Syftet med studien var att undersöka hur gymnasieelever använder matematikboken för att få en utökad förståelse för matematikboken som verktyg i undervisningen och lärandet. Vidare var syftet att synliggöra eventuella samband mellan motivationen till att studera matematik och hur matematikboken används. Både kvantitativ- och kvalitativ metod användes i undersökningen och datamaterialet samlades in via en digital enkät. Den teoretiska utgångspunkten för att undersöka gymnasielevernas motivation till matematik var förväntan-värdeteorin. Sammanlagt deltog 133 gymnasieelever från tre skolor som låg i Norrbotten och Västernorrland. Resultatet pekade på att gymnasieleverna främst arbetade med uppgifter i matematikboken, teoriavsnittet och exempeluppgifterna lästes inte lika frekvent men det förekom. Vidare använde en majoritet av gymnasieeleverna matematikboken flera gånger i veckan under lektionerna, medan det inte var lika vanligt att den användes utanför skolan. Kostnadsvärdet var den motivationstyp som korrelerade med flest aktiviteter med matematikboken. Det visade sig bland annat att de som ofta använde matematikboken utanför skolan hade högre kostnadsvärde än de som aldrig eller sällan gjorde det. / The purpose of the studie was to investigate how high school students’ use the mathematics textbook to gain an expanded understanding of the mathematics textbook as a tool in teaching and learning. Furthermore, the aim was to make visible any connections between the motivation to study mathematics and how the textbook is used. Both quantitative and qualitative methods were used in the studie and the data was collected via a digital survey. The theoretical starting point for investigating high school students' motivation for mathematics was the expectency-value theory. A total of 133 high school students participated from three schools located in Norrbotten and Västernorrland. The results indicated that the high school students mainly worked with tasks in the mathematics book, the theory section and the example tasks were not read as frequently, but it did occur. Furthermore, a majority of high school students used the mathematics textbook several times a week during lessons, while it was not as common that it was used outside of school. Cost value was the motivation type that correlated with the most activities with the textbook. Among other things, it turned out that those who often used the mathematics textbook outside of school had a higher cost value than those who never or rarely did so.

Syftet med denna studie är att få mer kunskap om användandet av digitala verktyg vid undervisning av problemlösning i inom matematik i årskurs 1–3. Studien är av kvalitativ karaktär med en induktiv ansats som tar utgångspunkt i det sociokulturella perspektivet. Semistrukturerade intervjuer har genomförts med fyra verksamma lärare som använder digitala verktyg vid undervisning av problemlösning. Resultatet påvisar att lärarna använder iPad, dator, smartboard samt projektor genom att utnyttja dessa i samspel med olika appar och plattformar. Vidare används digitala verktyg vid genomgångar av uppgifter i problemlösning. Lärarna framför en positiv inställning till digitala verktyg där samtliga uttrycker den vardagsanknytning digitala verktyg besitter, vilket motiverar eleverna. Samtidigt framgår vissa hinder med att använda digitala verktyg i undervisning av problemlösning. / The purpose of this study is to get a deeper understanding of the implementation of digital technology in mathematical problem-solving, targeting teachers in grades 1-3. The study is qualitative with an inductive approach. Four semi-structured interviews were conducted with teachers using digital technology during problem-solving. A qualitative content analysis was conducted on data collected, with the sociocultural perspective as a point of departure. The result showed that teachers use iPad, computers, smartboards, and projectors interplaying with different mathematical applications and platforms. The teachers frequently use digital technology during presentations of mathematical problem-solving in the classroom. The results also showed that the teachers are positive towards digital technology and the connection to everyday situations, which can motivate the pupils. However, the teachers also describe some obstacles when teaching problem-solving in regard to digital technology in the classroom.

Blockmodellen är en metod från Singapore som används inom problemlösning i matematiken. Det saknas svensk forskning på hur den fungerar i den svenska skolan trots att många skolor har läromedel och förutsättningar att använda metoden. Syftet med studien är att undersöka vad som bidrar till att elever i årskurs 6 förstår och kan använda blockmodellen och hur den kan bidra till deras problemlösningsförmåga utifrån planerade lektionstillfällen. Genom en designcykel skedde två lektionstillfällen, och med hjälp av inspelning av lektionerna kunde avgörande medierande handlingar identifieras utifrån Vygotskys medierande triangel. En deduktiv analys användes för att granska elevernas frågor och kommentarer i det inspelade materialet och utifrån det kunde elevernas mest avgörande handlingar presenteras. Eleverna visade sig förstå blockmodellen efter genomgångar om hur blocken ritas och med hjälp av en framtagen arbetsgång som fungerade som guide till en början. Eleverna visade även att algebraiska ekvationer var enklare att lösa med hjälp av blockmodellen, tack vare blockmodellens visuella framställning. När eleverna vet hur de ska rita och korrekt representera blocken i blockmodellen, är det en metod de kan tillämpa i sin problemlösning. / The bar model comes from Singapore and is used in word problems in mathematics. Swedish research on how the model works is missing even though many schools have the books and the conditions to use the method. The purpose of this study is to examine what it is that contributes to the understanding and usage of the method from pupils in year 6, and how it contributes to their problem-solving ability by planned lessons. Through a design cycle there were two lessons and with help from recording the lessons, crucial mediating actions could be found from the mediating triangle by Vygotsky. A deductive analysis was used to review the questions and comments from the recorded material and from that, the most crucial mediating actions could be presented. The pupils understood the bar model after briefings on how the bars should be drawn and with the help from a provided guide. The pupils also showed that algebraic equations were easier to solve with the bar model, thanks to its visual production. When the pupils know how to draw and correctly represent the bars in the bar model, they can apply the method in their problemsolving.

Text in Afrikaans / Die doel van hierdie navorsing is, om te bepaal of gesyferdheid by kleuters binne `n speelgroepsituasie ontwikkel kan word deur middel van `n program wat wiskundige konsepte aan kleuters oordra. Ten einde hierdie doel te bereik is `n wiskunde program waarin verskillende hulpmiddels gebruik word, vir die kleuters aangebied. Die wiskunde program wat gebruik is, is saamgestel aan die hand van Charner, Murphy en Clark (2007) se “The Giant Encyclopedia of Math Activities for Children 3 to 6”. Die aktiwiteite wat tydens die voortoets en natoets gebruik is, is uit verskillende bronne op die internet verkry. Die aktiwiteite is uit gemelde bronne geneem en aangepas om by kleuters se ontwikkelingsvermoë te pas. Aan die einde van die wiskunde program kon daar `n verbetering in al die leerders se wiskunde vaardighede waargeneem word. Die resultate van die studie dui dus daarop dat kleuters se begrip en vaardigheid met wiskundige konsepte op `n vroeë ouderdom in `n speelgroep ontwikkel kan word. / The aim of this study was to determine whether numeracy can be developed among preschoolers in `n playgroup situation by means of a numeracy programme which introduces them to mathematical concepts. To achieve this aim a numeracy programme was used to introduce the mathematical concepts. The numeracy programme that was used is a programme compiled from “The Giant Encyclopedia of Math Activities for Children 3 to 6” by Charner, Murphy and Clark (2007). The activities which were used during the pre-test and post-test were taken from different sources on the internet. The activities taken from these different sources were adapted to the appropriate developmental phase of the preschoolers. At the end of the programme the post-test indicated an improvement in the mathematical competence of all the learners. The results of the study prove that preschoolers in a playgroup can improve their numeracy skills in the early years. / Teacher Education / M. Ed. (Didaktiek)

Kognitive Diagnosemodelle (DCMs) sind konfirmatorische probabilistische Modelle mit kategorialen latenten Variablen, die Mehrfachladungsstrukturen erlauben. Sie ermöglichen die Abbildung der Kompetenzen in mehrdimensionalen Profilen, die zur Erstellung informativer Rückmeldungen dienen können. Diese Dissertation untersucht in zwei Anwendungsstudien und einer Simulationsstudie wichtige methodische Aspekte bei der Schätzung der DCMs. In der Arbeit wurde ein neuer Mathematiktest entwickelt basierend auf theoriegeleiteten vorab definierten Q-Matrizen. In den Anwendungsstudien (a) illustrierten wir die Anwendung der DCMs für empirische Daten für den neu entwickelten Mathematiktest, (b) verglichen die DCMs mit konfirmatorischen Faktorenanalysemodellen (CFAs), (c) untersuchten die inkrementelle Validität der mehrdimensionalen Profile und (d) schlugen eine Methode zum Vergleich konkurrierender DCMs vor. Ergebnisse der Anwendungsstudien zeigten, dass die geschätzten DCMs meist einen nicht akzeptablen Modellfit aufwiesen. Zudem fanden wir nur eine vernachlässigbare inkrementelle Validität der mehrdimensionalen Profile nach der Kontrolle der Personenparameter bei der Vorhersage der Mathematiknote. Zusammengenommen sprechen diese Ergebnisse dafür, dass DCMs per se keine zusätzliche Information über die mehrdimensionalen CFA-Modelle hinaus bereitstellen. DCMs erlauben jedoch eine andere Aufbereitung der Information. In der Simulationsstudie wurde die Präzision der Parameterschätzungen in log-linearen DCMs sowie die Sensitivität ausgewählter Indizes der Modellpassung auf verschiedene Formen der Fehlspezifikation der Interaktionsterme oder der Q-Matrix untersucht. Die Ergebnisse der Simulationsstudie zeigen, dass die Parameterwerte für große Stichproben korrekt geschätzt werden, während die Akkuratheit der Parameterschätzungen bei kleineren Stichproben z. T. beeinträchtigt ist. Ein großer Teil der Personen wird in Modellen mit fehlspezifizierten Q-Matrizen falsch klassifiziert. / Cognitive diagnostic classification models (DCMs) have been developed to assess the cognitive processes underlying assessment responses. Current dissertation aims to provide theoretical and practical considerations for estimation of DCMs for educational applications by investigating several important underexplored issues. To avoid problems related to retrofitting of DCMs to an already existing data, test construction of the newly mathematics assessment for primary school DMA was based on a-priori defined Q-matrices. In this dissertation we compared DCMs with established psychometric models and investigated the incremental validity of DCMs profiles over traditional IRT scores. Furthermore, we addressed the issue of the verification of the Q-matrix definition. Moreover, we examined the impact of invalid Q-matrix specification on item, respondent parameter recovery, and sensitivity of selected fit measures. In order to address these issues one simulation study and two empirical studies illustrating applications of several DCMs were conducted. In the first study we have applied DCMs in general diagnostic modelling framework and compared those models to factor analysis models. In the second study we implemented a complex simulation study and investigated the implications of Q-matrix misspecification on parameter recovery and classification accuracy for DCMs in log-linear framework. In the third study we applied results of the simulation study to a practical application based on the data for 2032 students for the DMA. Presenting arguments for additional gain of DCMs over traditional psychometric models remains challenging. Furthermore, we found only a negligible incremental validity of multivariate proficiency profiles compared to the one-dimensional IRT ability estimate. Findings from the simulation study revealed that invalid Q-matrix specifications led to decreased classification accuracy. Information-based fit indices were sensitive to strong model misspecifications.

Made available in DSpace on 2016-04-27T16:57:13Z (GMT). No. of bitstreams: 1 Denise Franco Capello Ribeiro.pdf: 16199362 bytes, checksum: 36c5c02d581138df6e2c1def4c8a0fb9 (MD5) Previous issue date: 2011-12-09 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This research has as objective the study of the historic way of the Mathematics scholar subject constitution to High School, at Gustavo Capanema Reform, time in which was made the reorganization of the Mathematics teachings to this teaching level and the rising of the Mathematic didactic books collection entitled Matemática 2º Ciclo , to the 1st, 2nd and 3rd grades, edited to assist the new Mathematics syllabus of these courses, by the authors Euclides Roxo, Roberto Peixoto, Haroldo Lisbôa da Cunha and Cesar Dacorso Netto, also known as the 4 authors Collection. This collection standardizes the structure of other Mathematics didactic collections books contributing to the teaching standardization and the Mathematics scholar subject constitution. This investigation uses mainly the theoric basis of André Chervel, Alain Choppin and Roger Chartier, the legislation related to this Reform and Mathematic didactic books edited to High School courses, whose authors were consulted by High School students (Classic and Scientific), in the scholar library of the current Sao Paulo State School, in the period between 1943 to 1961, as mainly research sources. The main question of this investigation is: How the Mathematics didactic books from the collection entitled Matemática 2º Ciclo , by Euclides Roxo, Roberto Peixoto, Haroldo Lisbôa da Cunha and Cesar Dacorso Netto, as known as the 4 authors Collection, written to High School courses, in the Capanema Reform period, contributed to the Mathematic scholar subject constitution, to this teaching level? This research seeks to give a contribution to the History of Scholar Mathematics and to the Mathematic Education in Brazil / Esta pesquisa tem como objetivo o estudo da trajetória histórica da constituição da disciplina escolar Matemática para o Curso Colegial, na Reforma Gustavo Capanema, período em que houve a reorganização dos ensinos de Matemática para este nível de ensino e o surgimento da coleção de livros didáticos de Matemática intitulada Matemática 2º Ciclo, para a 1ª, 2ª e 3ª séries, editados para atender aos novos programas de Matemática desses cursos, dos autores Euclides Roxo, Roberto Peixoto, Haroldo Lisbôa da Cunha e Cesar Dacorso Netto, também conhecida como a Coleção dos 4 autores. Esta coleção parametrizou a organização de outros livros didáticos de Matemática contribuindo para padronização dos ensinos e constituição da disciplina escolar Matemática. Esta investigação utiliza principalmente os aportes teóricos de André Chervel, Alain Choppin e Roger Chartier, a legislação pertinente a esta Reforma e livros didáticos de Matemática editados para os Cursos Colegiais, cujos autores foram consultados por alunos dos Cursos Colegiais (Clássico e Científico), na biblioteca escolar da atual Escola Estadual São Paulo, no período compreendido entre 1943 a 1961, como principais fontes de pesquisa. A questão norteadora desta investigação é: Como os livros didáticos de Matemática pertencentes à coleção intitulada Matemática 2º Ciclo, de Euclides Roxo, Roberto Peixoto, Haroldo Lisbôa da Cunha e Cesar Dacorso Netto, também conhecida como a Coleção dos 4 autores, escrita para os Cursos Colegiais, em tempos da Reforma Capanema, contribuíram para a constituição da disciplina escolar Matemática, para este nível de ensino? Esta pesquisa busca dar uma contribuição à História da Matemática Escolar e à Educação Matemática no Brasil

Made available in DSpace on 2016-04-27T16:57:16Z (GMT). No. of bitstreams: 1 Aspectos do Pens Matematico na RP-Segurity printing.pdf: 2060132 bytes, checksum: c0711be8b2de82245dd639a3d704a6be (MD5) Previous issue date: 2005-11-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This doctorate thesis aims to identify the characteristics and the dimensions of mathematical thinking in experimental and theoretical terms which may be useful to teachers with respect to teaching processes, development of mathematical ideas and the delineation of learning contexts. Our study began with a detailed analysis of the work of Krutetskii (1968). This book is very rich in theoretical examples and reflections. It is, however, a completely psychological work and provided few indications of the more general mathematic knowledge and thinking. For this reason we added detailed information about the work of other authors such as Gowers, Poincaré, Boutroux, Otte and Kurz, and this added other dimensions which assisted our understanding of the nature of mathematics. These authors were concerned with the problems of cognitive styles, cultural and historical differences, differences that are the results of mathematics itself and distinctive ways of representing mathematics. The experimental dimensions consisted of analysis of data obtained from qualitative research with students whereby one was taken from the literature (Krutetskii) and the other an exploratory survey which we carried out for the purposes of this thesis. Krutetskii carried out an experimental investigation involving 201 Russian students with different mathematic abilities, attending elementary school. These students were presented with a number of different series of mathematic problems and their mathematic abilities were observed during the problem solving process. In our survey we carried out case studies exploring mathematic problem solving involving 13 students from the Federal University of Mato Grosso with 9 students from the Mathematics/Education course and 4 students from the Computer Sciences Course. The exploratory survey was organized into 3 phases. The first was the completion of a questionnaire with subjective questions about Mathematics and preferred ways of thinking and dealing with this subject. The second phase was reserved for the solution of 13 varied mathematical problems. The final phase was the completion of another questionnaire with subjective questions which sought to obtain information about the experiences of the students when solving the problems set. With our exploratory survey we were able to document and verify several parameters and characteristics of mathematical thinking which were described in the theoretical chapters as well as being able identify the problems themselves and the experience of solving them also influenced mathematical thinking. As a general result we concluded that mathematical thinking must be considered in the light of different parameters since this can help to characterize more complete mathematical thinking / A presente Tese de Doutorado pretende indicar características e dimensões do pensamento matemático, em termos teóricos e experimentais, que podem ser úteis aos professores no que se refere aos processos de ensino, ao desenvolvimento de idéias matemáticas e ao delineamento de contextos de aprendizagem. Nosso estudo começou com uma análise detalhada do trabalho de Krutetskii (1968). Esse livro é muito rico em exemplos e reflexões teóricas. No entanto, é um trabalho completamente psicológico e forneceu poucas indicações a respeito dos aspectos mais gerais do conhecimento matemático e do pensamento matemático. Por esse motivo, adicionamos informações detalhadas sobre o trabalho de outros autores como Gowers, Poincaré, Boutroux, Otte e Kurz que acrescentaram outras dimensões que auxiliaram a nossa compreensão da natureza da Matemática. Esses autores se preocuparam com problemas de estilos cognitivos, de diferenças culturais e históricas, de diferenças que são resultados das várias áreas da própria Matemática e distintas formas de representação na Matemática. As dimensões experimentais consistiram na análise de dados obtidos em pesquisas qualitativas com estudantes, sendo uma da literatura (Krutetskii) e outra uma pesquisa exploratória realizada por nós para a presente Tese. Krutetskii realizou uma investigação experimental envolvendo 201 estudantes russos do Ensino Fundamental, com diferentes habilidades matemáticas. A esses estudantes foram propostas diversas séries de problemas matemáticos, em que foram observadas suas habilidades matemáticas durante o processo de resolução. Na nossa pesquisa, realizamos estudos de caso exploratório na resolução de problemas matemáticos envolvendo 13 estudantes da Universidade Federal de Mato Grosso, sendo 09 do Curso de Licenciatura Plena em Matemática e 04 do Curso de Ciências da Computação. A pesquisa exploratória foi organizada em três momentos. O primeiro foi destinado a responder um questionário com perguntas subjetivas acerca da Matemática e de preferências na forma de pensar e de lidar com a mesma. O segundo momento foi reservado para a resolução de 13 problemas matemáticos variados. E o último momento foi destinado para responder a outro questionário com perguntas subjetivas que procurava obter informações sobre a experiência dos estudantes na atividade de resolução dos problemas propostos. Com a nossa pesquisa exploratória pudemos documentar e verificar vários parâmetros e características do pensamento matemático que foram descritos nos capítulos teóricos, bem como identificar que os próprios problemas e as experiências com a resolução dos mesmos também influenciam o pensamento matemático. Como resultado geral, concluímos que o pensamento matemático deve ser considerado sob diferentes parâmetros, pois eles podem auxiliar na caracterização mais completa do pensamento matemático

Made available in DSpace on 2016-04-27T16:57:49Z (GMT). No. of bitstreams: 1 Renata Rossini.pdf: 2745582 bytes, checksum: 007ec2ee6081f4135356bd33173b27b8 (MD5) Previous issue date: 2006-11-13 / Conselho de Ensino e Pesquisas / The issues of this research are the conceptions and difficulties of a group of teachers regarding the function concept, and how they overcame them along a continuous formation process. Although there are some studies regarding the students' difficulties and possible obstacles to the teaching and learning of this theme, it is necessary to pay attention on what a formative action means to a group of primary and middle school teachers, since there are not many researches involving teachers. Therefore, this thesis answers to the following questions: Which mathematical organizations are mobilized during the construction of a teaching sequence on functions for an 8th grade of Middle Education? How do the teachers build or rebuild their teacher knowledge on the function concept? The adopted methodology used an action-research as a collaborative investigation, because it propitiates the interaction between the researcher and the teachers and their practice in formation and in action. The theoretical foundation was based on the Anthropological Theory of the Didactic of Chevallard (1999) to model the function concept as Mathematical Organization and Didactic Organization associated with function conceptions such as magnitude interdependence, in and out machine, analytical expression, pattern of regularity of geometric sequences and correspondence between sets. This foundation granted the analysis of some 8th grade mathematics books and teachers' production along a process of continuous formation. As the teachers build the didactic organizations by preparing a didactic sequence for the function teaching and learning for an 8th grade class, they analyse and rebuild their own knowledge on function. At the end, the teachers manage to get relative articulation between the mobilized organizations, and it allow them to innovate and create new exercises. Building a teaching sequence and following its applications in classrooms made the teachers look at their students more positively and also feel more valued at their work / Esta pesquisa trata das concepções e dificuldades de um grupo de professores sobre o conceito de função, da superação das mesmas ao longo de um processo de formação continuada. Embora existam alguns estudos a respeito das dificuldades de alunos e dos possíveis obstáculos ao ensino e aprendizagem deste tema, há necessidade de observar o que uma ação formativa significa para um grupo de professores do ensino fundamental e médio, devido não existir muitos trabalhos de pesquisa envolvendo docentes. Assim, este trabalho responde às seguintes perguntas: Quais organizações matemáticas são mobilizadas durante a construção de uma seqüência de ensino sobre funções para uma 8a série do Ensino Fundamental? Como os professores (re)constroem seus saberes docentes sobre o conceito de função? A metodologia adotada utilizou uma ação-pesquisa no sentido de uma investigação colaborativa, visto que propicia a interação entre pesquisador e professores e sua prática em formação e em ação. O fundamento teórico baseou-se na Teoria Antropológica do Didático de Chevallard (1999) para modelar o conceito de função em termos de Organização Matemática e Organização Didática, associadas às concepções de função: interdependência de grandezas, máquina de entrada e saída, expressão analítica, padrão de regularidade de seqüências geométricas, correspondência entre conjuntos. Este fundamento deu subsídios para a análise de alguns livros de Matemática da oitava série e da produção dos professores ao longo de um processo de formação continuada. À medida que os docentes constroem as organizações didáticas, ao preparar uma seqüência didática para o ensino e aprendizagem de função para uma classe de oitava série, eles (re)constroem os seus saberes sobre função. No final, eles conseguem fazer uma relativa articulação entre as organizações mobilizadas, dando-lhes a possibilidade de criar novos conteúdos. Construir uma seqüência de ensino e acompanhar a sua aplicação em sala de aula fez com que os professores olhassem seus alunos de forma mais positiva e se sentissem mais valorizados no seu trabalho

Made available in DSpace on 2016-04-27T16:58:09Z (GMT). No. of bitstreams: 1 dissertacao_marilene_moussa_miranda.pdf: 291834 bytes, checksum: 692a23cfd34a77403a0f62a0d4ba4443 (MD5) Previous issue date: 2003-12-16 / This dissertation is a study on the North American experiment of merging subjects such as Arithmetic, Algebra and Geometry, and the influence of this experiment over the Mathematic education in Brazil. We have analyzed a few changes occurred in the secondary school in North America between 1890 and 1930, and also how Professor Euclides Roxo used that initiative as he presented his proposal for a change in the curriculum of the D. Pedro II Secondary School, creating the subject of Mathematics. We finally make a comparative analyzes of the proposals on the teaching of Mathematics both in Brazil and in the USA. In our conclusion, we justify the lack of success of both proposals, in two different contexts, whose purpose was to merge the different branches of Mathematic for teaching / O trabalho estuda a experiência norte-americana de fusão da Aritmética, Álgebra e Geometria e sua influência na Educação Matemática Brasileira. São analisadas algumas modificações ocorridas no ensino secundário norte-americano, durante o período compreendido entre 1890 a 1930, e o modo como o professor Euclides Roxo apropria-se dessas iniciativas ao apresentar sua proposta de alteração na seriação do curso secundário do Colégio Pedro II criando a disciplina Matemática. Ao final é feito um estudo comparativo das propostas para o ensino de Matemática nos EUA e no Brasil concluindo por justificar o fracasso dessas duas reformas, em contextos diferentes, que visavam fundir os ramos matemáticos para o ensino

Made available in DSpace on 2016-04-27T16:58:12Z (GMT). No. of bitstreams: 1 dissertacao_rosemeiry_castro_prado.pdf: 413146 bytes, checksum: 6841bae3629f8a9185a6a574b52ddbe1 (MD5) Previous issue date: 2003-12-18 / The present work studies some elements for history of mathematics teacher formation to secondary school. Through the specific analysis of the contests to Pedro II School cathedra in Rio de Janeiro we try historically to understand the changes demanded from knowledge of mathematics teachers. We try to show that professional knowledge of mathematics teacher is referred by the contests suffering changes with the creation of philosophy universities. The approached period permit to study elements that are present on the transition from the engineers to the licensed teachers. That passage is analyzed from the changes related to the demands of professional knowledge of those who teach mathematics on secondary school / A pesquisa inventaria alguns elementos para a história da formação do professor de matemática do ensino secundário. Mais especificamente, através da análise de concursos à cátedra do Colégio Pedro II, no Rio de Janeiro, busca-se compreender historicamente as alterações exigidas ao saber dos professores de matemática. Procura-se mostrar que o saber profissional do professor de matemática está referenciado pelos concursos, sofrendo alterações com a criação das faculdades de filosofia. O período abordado permite estudar elementos que estão presentes na transição dos engenheiros para os licenciados. Essa passagem é analisada a partir das alterações relativas às exigências do saber profissional daqueles que ensinam Matemática no secundário