CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / A formaÃÃo de professores à perpassada por vÃrios dilemas. DiscussÃes e pesquisas sobre formaÃÃo continuada de professores mobilizam reflexÃes sobre as dimensÃes do desenvolvimento profissional docente e entendimentos distintos sÃo expressos. Pela vivÃncia e discussÃo sobre o assunto, busca-se compreender de que modo os professores de MatemÃtica reconstituem suas prÃticas pedagÃgicas com suporte em ensaios, interaÃÃes e acompanhamentos didÃticos. Ampliando os estudos, identificam-se a necessidade de se dispor de um desenho de formaÃÃo continuada especÃfico para o professor de MatemÃtica do Ensino Fundamental. Reunindo-se as dificuldades pedagÃgicas do professor em exercÃcio e aquelas inerentes ao cÃdigo da disciplina MatemÃtica, surgiu a proposta de se organizar uma metodologia de formaÃÃo que articulasse teoria-prÃtica para ampliar os conhecimentos docentes, e que se baseasse na SequÃncia Fedathi para mediar a formaÃÃo de conceitos matemÃticos. Com origem nessa ideia inicial, algumas questÃes passaram a nortear a reflexÃo: quais as bases pedagÃgicas para uma metodologia de formaÃÃo continuada para professores de MatemÃtica em exercÃcio? Qual o desenho dos encontros de formaÃÃo adequado ao emprego desta metodologia, tendo em vista as caracterÃsticas do pÃblico a que se destina? Quais as orientaÃÃes adequadas para a formaÃÃo de conceitos teÃrico-didÃticos desse professor e de seus alunos baseados na SequÃncia Fedathi? Este estudo procurou respostas para estas perguntas por meio do desenvolvimento de uma metodologia pedagÃgica para formaÃÃo continuada de professores de MatemÃtica em serviÃo e que atuem no Ensino Fundamental. Esse estudo se justifica pela importÃncia de investigar um modelo de formaÃÃo continuada que colabore com a orientaÃÃo de formaÃÃo dos professores de MatemÃtica da escola, tomando como pressuposto sua atuaÃÃo em serviÃo e suas necessidades de atualizaÃÃo, ressignificaÃÃo e troca de experiÃncias com seus pares naturais inseridos numa mesma comunidade. Mostramos um modelo de formaÃÃo composto por orientaÃÃes metodolÃgicas que contemplam as dimensÃes teÃricas, prÃtica, cultural e relacional baseada na SequÃncia Fedathi. / Teacher education is an issue transversed by several dilemmas. Discussion and research on continuing teacher education have mobilized reflections on the dimensions of teacher professional development and different understandings have been presented. In our experience and discussions, we attempt to understand how teachers of Mathematics rebuilding their teaching practices from studies, interactions and educational monitoring. Broadening our studies, we found out the need for a continuing education design specific for math teacher of elementary school. Bringing together difficulties both in teachers practice and in math language, has given rise to think about organizing an education methodology that articulate theory and practice to improve teaching skills based on Fedathi Sequence to mediate the formation of concepts. From this initial idea, some questions guided the discussion: What are the pedagogical basis for a continuing education methodology for math teachers in-service? What lecture design is suited to such methodology considering the characteristics of the target audience? Which are the appropriate guidelines for the math teachers and students formation on theoretical and didactic concepts, based on Fedathi Sequence? This study sought for answers to these questions through the design of a pedagogical methodology for continuing math teacher education in-service at elementary school. This study is justified by the importance of investigating a continuing education model to work with the guidance of training of school mathematics teachers taking for granted his performance in service and its upgrade needs, reframing and exchange experiences with their natural peers entered a same community.

The use of technology in Kindergarten to grade 12 classrooms provides opportunities for teachers to employ mathematical rigor, to integrate problem solving strategies and to extend mathematical ways of knowing (Drier, Dawson, & Garofalo, 1999). The presentation consists of two parts. One investigation maps secondary mathematics technology lessons and materials to the elementary school mathematics standards and converts the mathematics concepts to manageable elementary school lessons. The other investigation analyzes pre-service teacher lessons written using ASSURE instructional design format. The major aims of this paper are to present two teacher preparation practices, one for secondary mathematics pre-service teachers (converting secondary materials to elementary materials) and the other for elementary mathematics pre-service teachers (writing lessons using the ASSURE model).

The transition from school to tertiary study of mathematics is rightly coming under increasing scrutiny in research. This paper employs Tall’s model of the three worlds of mathematical thinking to examine key variables in teaching and learning as they relate to this transition. One key variable in the transition is clearly the teacher/lecturer and we consider the perspectives of both teachers and lecturers on teaching related matters relevant to upper secondary and first year tertiary calculus students. While this paper deals with a small part of the data from the project, which aims to model the transition, the results provide evidence of similarities and differences in the thinking of teachers and lecturers about the transition process. They also show that each group lacks a clear understanding of the issues involved in the transition from the other’s perspective, and there is a great need for improved communication between the two sectors.

Syftet med studien är att undersöka och följa matematiklärares resonemang kring ämnesplanens förmågor, genom problematisering av nationella provuppgifter.   Matematikundervisningen både på grundskolan och gymnasiet har visat sig vara begränsad när det gäller målstyrning av undervisningen som bygger på medvetenhet och kunskap om förmågorna. En förutsättning för att undervisningen ska kunna vara målstyrd med avseende på förmågorna ser vi är lärares kunskap och medvetenhet om desamma. Avsikten med studien är därför att ur ett utvecklingsperspektiv hitta sätt att för lärare ge ämnesplanens förmågor innebörd. De nationella proven konkretiserar flera av förmågorna, och skulle därför kunna fungera som vägledare i lärares kompetensutveckling kring förmågornas innebörd.  Undersökningen baseras på två filmade fokusgruppsdiskussioner i vilka gymnasielärare i matematik deltar. Diskussionerna utgår från nationella provuppgifter i matematik, med stegvis introducering av skolverkets definitioner av förmågorna och senare också av skolverkets bedömning av desamma.  Studiens teoretiska ramverk utgörs av ett kollegialt lärandeperspektiv och ett multimodalt och socialsemiotiskt perspektiv, som också används i den kvalitativa videoanalysen.   Studien visar att lärarnas resonemang förändras under diskussionen utan Skolverkets definitioner, så till vida att en slags överenskommelse görs, av på vilket sätt förmågorna kan tolkas. Skolverkets definitioner visade sig ha marginell inverkan på resonemangets utveckling i riktning mot Skolverkets intentioner. Skolverkets bedömning tillsammans med definitionerna fungerade däremot som utmanare till lärarnas egen tolkning och skapade genom det ett ökat resonemang. Resonemanget visade dock inte på ökad kunskap och medvetenhet kring förmågornas innebörd, som är förenligt med Skolverkets intentioner. Med stöd av forskning kring kollegialt lärande, skulle ledning av expertis på området kunnat möjliggöra ett resonemang i riktning mot intentionerna. / The aim of this study is to investigate and to monitor teachers of mathematics when they reason on the abilities as expressed in the curriculum, through problematisation of Swedish national test questions.   Teaching mathematics in Sweden has shown itself to be limited when it comes to setting objectives when based on awareness and knowledge of the abilities. One condition for the teaching to be manageable is that the teachers are aware of the abilities. The intention of this study is to find a way for the teachers through a perspective of development, where the abilities are given meaning. The national tests define many of the abilities and therefore the tests could be a guide in the teachers’ development of the reasoning of the abilities.   The investigation is based on two videotaped focus discussions by high school teachers of mathematics. These discussions are based on national test questions, where the teachers are gradually introduced to the national educational agency’s (henceforth Skolverket) definitions of the abilities and assessments that are given by Skolverket. The theoretical framework of the study is based on collegial teaching perspective and a multimodal- and social semiotic perspective, which is also being used in the qualitative video analysis.   The study shows that the teachers’ reasoning changes during the discussions without Skolverket’s definitions, and the teachers reach a consensus on how the abilities should be interpreted. Skolverket’s definitions had only marginal effects on the teachers’ reasoning regarding the intentions of the abilities. However, the teachers’ interpretations were challenged by the assessments which resulted in an increase in the teachers’ reasoning and interpretations. But the outcome of the study has not given any convincing evidence that an actual increase in knowledge nor awareness of the abilities has occurred. According to research into collegial learning, experts in this field would have been able to support more developed reasoning in line with the intentions.

In this paper the notion of “mathematics profiles” and “instructional behaviour profiles is introduced. A brief explanation of what these profiles are and how they were constructed and represented for preservice mathematics teachers is provided. An example of one of the participants’ profiles is included as an example. The influence of the pre-service teachers’ mathematics profiles on their instructional behaviour is then discussed. This is done with regard to using the mathematics profiles as a potential tool to optimise the development of pre-service mathematics teachers’ instructional behaviour towards a more reform-oriented approach.

The aim for this study is to describe what previous work-related experiences Special Education teachers in mathematics have about their professional role and how these experiences can be understood based on professional theories. The focus with these professional theories is to observe the status of the occupation and two different ideal-types of control of the profession. The aim for this study is also to contribute with knowledge about how the Special Education teachers express the expectations and challenges they encounter in mathematics education. Digital surveys and qualitative interviews were the methods used for collecting data of which 63 answers from the survey were collected and 12 interviews were conducted. The main results show that the experiences of the special education teachers in this study are scattered. It shows that their status and how the profession is controlled is affected by surrounding factors. It can show that the profession is under construction. Hopefully will the thesis contribute with new knowledge to newly educated Special Education teachers about the expectations and challenges in their new occupational role.