Browsing by Author "Ngirishi, Harrison."

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The application of Rasch measurement theory to improve the functioning of a mathematics assessment instrument.
(2021) Ngirishi, Harrison.; Bansilal, Sarah.
Assessment is an integral part of the teaching and learning process. Concerns about student performance in assessments often drive the teaching and learning. In South Africa there has been numerous concerns about poor learning outcomes in mathematics and this has led to calls for all stakeholders to work together to try and find solutions. This study focuses on the assessment of mathematics with particular interest in the KZN provincial Grade 12 mathematics trial examination paper 2. The study explored the use of Rasch analysis in improving the functioning of the mathematics assessment instrument. The aim of the study was to use the Rasch analysis to report on the functioning of the test instrument in measuring proficiency in mathematics, checking on the targeting and reliability of the test instrument, explain anomalies where data did not fit the Rasch model, investigate differential item functioning (DIF), response dependency and multidimensionality. The study also sought the teachers’ views about the findings of the Rasch analysis. A sequential explanatory design was used in this study, where the Rasch analysis provided the theoretical framework for the analysis of the quantitative data. The qualitative analysis of the teachers’ responses helped to get more understanding of the results of the quantitative analysis of the leaners’ responses. The study found that the assessment instrument was difficult for this particular cohort, some items displayed DIF for language and response dependency due to some teachers not applying continuous accuracy marking. The study revealed that some teachers were not applying the continuous accuracy marking process. Items which carried more than two accuracy marks, showed misfit to the Rasch model. Teachers cited not applying continuous accuracy marking due to time constraints and large number of learners in classes. Teachers blamed poor performance on learners’ lack of basic understanding, adequate preparation and motivation, societal influences, poor understanding of proof type questions, allocation of many accuracy marks on one item and the language barrier. The recommendations of this study if implemented may help teachers in the teaching process and examiners in producing fair assessment instruments. The recommendations may lead to improvement of mathematics results.
An exploration of FET mathematics learners' understanding of geometry.
(2015) Ngirishi, Harrison.; Bansilal, Sarah.
This research study explored the FET learners’ understanding of geometry. The aim of this research study was to explore how grade 10 and grade 11 learners perform on tasks based on basic geometric concepts. The research also aims to make deductions about the van Hieles’ levels of geometry thinking of the learners. The research study will also provide recommendations on how some of the arising issues could be addressed. The study is framed within the theoretical framework of social constructivism and is located within the qualitative research paradigm. This study was carried out in three high schools in rural KwaZulu-Natal, South Africa. The study used qualitative data analysis methods to analyse data generated through task based worksheets and semi-structured interviews for individuals. A total of 147 learners completed the task based worksheet, of which 74 learners were doing grade 10 and 73 were doing grade 11. Eighteen learners were invited to participate in the interviews after the analysis of the task based worksheets. The research revealed a lack of understanding of many geometric concepts by the learners. Learners had difficulties with problems involving definitions of geometry terms, interrelationships of properties and shapes, class inclusion and proof type questions. Learners also showed lack of procedural and conceptual understanding. The study also revealed that the majority of the learners involved in the study were operating at the visual level and analysis level of the van Hiele levels of geometry thinking with a few learners able to reason at the informal deduction level. The research recommends that educators should explain and use relevant geometry vocabulary in their everyday teaching of geometry to try and address the issue of the language barrier, allow learners to work with a diversity of registers of semiotic representations of geometric concepts instead of sticking to the traditional geometric figures only, expose learners to shapes involving common properties (class inclusion) and allow them to come up with their own conclusions, use manipulatives, real life objects and cite real life examples when teaching geometry to make it more relevant to everyday life, use teaching methods that encourage conceptual understanding instead of rote learning and provide learning experiences that improve learners’ proof skills.