημείων πάνω στην επιφάνεια της σφαίρας και η κατασκευή μοντέλου της Ελλειπτικής Γεωμετρίας. / In this thesis, we investigate university students' interaction in an attempt to construct a model of elliptic geometry. In order to study the several ways in which geometrical meaning is produced through context and practices, we introduce three different types of use of geometrical concepts, namely as (1) elements of representation of spatial experience, (2) objects of traditional school practice, and (3) constituents of an abstract mathematical theory. The analysis of students' dialog according to this framework reveals how students develop their ability to communicate mathematically and negotiate their meanings. Students with a different use of geometrical concepts were able to interact and understand their peers.

Submitted by ANA CRISTINA DE SOUZA MARIN null (crismarinn5@gmail.com) on 2018-01-08T14:49:35Z No. of bitstreams: 1 Dissertação Final - ANA CRISTINA DE SOUZA MARIN.pdf: 6032728 bytes, checksum: b50a3b8d3d2ccb2cecf43815c8cced82 (MD5) / Approved for entry into archive by Telma Jaqueline Dias Silveira null (telmasbl@marilia.unesp.br) on 2018-01-08T15:39:01Z (GMT) No. of bitstreams: 1 marin_acs_me_mar.pdf: 6032728 bytes, checksum: b50a3b8d3d2ccb2cecf43815c8cced82 (MD5) / Made available in DSpace on 2018-01-08T15:39:01Z (GMT). No. of bitstreams: 1 marin_acs_me_mar.pdf: 6032728 bytes, checksum: b50a3b8d3d2ccb2cecf43815c8cced82 (MD5) Previous issue date: 2017-12-13 / Não recebi financiamento / O presente trabalho versou sobre questões relacionadas à Didática da Matemática e analisou como o software matemático Winplot pode ser utilizado como estratégia potencializadora dos processos de ensino e aprendizagem. Os objetivos foram compreender se e como os softwares matemáticos podem auxiliar nos processos de ensino e aprendizagem, investigando a importância da utilização dos mesmos como facilitadores dos processos de ensino e aprendizagem da matemática, bem como verificar como a aplicação foi vista perante aos alunos enquanto recurso pedagógico alternativo para o ensino da matemática. Partimos do pressuposto de que é imprescindível o preparo dos docentes para utilizar tais ferramentas, assim como planejar suas aulas, elaborar estratégias interessantes e executar ações com recursos didáticos adequados para que se alcancem os objetivos almejados sempre dentro de um contexto alinhado com o Projeto Pedagógico da instituição. O interesse pelo tema surgiu a partir da observação das dificuldades encontradas pelos professores quanto ao ensino da matemática no tocante à articulação entre a teoria e prática, tanto a prática social global pertinente à vida social do homem, quanto a prática em sala de aula relacionada aos conteúdos matemáticos, por meio de softwares educacionais, em especial ao Winplot. A escolha pelo software Winplot justificou-se pelo fato de ser considerada uma ferramenta potencializadora dos processos de ensino e aprendizagem na matemática, uma vez que propicia aos professores um recurso tecnológico no preparo das aulas e atividades como forma de aprimoramento metodológico. Para atender a este objetivo, a presente pesquisa teve como sujeitos os alunos do 1º ano do Ensino Médio de escola pública juntamente com a professora que leciona a disciplina em questão. A pesquisa foi desenvolvida segundo a abordagem qualitativa do tipo pesquisa-ação cooperativa. Teve como resultados a conclusão de que uma aula para ter uma aprendizagem significativa, sendo pautada na Teoria Histórico-Cultural, deve conter elementos para torná-la colaborativa entre os alunos, sendo fundamental a presença do professor mediador, mas deixando os estudantes serem protagonistas dos próprios conhecimentos. O professor tem a responsabilidade de conduzir o processo de forma tal que os alunos tenham condições de atribuir sentido e significado aos conteúdos trabalhados. Os resultados indicam que houve um aumento no interesse dos alunos pelas aulas, comprovando que o uso de tecnologias no ensino da Matemática proporciona melhoria da compreensão dos conceitos e conteúdos matemáticos. Todavia, destaca-se a necessidade de um melhor preparo dos professores no tocante à utilização do recurso tecnológico, bem como de se oferecer melhores condições de trabalho a eles, para que assim os mesmos possam ter condições de planejar uma aula diferenciada, embasada em teorias consistentes como a Teoria Histórico-Cultural, na qual os alunos possam ser efetivamente os protagonistas da ação pedagógica, participando de forma ativa no processo educacional. / The present work dealt with questions related to Mathematics Didactics and analyzed how Winplot mathematical software can be used as a potential strategy for teaching and learning processes. The objectives were to understand if and how mathematical software can aid in teaching and learning processes, investigating the importance of using them as facilitators of the teaching and learning processes of mathematics, as well as verify how the application was seen before the students as a resource an alternative pedagogy for the teaching of mathematics. We assume that it is essential to prepare teachers to use such tools, as well as to plan their classes, to devise interesting strategies and to execute actions with adequate didactic resources so that the objectives always achieved within a context aligned with the Pedagogical Project of the institution. The interest in the subject arose from the observation of the difficulties encountered by the teachers regarding the teaching of mathematics in relation to the theory and practice, both the global social practice pertinent to the social life of the man, and the practice in the classroom related to the mathematical content, through educational software, especially to Winplot. The choice of Winplot software was justified by the fact that it is considered a potential tool for teaching and learning processes in mathematics, since it provides teachers with a technological resource in the preparation of classes and activities as a methodological improvement. In order to meet this objective, the present research had as subjects the students of the 1st year of high school public school together with the teacher who teaches the discipline in question. The research was developed according to the qualitative approach of the cooperative research-action type. The conclusion was that a lesson to have a meaningful learning, based on the Historical-Cultural Theory, should contain elements to make it collaborative among the students, being fundamental the presence of the mediating teacher, but leaving the students to be protagonists of the own knowledge. The teacher has the responsibility to conduct the process in such a way that the students are able to give meaning and meaning to the contents worked. The results indicate that there has been an increase in students' interest in classes, proving that the use of technologies in teaching mathematics improves the understanding of mathematical concepts and contents. However, there is a need for teachers to better prepare for the use of technological resources, as well as to offer better working conditions to teachers, so that they may be able to plan a differentiated class based on theories consistent as the Historical-Cultural Theory, in which students can be effectively the protagonists of the pedagogical action, participating actively in the educational process.

Orientador: Mara Sueli Simão Moraes / Banca: Dermeval Saviani / Banca: Lizete Maria Orquiza Carvalho / Banca: Manoel Oriosvaldo de Moura / Banca: Romulo Campos Lins / Resumo: A pesquisa teve como objetivo geral o ensaio de uma Didática da Matemática, embasada na Pedagogia Histórico-Crítica, utilizando a Seguridade Social como tema político-social estruturador. O método de abordagem adotado foi o da Dialética Materialista Histórica e a pesquisa desenvolveu-se com a participação de professores e alunos de escolas públicas na aplicacao da proposta que enfocou conteúdos matemáticos selecionados para compreensão dos conteúdos político-sociais relacionados a Seguridade Social. O reconhecimento da Previdencia Social como componente da Seguridade Social e desta como Direito Humano e importante para todos os cidadãos mas o conhecimento que se tem desses temas ou da Matemática neles contidas é, muitas vezes, insuficiente e pouco científico. Para interessar aos estudantes, é necessário abordá-lo de forma adequada, apoiando-se nos fundamentos da Psicologia Sócio-Histórica. A proteção social, da forma como foi desenvolvida pelos homens, tem sua sustentabilidade econômico-financeira dependente de inúmeros fatores como envelhecimento da população, níveis de emprego, níveis de faixas salariais e outros. Os conhecimentos matemáticos e atuariais desenvolvidos até nossos dias permitem que os sistemas existentes nos diversos países sejam constantemente avaliados de modo a se determinar, de tempos em tempos, se as regras sociais acordadas estão adequadas ou se há necessidade de reformá-las, no todo ou em parte. Mas, o imenso volume de dinheiro movimentado pela Seguridade Social, um dos maiores do planeta, desperta outros interesses nas reformas, nem sempre compromissados com a proteção social. A Matemática pode ajudar-nos a compreender as intenções explícitas e implícitas de cada uma das reformas ocorridas ou a ocorrer e os resultados da pesquisa mostram que é possível levar esse conhecimento para a Educação Básica. / Abstract: The general purpose of this research was essay of Mathematics' didactics based on historical-critical pedagogy focusing the Social Security as structural sociopolitical theme. The Historical-materialist dialectic approach method was applied and the research was developed by the public schools' teachers and students participation in the proposal's application that focused selected mathematical contents for understanding the sociopolitical contents relating to Social Security. The recognition of the social welfare and Social Security as Human Right is important for all the citizens but their knowledge on these subjects or about the Mathematics they contain is many times insufficient and poorly scientific. To the students' interest, it is necessary to approach it adequately, supporting itself in the grounds of Social-Historical Psychology. The social protection, the manner by which it was developed by the humanity has its economic-financial sustainability dependent of several factors as population aging, level of employment, income strata and others. The mathematical and actuarial knowledge developed so far allows that the existing systems in the several countries be constantly evaluated in order to determine between times if the dealt social rules are appropriate or there is need to remodel them, in whole or in part. However, the huge quantity of money moved up by the Social Security, one of the greater of the planet, stimulate other interests toward to restructures, not always compromised with the social protection. The Mathematics can help us to understand the explicit and implicit intentions of each one of the implemented or to implement changes and research's results they shows that it is possible bring this knowledge for the Elementary Education. / Doutor

Tidigare studier visar att det finns skillnader mellan flickor och pojkar avseende hur de upplever ämnet matematik, vilket återspeglas i utbildnings- och yrkesval. Tidigare studier visar även att det finns skillnader mellan flickor och pojkar avseende hur de lär och tänker när de löser matematiska problem och attlärare inte alltidtar hänsyn till dessa skillnader. Denna studie syftar till att undersöka hur flickor och pojkar löser aritmetiska uppgifter genom kognitiva, kroppsliga och externa strategier samt likheter och skillnader mellan flickor och pojkar. Totalt har 23 barn (11 flickor och 12 pojkar) i grundskolans årskurs ett löst nio aritmetiska och fyra andra matematiska uppgifter. Barnen instruerades att tänka högt och blev videofilmade. Resultaten visar att pojkarna oftare använder kognitiva strategier (75% av uppgifterna) än flickorna gör (66%). Särskilt ofta använder pojkarna de kognitiva strategier som kallas härledning och talfakta (62%) medan flickorna använder dessa strategier mindre ofta (40%). Flickorna använder oftare kognitiva och kroppsliga strategier där de räknar upp eller ned (49%) än pojkarna gör (20%). Flickorna använder även oftare kroppsliga strategier (30%) än pojkarna gör (13%). Dessa skillnader pekar på att lärare bör kartlägga vilka strategier eleverna använder för att därigenom kunna anpassa sin undervisning. / Previous research show there are differences between girls and boys as it comes to how they experience school mathematics, which has consequences for educational and professional career choices. Previous studies also show there are differences between girls and boys concerning how they learn and think when solving mathemtical problems and that teachers do not always take these differences into consideration. This study aims at describing and anaysing how girls and boys solve arithemtic tasks by using cognitive, bodily and external strategies and similarities and differences betweeen girls and boys. In total, 23 children (11 girls and 12 boys) first graders in elementary school solved nine arithmetic and four other mathematical tasks. The children were instructed to think aloud and they were video recorded. The results show that boys more often used cognitive strategies (in 75% of tasks) than girls did (66%). In particular, the boys tended to use the cognitive strategies that are called decomposition and direct retrieval of artithmetic facts (62%) while the girls used these strategies less often (40%). The girls more often used cognitive and bodily strategies involving counting up or down (49%) than the boys did (20%). The girls more often used bodily strategies (30%) than the boys did (13%). These differences indicate that teachers should be provided tools for mapping strategies that pupils use in order to be able to adapt their teaching to individual differences.

Several years of my experiences in the use of real-time experiments are now upgraded in order to enhance also the teaching of mathematics. The motion sensor device enables us to get real time x(t) and v(t) graphs of a moving object or person. We can productively use these graphs to introduce differentiation on visual level as well as to show the integration procedure. The students are fully involved in the teaching as they are invited to walk in front of the sensor. This approach motivates them by the realistic aspects of mathematical structures. The method could help to fulfill the credo of teaching: comprehension before computation. The steps of such an approach are explained and discussed in further detail below.

Matematik är ett komplext ämne som upplevs som svårt av många elever, därför behöver undervisningen ge goda förutsättningar för att utveckla elevers matematikkunskaper. En teoretisk grund som används av allt fler lärare och skolor för att utveckla matematikundervisningen är variationsteorin. Det är därför relevant att undersöka hur variationsteorin kan användas i planering, genomförande och utvärdering av matematikundervisningen.  Syftet med studien är att sammanställa forskning om hur variationsteorin har använts i matematikdidaktiska studier i grundskolans tidigare skolår. Detta syfte vill vi uppfylla genom att analysera vilka forskningsfrågor som ställs och vad som karaktäriserar resultaten i variationsteoretiska studier. Litteraturstudien bygger på såväl nationella som internationella vetenskapliga artiklar. Materialet är hämtat från två söktjänster och dess relevans för studien säkerställs med inkluderings- och exkluderingskriterium. En översiktstabell har använts som analysverktyg samt för att sammanställa studiernas syfte, genomförande och resultat.  Resultatet visar att variationsteorin kan användas för att urskilja relationen mellan undervisning och lärande, då den används både för planering och utvärdering av genomförd undervisning samt för att analysera hur eleverna uppfattar ämnesinnehållet. Studiernas resultat ger ämnesdidaktiska implikationer i form av kritiska aspekter samt gynnsamma variationsmönster för specifika ämnesinnehåll inom exempelvis aritmetik och taluppfattning. Resultatet visar även svårigheterna i att identifiera kritiska aspekter samt behovet av en teori för att förbättra undervisningen. Avslutningsvis diskuteras huruvida variationsteorin kan användas för att effektivisera undervisning samt huruvida studiernas resultat är generaliserbara till andra kontexter.