Syftet med denna studie var att undersöka skolår 4 elevers förståelse av likhetstecknet. Vi ville även studera hur symbolen presenteras i elevernas läroböcker och mot bakgrund av tidigare forskning diskutera hur detta kan påverka deras förståelse av begreppet. I studien använde vi oss av tre insamlingsmetoder: en kvantitativ undersökning, kvalitativa intervjuer och en textanalys av läroböcker för skolår 3 och 4. Vår undersökning visar att även om eleverna uppvisar bra förståelse av likhetstecknet när de löser uppgifter av strukturell typ, har de svårigheter med att muntligt beskriva likhetstecknets funktion. Textanalysen synliggör att andelen utsagor av operationell typ som framhävs i läroböckerna för åk 3 minskar betydligt i läroböckerna för åk 4. Från vår studie drar vi slutsatsen att matematikböckernas ensidiga presentation av likhetstecknet kan vara anledningen till elevers bristande förståelse av dess innebörd.

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)

In the school mathematics curriculum functions play a pivotal role in accessing and mastering algebra and the whole of mathematics. The study investigated the extent to which pupils with little experience in algebra would develop the function concept and was motivated by the need to bring the current Zimbabwean mathematics curriculum in line with reform ideas that introduce functions early in the secondary school curriculum. An instrument developed from literature review was used to assess the extent to which the Form1/Grade 8 pupils developed the concept. The teaching experiment covered a total of 26 lessons, a period of about eight weeks spread over two terms starting in the second term of the Zimbabwean school calendar. The problem-centred teaching approach based on the socio-constructivist view of learning formed the background to facilitate pupils' individual and social construction of knowledge. Data was collected from the pupils' written work, audio taped discussions and interviews with selected pupils. The extent to which each pupil of the seven pupils developed the aspects of function, change, relationship, rule, representation and strategies, was assessed. The stages of development and thinking levels of functional reasoning at the beginning of the experiment, then during the learning phase and finally at the end of the experiment, were compared. The results showed that functions can be introduced at Form 1 and pupils progressed in the understanding of most of the aspects of a function. / Educational Studies / M. Ed. (Mathematics Education)

I mitt arbete med elever i de tidiga skolåren upptäckte jag att många elever hamnade i svårigheter när de skulle lösa mönsteruppgifter i olika sammanhang. Jag funderade över vad orsakerna kunde vara. I massmedia diskuterades TIMMS 2003 som visade att svenska elever hade svårigheter med algebra i jämförelse med elever i andra länder. Kunde det finnas ett samband? Jag blev intresserad och ville skaffa mig kunskaper om vilka svårigheter elever hamnar i när de analyserar mönster och vilka generaliseringar de ser i ett växande mönster. Jag använde mig av enskilda kvalitativa intervjuer och jag hade två undersökningsuppgifter som vi arbetade med och samtalade om. Resultatet i undersökningen visade att det finns behov av att arbeta med analyser och generaliseringar av olika slags mönster. Intervjuerna visade okså vikten av att elever får träning i att kommunicera matematik. / In my work with children in the early years in school i noticed that they often had trouble when they were working with patterns in different ways. At the time TIMSS 2003 was discussed in media and the result showed that the swedish students had difficulties with algebra compared with students from other countries.Could there bee some connections? I got interested and wanted to learn about which difficulties students in the early years have when they analyze patterns and what generalizations they make in growing patterns.

Made available in DSpace on 2016-04-27T16:57:47Z (GMT). No. of bitstreams: 1 EDM - HUMBERTO MESTRADO PROFISSIONAL.pdf: 6034166 bytes, checksum: 3482e42fe5798307bbd8da4d3a402923 (MD5) Previous issue date: 2006-10-23 / Secretaria da Educação do Estado de São Paulo / The objective of this dissertation was to investigate the possible performance of introducing the entire negative number on the 3rd cycle of the fundamental school in a public organization on replication of part of the Passoni (2002) work so as to respond the following questions of the investigation: Starting from a sequence formed by a familiar and significant context, what is the comprehension that the 3rd cycle school children will have over negative numbers? To what extended level this sequence might aid on introducing this concept? At last, what s this improvement consisted of? On this approach, an interventionist investigation was developed with students of two groups of the 3rd cycle fundamental public school in the city of Sao Paulo; one of them named as the control group (CG) and the other one being the experimental group (EG). The field survey had two steps execution of diagnostic instruments (before and after tests) on the CG as well as the EG group and carrying out the teaching intervention with the usage of manipulative material only at the EG.The results obtained in each of these steps were evaluated considering the possible introduction of the negative numbers to the students of the 3rd fundamental cycle. In theory, we lay down on the ideas of Jean Piaget and Raymond Duval related to the kind of representations that can act upon the Mathematic conception. The target is to make students able to convert intentional treatments of semiotic representations in roughly instantaneous treatments. The results show a 50% increase on student s performance of EG group, at pos test. Taking into account these results, it can be concluded that the associative intervention on teaching with manipulative material has developed strategies for the solution of the activities. The activities were developed with 17 children of EG and 18 ones of the CG. The results are said to be satisfactory / O objetivo desta dissertação foi investigar a possibilidade e eficiência de se introduzir o número inteiro negativo na 3ª. série do Ensino Fundamental de uma escola pública, reaplicando parte do estudo desenvolvido por Passoni (2002), a fim de responder às seguintes questões de pesquisa: Partindo de uma seqüência elaborada que utilize um contexto familiar e significativo, qual a compreensão que as crianças de 3ª. série passam a ter sobre os números negativos? Até onde tal seqüência pode ajudar na introdução desse conceito? E, por último, em que consiste o avanço? Para tanto, foi desenvolvida uma pesquisa de caráter intervencionista com alunos de duas classes de 3ª. série do Ensino Fundamental de uma escola da rede pública municipal de São Paulo; uma delas constituiu-se em grupo controle (GC) e a outra em grupo experimental (GE). A pesquisa de campo complementou duas etapas aplicação dos instrumentos diagnósticos (pré e pós-testes), tanto no GE como no GC e aplicação da intervenção de ensino com uso de material manipulativo apenas no GE. Os resultados obtidos em cada uma dessas etapas foram analisados considerando a possibilidade da introdução dos números inteiros negativos na 3ª. série do Ensino Fundamental. Do ponto de vista teórico, apoiamos-nos nas idéias de Jean Piaget e Raymond Duval relacionados ao papel que as representações desempenham na compreensão da Matemática. A meta é de tornar os alunos capazes de transformar tratamentos intencionais de representações semióticas em tratamentos quase-instantâneos. Os resultados mostraram um crescimento de quase 50% no desempenho dos alunos do GE, no pós-teste. Tendo por base tais resultados pode-se concluir que a associação da intervenção de ensino com o material manipulativo possibilitou o desenvolvimento de estratégias para resoluções das atividades. As atividades foram desenvolvidas com 17 crianças do grupo GE e 18 crianças do grupo GC. Os resultados obtidos foram satisfatórios