The purpose of this narrative inquiry study was to investigate the influence of curricular mandates on the teaching practices of high school mathematics teachers. Narrative inquiry, philosophically based on John Dewey’s theory of experience (Dewey, 1938), provides the intimate study of an individual's experience over time and in context(s) (Clandinin & Connelly, 2000). This study focused on the experiences of three high school mathematics teachers’ stories of educational change with data collected through interviews and personal documents. Socio-cultural narrative analysis was used to interpret the participants’ stories of adaptation. The data, presented as an ethnodrama, is composed of scenes taken from the interviews and interweaves the participants’ stories of evolution as they tackled the struggles of change on multiple levels: curriculum, student assessment, and teacher evaluation. Results indicated teachers adopt both traditional and reform strategies when deciding on appropriate teaching practices. Collaboration and professional development were two important aspects used by the participants to enlarge their toolbox of teaching practices when forced to challenge their existing beliefs. This study contributes to the scarce research on the impact of curricular mandates on teaching practices. It also highlights the experiences of high school mathematics teachers as they embrace the paradigm shift associated with the mandates and implement changes to their practices to promote a more student-centered, collaborative environment.

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Syftet med denna studie är att undersöka lärarnas upplevelse av elevers missuppfattningar vid inlärning av bråk och sannolikhet samt om det är möjligt att minska missuppfattandet med hjälp av kategorisering av dessa. Genom att fråga matematiklärare om de upplever att eleverna de undervisar ofta har missuppfattningar och om samma missuppfattningar är återkommande, kan vi få en bild av vilka delar av de matematiska begreppen som kan uppfattas svåra av eleverna. De missuppfattningar som tenderar att återkomma kan komma att behöva mer fokus på förklaring. Studien genomfördes genom en surveyundersökning i enkätform som publicerades i grupper som samlar matematiklärare på sociala medier, samt skickades till matematiklärare via mail. Det resulterade i 41 enkätsvar som analyserades genom beskrivande statistik i kombination med en induktiv innehållsanalys. Studien visar att orsaken till att missuppfattningar kopplade till matematiska begrepp kan bero på ett för stort fokus på procedurinriktad undervisning i de tidigare skolåren. Detta upplever lärarna medför att eleverna inte har tillräcklig begreppsförståelse när de börjar på gymnasiet. Det vanligaste åtgärdsförslaget är kopplat till undervisningsstrategier med mer sociokulturella inslag i undervisningen. De allra flesta av studiens deltagare upplever att begreppsförståelse är viktigt och utgör en förutsättning för att klara av både problemlösning och mer avancerad matematik. För att skapa förståelse för matematiska begrepp är det nyttigt för lärare att känna till vanliga missuppfattningar. Kategorisering av missuppfattningar kan därför vara till nytta för lärarna i undervisningen, som ett stöd i lektionsplanering och som ett pedagogiskt verktyg för att utveckla elevernas matematiska kunskaper. / The purpose of this study is to investigate the teachers' experience of students' misconceptions when learning fractions and probability, and whether it is possible to reduce misconceptions by categorizing them. By asking mathematics teachers if they feel that the students they teach often have misconceptions and if the same misconceptions are repeated, we can get a picture of which parts of the mathematical concepts may be perceived as difficult by the students. The misconceptions that tend to recur may need more focus on explanation. The study was carried out through a survey in questionnaire form that was published in groups that bring together mathematics teachers on social media and was also sent to mathematics teachers via email. This resulted in 41 survey responses that were analysed through descriptive statistics in combination with an inductive content analysis. The study shows that the reason for misconceptions connected to mathematical concepts may be due to too much focus on procedure-oriented teaching in the earlier school years. The teachers feel that this means that the students do not have sufficient conceptual understanding when they start high school. The most common proposed measure is linked to teaching strategies with more socio-cultural elements in the teaching. The vast majority of the study's participants feel that conceptual understanding is important and constitutes an essentiality for being able to cope with both problem solving and mathematics at more advanced levels. In order to create an understanding of mathematical concepts, it is useful for teachers to know about common misconceptions. Categorization of misconceptions can therefore be useful for teachers in teaching, as a support in lesson planning and as a pedagogical tool to develop students' mathematical knowledge.

Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_eduardo_sad_costa.pdf: 3568903 bytes, checksum: 4e09f1b15f7714b64ad56708b0bd9974 (MD5) Previous issue date: 2007-05-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work involves a qualitative study about whether and how mathematics High-School teachers work with their students the trouble-situations regarding linear Diophantine equations. The study was performed by means of analyzing semi-structured interviews applied on six mathematics teachers from the states of São Paulo and Minas Gerais, teaching at high-school level. The Numbers Elementary Theory has been treated by several researchers on Mathematical Education, as Campbell e Zazkis (2002), Resende (2007), as an adequate subject for the introduction and development of fundamental Mathematical ideas in High- School. However, the results of such investigation show that, although the interviewed teachers affirmed that they did work with problems of discreet mathematics that can be modeled through linear Diophantine equations, none of them seemed to work with their students using the knowledge of these equations properties in order to decide whether they have solution, and what these solutions would be / Neste trabalho apresento um estudo qualitativo sobre se, e como, professores de Matemática do Ensino Médio trabalham com seus alunos situações-problema que recaem em equações diofantinas lineares. O estudo foi feito por meio da análise de entrevistas semi-estruturadas realizadas com seis professores de Matemática dos estados de São Paulo e Minas Gerais que lecionam no Ensino Médio. A Teoria Elementar dos Números vem sendo tratada por diversos pesquisadores de Educação Matemática, como Campbell & Zazkis (2002), Resende (2007), como assunto propício para a introdução e desenvolvimento de idéias Matemáticas fundamentais no Ensino Básico. No entanto os resultados desta investigação indicam que embora os professores entrevistados afirmassem trabalhar com problemas de matemática discreta modeláveis via equação diofantina linear, nenhum deles deu indícios de trabalhar com seus alunos utilizando conhecimentos das propriedades dessas equações para decidir se as mesmas tem solução e quais seriam essas soluções