Det här är en läromedelsgranskning som har syftet att granska hur tre olika matematikläromedel i årskurs 1 behandlar likhetstecknets innebörd och dess koppling till pre-algebra. Tidigare forskning visar att många elever har svårigheter inom just detta område. En djup och relationell förståelse för likhetstecknet är av stor vikt för att kunna utveckla ett algebraiskt tänkande och för att klara av högre studier inom matematik. För att nå denna typ av förståelse lyfter forskning flera olika undervisningsstrategier.  För att besvara studiens frågeställningar kring hur läromedel behandlar dessa undervisningsstrategier och pre-algebraiska uppgifter används ett analysverktyg, framtaget av oss studenter, vid granskningen. Varje läromedel undersöktes i relation till utvalda frågor som byggde på studiens teoretiska ramverk kring hur förståelsen för likhetstecknet påverkas av undervisning. Resultatet visade att alla tre läromedel innehöll uppgifter som stödjer en djup och relationell förståelse för likhetstecknet, men i olika utsträckningar och på olika sätt. Samtliga läromedel visade både likheter och skillnader till tidigare forsknings rekommenderade undervisningstrategier. Med denna insikt kan studien vara en hjälpande hand för lärare vid val av läromedel och vid undervisning av likhetstecknet.

Syftet med vår undersökning var att utvärdera om utomhusmatematik påverkade elevers förståelse för algebra samt hur denna inlärningsmiljö kunde påverka gruppdynamiken. Vi genomförde två undervisningsförsök, ett utomhus och ett inomhus, med elever i skolår 4 och observationer av dessa. Dessutom använde vi oss av gruppsamtal före och kvalitativa intervjuer efter undervisningsförsöken. Resultatet visade att eleverna fick en ökad förståelse för algebraiska likheter vid undervisning utomhus. Resultatet visade även att samarbetet ökade mellan eleverna, det blev ett lugnare klimat i gruppen och eleverna blev mer engagerade under utomhusundervisningsförsöket.

The purpose of this study was to improve the mean scores on the COMPASS college placement test after guiding students through a PowerPoint presentation referred to as COMPASS orientation. Scores obtained from college placement tests indicated a large number of entering college students were not prepared for college-level classes. During the 2006–2007 academic year, 1,427 COMPASS placement tests were administered to students enrolling in the Big Sandy Community and Technical College (BSCTC). Of that number, over 70% produced scores at or below the level requiring developmental education. Data showed that only 28% of the students taking the COMPASS placement tests required no developmental course work and could enter college-level general education classes and receive college credit. This study proposed that a short orientation immediately preceding the COMPASS placement test would increase COMPASS placement test scores. Findings from the study showed that a 5-minute pre-test orientation did not significantly improve the mean test scores in reading, writing, or pre-algebra on the COMPASS placement tests. The study showed that algebra scores had a significantly improved mean score on the exam after intervention with the COMPASS orientation tutorial PowerPoint presentation. Recommendations from this study suggest that orientations and workshops should be mandatory for all college applicants. Online web sources should contain materials and web links for COMPASS study questions, COMPASS Web site addresses, and college pre-test workshops and orientation dates. Stakeholders such as local advisory committees, community businesses, and high schools should be involved with college application requirements. How underprepared college students impact the available workforce pool and the local economy should be discussed, and these businesses should be enlisted to suggest avenues for improving testing outcomes and college success.

The teaching and learning of algebraic linear graphs in the school have experience problems with regards to understanding this topic. The learner's inability to understand algebraic linear graphs as a result of scaling was evidence in this study. Learners experience difficulties in interpreting, constructing and predicting from linear graphs without the knowledge of scaling. Four tasks were considered necessary for constructing linear graphs. This research focused on scaling task. The objective of the research is to establish the fact that scaling has influence on the understanding of algebraic linear graphs. An empirical method of research was employed to carry out this research. The results proved that scaling has influence on the understanding of algebraic linear graphs at grade 9 (Form B). Learners will find it easy to construct, interpret and make prediction from a graph drawn by scaling. / Mathematical Sciences / M.A. (Mathematics Education)

Made available in DSpace on 2016-04-27T16:58:19Z (GMT). No. of bitstreams: 1 joao.pdf: 7791795 bytes, checksum: 6083730ab3e399494c03a8cffdf14609 (MD5) Previous issue date: 2002-05-22 / This research is mainly concerned with the convenience and viability of introducing nine-year-old students to the study of the integers and of (pre-)Algebra. We begin with the integers and use their additive structure to model and solve additive problems, with special attention to the problems proposed by Vergnaud in 1976. The point here is to show that students can more easily solve problems, if we use the additive structure of the integers and some (very little) amount of algebraic manipulation, than by considering the addition and subtraction of natural numbers. The theoretical background is provided by some ideas of Raymond Duval related to the role that representations play in the understanding of mathematics. The aim is to enable the students to transform intentional treatments upon semiotic representations into quasiinstantaneous treatments. A consistent and sistematic effort is made to achieve this goal. The main emphasis is placed in the sum of integers. We performed a series of activities with thirty-eight students (average age 9) of a private elementary school in the city of São Paulo. We arrived at satisfactory results / O tema central deste trabalho é o estudo da possibilidade e da conveniência de ensinar estudantes de nove anos a trabalhar com números inteiros e com noções de (pré-)Álgebra. Começamos com o estudo dos inteiros e usamos sua estrutura aditiva para modelar e resolver problemas aditivos, dando especial atenção aos que foram propostos por Vergnaud em 1976. Aqui, a principal preocupação é mostrar que os estudantes podem resolver problemas de maneira mais fácil se usarmos os inteiros e uma pequena dose de manipulação algébrica em vez de utilizar a adição e a subtração dos naturais. Do ponto de vista teórico, apoiamo-nos em algumas idéias de Raymond Duval relacionadas ao papel que as representações desempenham na compreensão da Matemática. A meta é tornar os estudantes capazes de transformar tratamentos intencionais de representações semióticas em tratamentos quase-instantâneos. Um esforço sistemático e consistente foi feito nessa direção. A principal ênfase foi posta na adição de inteiros. As atividades foram desenvolvidas com 38 crianças de nove anos de uma escola particular da cidade de São Paulo. Os resultados obtidos foram satisfatórios

The teaching and learning of algebraic linear graphs in the school have experience problems with regards to understanding this topic. The learner's inability to understand algebraic linear graphs as a result of scaling was evidence in this study. Learners experience difficulties in interpreting, constructing and predicting from linear graphs without the knowledge of scaling. Four tasks were considered necessary for constructing linear graphs. This research focused on scaling task. The objective of the research is to establish the fact that scaling has influence on the understanding of algebraic linear graphs. An empirical method of research was employed to carry out this research. The results proved that scaling has influence on the understanding of algebraic linear graphs at grade 9 (Form B). Learners will find it easy to construct, interpret and make prediction from a graph drawn by scaling. / Mathematical Sciences / M.A. (Mathematics Education)

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.