M.Ed. (Educational Psychology) / Please refer to full text to view abstract.

M.Ed. (Mathematics Education) / This research aimed to explore errors associated with the concept of fractions displayed by Grade 5 learners. This aim specifically relates to the addition and subtraction of common fractions. In order to realize the purpose of the study, the following objective was set: To identify errors that learners display when adding and subtracting common fractions. The causes which led to the errors were also established. Possible ways which can alleviate learners' misconceptions and errors associated with them were also discussed. The study was conducted at Dyondzo (Fictitious name) Primary School, Vhembe District in Limpopo Province. The constructivist theory of learning was used to help understand how learners construct their meanings of newly acquired knowledge. It was a qualitative study where most of the data and findings were presented with think descriptions using descriptive analysis techniques. A group of forty nine learners was selected purposively within two classes of Grade 5 to write the class work, home work and test on addition and subtraction of fractions. Learners were interviewed and so were two teachers. The five teachers also completed a questionnaire of five questions to supplement the interviews. The study found that learners made a number of errors in the addition and subtraction of fractions, including conceptual errors, carelessness errors, procedural errors and application errors. This finding supports findings that primary school children experience difficulties when learning the concept of fractions.

The purpose of this study is to investigate various solution strategies employed by Grade 7 learners and their teachers when solving a given set of mathematical tasks. This study is oriented in an interpretive paradigm and is characterised by qualitative methods. The research, set in nine schools in the Eastern Cape, was carried out with nine learners and their mathematics teachers and was designed around two phases. The research tools consisted of a set of 12 tasks that were modelled after the Third International Mathematics and Science Study (TIMSS), and a process of clinical interviews that interrogated the solution strategies that were used in solving the 12 tasks. Aspects of grounded theory were used in the analysis of the data. The study reveals that in most tasks, learners relied heavily on procedural understanding at the expense of conceptual understanding. It also emphasises that the solution strategies adopted by learners, particularly whole number operations, were consistent with those strategies used by their teachers. Both learners and teachers favoured using the traditional, standard algorithm strategies and appeared to have learned these algorithms in isolation from concepts, failing to relate them to understanding. Another important finding was that there was evidence to suggest that some learners and teachers did employ their own constructed solution strategies. They were able to make sense of the problems and to 'mathematize' effectively and reason mathematically. An interesting outcome of the study shows that participants were more proficient in solving word problems than mathematical computations. This is in contrast to existing research on word problems, where it is shown that teachers find them difficult to teach and learners find them difficult to understand. The findings of this study also highlight issues for mathematics teachers to consider when dealing with computations and word problems involving number sense and other problem solving type problems.

The following study aims to investigate how pupils benefit from the work with problem solving in cooperative learning and what mathematical abilities the pupils develop in this type of work. The target of this study is elementary school. The result of this study is based on a selection of scientific articles. The problem statement has been a decisive factor in the choice of articles. The conclusion of this study is that the pupils benefit from problem solving within cooperative learning because it supports pupils' ability to solve mathematical problems. Also the students benefit from discussions with their peers when they are reasoning together and use mathematical terms. The abilities that develop using problem solving in mathematics education are abilities that are stated in Lgr11 (Skolverket, 2019) and creative abilities. Other abilities that develop using problemsolving within cooperative learning are logical thinking and reasonableness assessment.

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The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers' performance on line graphing. Predictors included Illinois teacher education basic skills sub-component scores in reading comprehension and mathematics, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. This study also determined the strength of the relationship between each prospective predictor variable and the line graphing performance variable, as well as the extent to which measures of attitude towards science, mathematics and graphing mediated relationships between scores on mathematics, reading, logical thinking and line graphing. Ninety-four pre-service elementary education teachers enrolled in two different elementary science methods courses during the spring 2009 semester at Southern Illinois University Carbondale participated in this study. Each subject completed five different instruments designed to assess science, mathematics and graphing attitudes as well as logical thinking and graphing ability. Sixty subjects provided copies of primary basic skills score reports that listed subset scores for both reading comprehension and mathematics. The remaining scores were supplied by a faculty member who had access to a database from which the scores were drawn. Seven subjects, whose scores could not be found, were eliminated from final data analysis. Confirmatory factor analysis (CFA) was conducted in order to establish validity and reliability of the Questionnaire of Attitude Toward Line Graphs in Science (QALGS) instrument. CFA tested the statistical hypothesis that the five main factor structures within the Questionnaire of Attitude Toward Statistical Graphs (QASG) would be maintained in the revised QALGS. Stepwise Regression Analysis with backward elimination was conducted in order to generate a parsimonious and precise predictive model. This procedure allowed the researcher to explore the relationships among the affective and cognitive variables that were included in the regression analysis. The results for CFA indicated that the revised QALGS measure was sound in its psychometric properties when tested against the QASG. Reliability statistics indicated that the overall reliability for the 32 items in the QALGS was .90. The learning preferences construct had the lowest reliability (.67), while enjoyment (.89), confidence (.86) and usefulness (.77) constructs had moderate to high reliabilities. The first four measurement models fit the data well as indicated by the appropriate descriptive and statistical indices. However, the fifth measurement model did not fit the data well statistically, and only fit well with two descriptive indices. The results addressing the research question indicated that mathematical and logical thinking ability were significant predictors of line graph performance among the remaining group of variables. These predictors accounted for 41% of the total variability on the line graph performance variable. Partial correlation coefficients indicated that mathematics ability accounted for 20.5% of the variance on the line graphing performance variable when removing the effect of logical thinking. The logical thinking variable accounted for 4.7% of the variance on the line graphing performance variable when removing the effect of mathematics ability.

Syftet med undersökningen är att ta reda på vilka matematiska förmågor enligt Krutetskiis teori som synliggörs hos elever i skolår 5 som arbetar gruppvis med problemlösning. Dessutom undersöktes vad läraren uppmärksammar som matematisk förmåga och hur läraren organiserar sin undervisning för att utveckla matematisk förmåga. Krutetskii (1976) har definierat de matematiska förmågorna genom en studie som gjordes 1955-1966. Dessa tolkades och analyserades från en översatt version av hans verk. Med inspelat material från två observationer synliggjordes flera matematiska förmågor hos eleverna. Det framkom av intervjun att läraren erbjuder berikning, flera gruppkonstellationer, olika undervisningsformer och metoder. Utifrån forskning och resultatbild från undersökningen finns det viktiga aspekter att ta hänsyn till för att elever ska utveckla matematiska förmågor. Det gäller att arbeta med problemlösning tillsammans med andra i praxisgemenskap. Problemet måste innehålla flera olika abstraktionsnivåer för att eleverna ska kunna arbeta från den individuella utvecklingszonen till den närmaste utvecklingszonen. Läraren måste ha stor ämneskunskap och använda rätt terminologi. De affektiva föreställningarna spelar en stor roll där en positiv och aktiv inställning gynnar progression av matematiska förmågor. Även intresset för matematik samt elevens flit och koncentration påverkar rätt riktning.

Thesis (M. Ed. (Mathematics)) -- University of Limpopo, 2022 / The purpose of this study was to document my enactment of the five key strategies of assessment for learning in my mathematics classroom to account for learners' mathematical understanding. I used a constructivism teaching experiment methodology to explore learners' mathematical activities as they interacted in the classroom. Twenty-five learners from my Grade 10 mathematics class took part in the study. Data were gathered through classroom observations, written work samples from learners, and the teacher's reflective journal. My enactment of the five key strategies enabled learners to participate in classroom discussions, collaborate with their peers, and use self-assessment tools while engaging in classroom interactions. The major findings revealed that, through my enactment of the five key strategies, learners developed conceptual understanding, procedural fluency and strategic competence of the concepts taught. In addition, practices such as the development of lesson plans detailing how the five key strategies will be enacted in the classroom, use of comment – only feedback for grading learners’ work, creating a conducive learning environment to allow the use of peer and self-assessment allowed for a meaningful enactment of assessment for learning in my classroom. Strategies four and five, whose primary goal is to encourage learners' participation in the lesson, were critical in promoting learners' mathematical understanding.

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