ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


Please note: Digitised content is made available at the best possible quality range, taking into consideration file size and the condition of the original item. These restrictions may sometimes affect the quality of the final published item. For queries regarding content of ETD collection please contact IR specialists by email : IR specialists or Tel : 011 717 4652 / 1954

Follow the link below for important information about Electronic Theses and Dissertations (ETD)

Library Guide about ETD

Browse

Subject: search.filters.subject.Problem solving

Search Results

Now showing 1 - 3 of 3
  • No Thumbnail Available
    Item
    Exploring multiplicative reasoning with grade four learners through structured problem solving
    (2017) Hansa, Sameera
    South Africa’s performance in mathematics education is ranked amongst the world’s worst. This performance is not only alarming at an international level, but also nationally. Annual National Assessments (ANA) conducted by the Department of Education have showed that the level of mathematics across the foundation and intermediate phase is poor with a pronounced dip in performance at a Grade 4 level (Department of Basic Education, 2014). Multiplication and division are common challenging areas that contribute to this poor performance. This is concerning as mathematics is globally recognised as a key competence for providing access to higher education and developing a country’s society and economy. My study, aimed at exploring multiplicative reasoning with Grade 4 learners through structured problem solving, is focused on the learning of multiplication and division within the context of an intervention concentrated on developing learners’ ability to model multiplicative situations. Shifts in the use of models were investigated following a smallscale intervention in which different modelling approaches (particularly ratio modelling) were introduced and developed. A control group was used to determine the usefulness of the intervention. Questions which I sought to answer were: (a) what kinds of multiplicative reasoning (models) are Grade 4 learners using prior to intervention, (b) what changes, if any, are seen in overall performance, across the intervention and control group, in the post-test, and, (c) what kinds of differences in model use were associated with the shifts in performance? The main dataset comprised of 61 pre- and post-test scripts across three Grade 4 classes in a former Model C school in a Johannesburg district. A sample of 15 interviews were also conducted across the classes. Document analysis and transcription notes were used to analyse data with a Realistic Mathematics Education (RME) framework informing my analysis. Findings from my study reveal that prior to intervention, Grade 4 learners presented limited multiplicative models which were predominantly confined to traditional algorithms. After the small-scale intervention, learners used a broader range of models with an emerging take up of ratio models. The success rate associated with the models presented by learners also improved. Limited and/or no changes in model use and their respective success rates were seen in the control group suggesting that the intervention program was useful. These findings suggest that, as a future recommendation, it would be worthwhile to investigate the outcomes of running a similar intervention in less privileged settings.
  • No Thumbnail Available
    Item
    Creating opportunities to learn through resourcing learner errors on simplifying algebraic expressions in Grade 8
    (2017) Matuku, Olinah
    This research problematised the teaching and learning of the grade 8 topic of simplifying algebraic expressions via the errors and misconceptions learners’ show on that topic. The study conducted at a secondary school in Johannesburg identified the nature of grade 8 learners’ errors and misconceptions on simplifying algebraic expressions. A teaching intervention through using those errors as resource to help learners reduce them was undertaken. There was an implementation of discovery learning as an intervention strategy to help learners to explore algebraic concepts with the minimum involvement of the researcher. The researcher used constructivism, sociocultural learning and variation theories since these theories affect the learners learning of algebra. The researcher used an interpretive paradigm which is concerned about the individuals’ interpretation of the world around them. Purposive and convenience sampling were used in the study. Data was collected using a sample of thirty grade 8 learners. The learners wrote a pre-test as one of the assessment task in the study. The purpose of the pretest was to identify learners’ errors on simplifying algebraic expressions. After the learners’ errors were identified and analysed, the researcher conducted a semi-structured, focus group interview with six learners in the study. The selection of the interviewees depended on the type and frequency of errors they have displayed in their pre-test scripts. The purpose of the interview was to investigate the reasons behind the learners’ errors as identified in the pre-test. An intervention strategy which implemented guided discovery learning was employed to learners with the use of the identified errors as a resource to help learners reduce them. After the intervention, the learners wrote a post-test to check if there was an improvement in learners’ performance after the intervention. Pre- and post-tests results were analysed for errors revealed by learners. The teaching intervention periods were introduced to create learning opportunities for learners. The findings of the study revealed that before intervention learners encountered a lot of difficulties when simplifying algebraic expressions but the learners’ performance improved after the intervention. The recommendations of the study are, teachers should welcome learners’ errors in teaching and learning of mathematics and use them as a resource to help learners reduce them in solving mathematical problems Key words: Learners’ errors, misconceptions, simplification of algebraic expressions.
  • No Thumbnail Available
    Item
    Problem solving in mathematical and everyday contexts : teachers' practices and knowledge.
    (2012-02-29) Fonseca, Kathleen
    The Revised National Curriculum requires that mathematics teachers make shifts in their pedagogical content knowledge about teaching non-routine problems. One of the shifts is to move from a traditional approach of teaching routine tasks to an approach which includes problem solving. Teaching non-routine problems develops flexible forms of knowledge, which allow learners to construct their own strategies and not merely follow steps shown to them by the teacher. In this study I explore what pedagogical content knowledge grade 6 teachers have about problem solving in everyday and mathematical contexts. A qualitative study was used to explore Grade 6 teachers’ pedagogical content knowledge about problem solving in these contexts. Data was collected by means of interviews and lesson observations. The study found variations in the teachers’ content knowledge but very similar pedagogical content knowledge among the teachers. Teachers have different understandings of teaching non-routine problems and they are faced with the challenge of how much to make knowledge accessible to their learners in order to lay a conceptual foundation to solve non-routine problems while not lowering the demands of the task. Teachers taught everyday context tasks differently to mathematical context tasks by focusing on the linguistic aspects of the tasks.