Undersökningen beskriver den matematiska kommunikationen mellan speciallärare och matematiksvaga elever. Den empiriska datan består av två matematiklektioner från år 9 i grundskolan. Datan analyserades för att finna olika typer av kommunikation. Lärarna var i många delar medvetna i sitt sätt att kommunicera med eleverna och undervisningsmiljön kändes trygg. Under lektionerna observerades två parallella språk, ett vardagsanknutet och ett matematiskt språk. Det framkom att ett tydligt förhållningssätt beträffande matematiskt språk kan underlätta för elevens inlärning samt medvetandegöra läraren om den kommunikativa betydelsen i undervisningen med styrdokumentens mål i fokus. / The present investigation describes the mathematical communication between the special needs teacher and pupils with mathematical disabilities. The empirical data consists of two mathematics lessons from grade 9 in the compulsory school. The data was analyzed in order to find different kinds of communication. The teachers were in many ways aware of their way to communicate with pupils and the teaching environment felt confident. During the lessons two parallel languages were observed, one everyday related and one mathematical language. It was found that keeping a distinct approach to the mathematical language can facilitate student learning and make the teacher aware about teaching communicatively with steering documents goals in focus.

Esta pesquisa tem por base a observação da realidade da sala de aula de quatro professoras dos anos iniciais (duas brasileiras e duas portuguesas), sendo seu objetivo investigar possíveis influências no seu desenvolvimento profissional a partir de sua participação num programa de formação contínua em Matemática o Pró-Letramento Matemática, no Brasil; e o Programa de Formação Contínua em Matemática para Professores dos 1.º e 2.º ciclos, em Portugal. Considerando as concepções e dinâmicas de formação dos professores de matemática desses países, tem-se por hipótese que os trabalhos conjuntos criados nos ciclos de conhecimento e a troca de ideias interpretadas em contextos colaborativos podem ser geradores de práticas profissionais transformadoras. A análise tem como referencial teórico a formação contínua de professores e o desenvolvimento profissional docente, o conhecimento profissional do professor, e as práticas letivas dos professores em matemática. Em termos metodológicos o estudo realiza uma abordagem qualitativa de natureza interpretativa, incluindo quatro estudos de caso, cujos instrumentos se pautam em entrevistas, questionários, observação de aulas, notas de campo e a análise documental dos materiais e planos de aula produzidos pelas docentes durante e após o curso, além dos documentos legais relativos aos processos de formação nos dois países. Os resultados evidenciam que os programas em causa contribuíram de forma significativa e diferenciada para o desenvolvimento profissional de cada uma das professoras analisadas, destacando-se três mudanças importantes nas suas práticas letivas: (i) o modo como passaram a explorar a apresentação e a resolução das tarefas atentando para o respectivo grau de desafio, (ii) a valorização da comunicação matemática por meio do estabelecimento constante de questionamentos, e (iii) a organização dos alunos na sala de aula. Contudo, sugere-se que cursos dessa natureza devem valorizar a planificação das aulas e procurar modos práticos de auxiliar o professor nesse processo. / This research is based on observing the classroom reality of four teachers of early years (two Brazilian and two Portuguese). Its aim is to investigate possible influences on teachers professional development from their participation in an in-service teacher education program in mathematics Mathematical Pro-Literacy in Brazil; and In-service Teacher Education Programme for Mathematics Teachers of the First and Second Cycles, in Portugal. Considering the conceptions and teacher education dynamics for mathematics teachers in these countries, it is conjectured that the joint work created in the cycles of knowledge and the exchange of ideas interpreted in collaborative contexts can be generators of transformative professional practices. The analysis has as its theoretical frame in the in-service education of teachers and teacher professional development, teacher professional knowledge, and mathematics teachers teaching practice. In methodological terms, the study follows a qualitative and interpretative approach, including four case studies, whose data collection instruments are interviews, questionnaires, classroom observations, field notes, and document analysis of materials and lesson plans produced by teachers during and after the course, in addition to the legal documents related to teacher education processes in both countries. The results show that the programs contributed in a significant and differentiated way for the professional development of all teachers analyzed, highlighting three important changes in their teaching practice: (i) how they began to explore the explanation and solution of tasks paying attention to their degree of challenge, (ii) the appreciation of mathematical communication through the establishment of constant questioning, and (iii) the organization of the students in the classroom. However, it is suggested that such courses should enhance the attention to lesson planning and look for practical ways to help teachers in this process.

Syftet med denna studie är att undersöka hur lärare ser på förmågan att föra och följa matematiska resonemang och hur lärares matematikundervisning kan organiseras för att möjliggöra för elever att främja denna förmåga. Vi har använt oss av ett ramverk beskrivet av Herbert m.fl. (2015) om lågstatielärares uppfattning om matematiska resonemang. Vi har även utformat ett eget ramverk baserat på vad forskning visar främjar elevers matematiska resoenamngsförmåga och utifrån det genomfört en deduktiv innehållsanalys. Genom semisturkturerade intervjuer har 12 lärare i årskurs 2-3 gett sin syn på matematiska resonemang och hur de organiserar undervisningen för att främja elevers matematiska resonemangsförmåga. Resultatet visar att lärare ser resoneamng som svårdefinerat men att de ändå bedriver en undervisning som möjliggör för eleverna att främja denna förmåga. Vidare visade resultatet att undervisningen lärarna bedrev visade på djupare uppfattning av matematiska resonemang än vad de själva uttryckte. Däremot ser de flesta lärare att matematikboken inte ger eleverna möjlighter till matematiska resonemang. Några lärare lyfter materialet Sluta räkna-serien av Ulla Öberg som särskilt gynnsamt för att utveckla elevers matematiska resonemangsförmåga. Det som dominerar lärarnas undervisning i arbetet med matematiska resonemang är problemlösning, öppna uppgifter, arbete i par eller grupp samt arbete med konkret material. / The aim of this study is to examine how teachers view the ability to make and follow mathematical reasoning and how teachers' mathematical lessons can be organized to enable students to develop this ability. We have used the framework described by Herbert et al. (2015) for primary teachers' perceptions of mathematical reasoning. We have also created our own framework based on what research shows fosters students' matehematical reasoning ability and based on this made a deductive content analysis. Through semi-structured interviews 12 teachers in grades 2-3 gave their views on mathematical reasoning and how they organize their lessons to foster students' mathematical reasoning ability. The results show that teachers view reasoning as hard to define but that they still conduct lessons that make it possible for students to foster this ability. Furtthermore, the results show that the lessons the teachers conduct show a higher perception of mathematical reasoning than what they themselves express. Most of the teachers express that the mathematical textbook does not give students the possibility for mathematical reasoning. Some teachers mention the material Sluta räkna-serien by Ulla Öberg as especially effective to foster students' mathematical reasoning ability. What dominates the teachers' lessons when working with mathematical reasoning are problem solving, open tasks, working in pairs or groups and working with concrete material.

Matematik har ett unikt ämnesspråk som elever behöver behärska både skriftligt som muntligt. Brister i den muntliga matematiska kommunikationsförmågan bidrar till att elever med matematiksvårigheter inte får godkänt betyg i matematik för årskurs 9. Dessa elever behöver hjälp och stöd från sin omgivning för att inte riskera att bli underkända. Denna studie har genomförts med syftet att skildra och analysera matematiklärares syn på stödjande faktorer för elever med matematiksvårigheter med fokus på den muntliga matematiska kommunikationsförmågan. Som metod har en innehållsanalytisk forskningsansats med induktiv tematiseringsmetodik använts och studien baseras på fem semistrukturerade intervjuer. Matematiklärares synsätt har bedömts vara möjliga att skildras och analyseras genom följande sex teman: 1. Balansen mellan muntlig och skriftlig kommunikation 2. Den muntliga kommunikationsförmågans beståndsdelar 3. Aktiviteter baserade på elevernas behov 4. Stödjande lärandemiljö för eleven 5. Elevens deltagande i matematiska diskussioner 6. Samarbete med föräldrar De intervjuade lärarna är eniga om att elever med matematiksvårigheter behöver anpassningar av innehåll och kunskapsmål för den muntliga matematiska förmågan. Det råder dock ingen enighet i lärares syn på adekvata mål och innehåll, utan detta anses vara ett resultat av en mängd faktorer såsom elevernas förkunskaper, lärares tolkning av läroplanen, den skriftliga tyngdpunkten i matematik, få bedömningsmoment för den muntliga förmågan, stress och tidsbrist samt den mindre bra tillgången på specialpedagoger. Elever med matematik‐svårigheter behöver även få stöd i det sammanhang som de befinner sig i. Detta anser lärare kan hanteras genom att antingen blanda sammanhanget med olikheter i kunskap hos elever eller se till att elever med matematiksvårigheter får samarbeta med elever de känner sig trygga med. Lärare försöker även stödja eleverna med styrning, kontroll och ordning, vilket kan förklaras av att dessa elever upplevs gå igenom tonåren. Läraren gör en subjektiv bedömning av elevernas behov av styrning och detta slår då igenom på elevernas möjligheter att få vara med och påverka i olika grad. Lärare har vidare olika förväntningar på elevernas prestationer i ett deltagande, där vissa lärare anser att eleverna ska prestera varmed vissa nöjer sig med ett deltagande. Lärare har således olika fokus för dessa elever – antingen kunskapsmål eller värdemål. Det sista temat berör lärares syn på samarbetet med föräldrarna. Vissa lärare upplevs tro att denna kontakt bidrar positivt varmed andra inte har tolkats riktigt ha samma övertygelse. / Mathematics has a unique subject language that students need to master in writing as well as verbally. Shortcomings in the oral mathematical communication capacity contribute to the fact that students with mathematical difficulties do not receive an approved grade in mathematics for grade 9. These students need help and support from their environment in order not to risk being disapproved. This study has been conducted with the purpose of portraying and analyzing mathematics teachers' views on supportive factors for students with mathematical difficulties focusing on oral mathematical communication skills. As a method, a content analytical research approach with inductive thematic methodology has been used and the study is based on five semi structured interviews. Mathematics teachers' views have been judged to be possible to be depicted and analyzed by the following six themes: 1. The balance between oral and written communication 2. The oral mathematical communications skills components 3. Activities based on the students' needs 4. Supporting learning environment for the student 5. The student's participation in mathematical discussions 6. Cooperation with the parents Teachers agree that students with mathematical difficulties need adaptations of content and knowledge objectives for oral mathematical ability. However, there is no unanimity in the teacher's view of adequate goals and content, but this is considered being the result of a variety of factors such as the student's knowledge, teacher's interpretation of the curriculum, the written focus in mathematics, the lack of adequate situations to assess oral capacity, stress and time shortages and the less good availability of special educators. Students with mathematical difficulties also need support in the context they are in. This believes teachers can be managed by either blending the context of differences in student knowledge or ensuring that students with mathematical difficulties interact with friends who they feel safe interacting with. Teachers also try to support the students with control, control and order, which can be explained by the fact that these students experience through their teens. The teacher makes a subjective assessment of the students' need for governance, and this then paves the way for the students to participate and influence in different ways. Teachers also have different expectations of student performance in a participation, where some teachers believe that the students are performing, with which some people are content with a participation. Teachers thus have different focus on these students ‐ either knowledge or value goals. The last theme concerns teachers' views on cooperation with the parents. Some teachers are interpreted believing that this contact contributes positively whereas others have not been interpreted having the same beliefs.