Thesis (M.Sc. ( Physiology )) --University of Limpopo, 2011 / Refer to document / the National Research Foundation

This study is based on an interest in trying to understand what is needed to ensure that students actually learn in a learning object, in this study equations. Algebra is an area of mathematics in several studies proved to be a stumbling block for many students. Using letters in mathematis is difficult for most students according to research reports and it is also consistent with my own experince as a teacher. The purpose of this study was to seek answers to what in the lesson content and also during the interview that allowed the students to learn more about the learning object. Based on students' prior knowledge and the difficulties students might have with the learning object and the offer of learning, I try to get an answer to what might have contribut the students to developed knowledge of the learning object. This qualitative study is based on a variation theory perspective. The two students who participated in the study attended the same class in high school. By using the theory of variation patterns, it made it possible for me to describe how students learn new things about the learning object, equations. To gain insight into how the students solved the data and developed new knowledge, I had the lesson content and their statements in the interviews to help me understand the difficulties in solving the equtionatask and what in the lessons that have contributed to new knowledge. The results show that pupils' understanding and difficulties in learning objects are relevant to how they can perceive, discern and assimilate new knowledge. One student was able to experience learning from their prior knowledge and assimilate what he had to develop in the variety in the offer of learning. The offered learning did not give the second student the same opportunity. The results indicates that the knowledge of students' prior knowledge, the difficulties the learning object can create and students' own narrative, I argue on the basis of the study'sresults, it is important knowledge for every teacher to be aware of befor the presentation of the lesson if it will give every student opportunities to learn.

Undervisningsmodellen bianshi med ursprung i Shanghai anses vara en möjlig förklaring till kinesiska elevers goda matematikprestationer. Variationsteorin, en annan undervisningsmodell med ursprung i väst beskrivs ha flera likheter med bianshi. I forskning benämns bianshi och variationsteorin även som teoretiska ramverk. I Learning Study, en studie för undervisningsutveckling är det vanligt förekommande att variationsteorin används som teoretiskt ramverk. Antaganden om att bianshi är en framgångsrik undervisningsmodell skapade ett intresse att undersöka möjligheterna att använda bianshi som teoretiskt ramverk i en interventionsstudie som hämtat komponenter från Learning Study.Syftet med denna studie är att utforska bianshi som teoretiskt ramverk i en interventionsstudie. Det gjordes i jämförelse med variationsteorin. Tal som bråk var studiens undervisningsinnehåll. Studien grundar sig i två interventionsstudier. En med bianshi och en med variationsteorin som teoretiskt ramverk. Genomförandet av respektive modell hämtade delar av processen för en Learning Study. Urvalet bestod av två klasser i årskurs 4 som delades i fyra mindre grupper. Förtest, eftertest och lektionsobservationer stod för datainsamlingen.Studiens resultat visar en förbättring av elevgruppernas förståelse för tal som bråk, oberoende av vilken modell som var det teoretiska ramverket. Lektionsinnehållet relaterat till begreppsförståelse resulterade i större utveckling för de elever som undervisades med bianshi. Elevgrupperna med variationsteorin som undervisningsmodell visade en större förbättring kopplat till metoder. Därmed visade bianshi i jämförelse med variationsteorin både högre och lägre utveckling av bråk som tal. Resultatet i vår studie antyder att bianshi går att använda som teoretiskt ramverk i en interventionsstudie. Antagandet styrks av den positiva lärandeutvecklingen och möjligheten att implementera bianshi i samtliga steg av processen. / The teaching model bianshi, originating from Shanghai, is considered as a possible explanation for the exceptional mathematical performances by Chinese students. Variation theory of learning, another teaching model originating from the Western tradition is assumed to share several similarities with bianshi. In research, bianshi and the variation theory of learning are also referred as theoretical frameworks. In a Learning Study, an intervention study focused on educational development, variation theory of learning is common to be used as a theoretical framework. The assumption that bianshi is a successful teaching model created an interest in exploring the possibilities of using bianshi as a theoretical framework in an intervention study that incorporates components from Learning Study.The aim of the study is to explore bianshi as a theoretical framework in an intervention study. This was done in comparison with the variation theory of learning. The teaching content of the study was numbers as fractions. The study is based on two intervention studies. One using bianshi and the other using the variation theory of learning as a theoretical framework. The implementation of each model incorporated elements from the Learning Study process. The sample consisted of two fourth-grade classes, which were divided into four smaller groups. Data collection included pre-tests, post-tests and lesson observations.The results of the study present an improvement of the students’ understanding of numbers as fractions, regardless of which model was used as a theoretical framework. The lesson content related to conceptual understanding resulted in greater development for the students taught by bianshi. Student groups taught with the variation theory of learning as the teaching model showed greater improvement related to methods. Thus, compared to the variation theory of learning, bianshi showed both higher and lower development of fractions as numbers. Our study suggests that bianshi can be used as a theoretical framework in an intervention study. This is supported by the positive learning development and the opportunity of implementing bianshi in all steps of the process.