Grade eleven learners participation in the functions discourse: the case of a hyperbola and exponential function.
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Date
2018
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Abstract
The purpose of the study was to investigate the mathematical discourses of grade eleven learners related to the worded, numerical, tabular, and graphic asymptotes of the The purpose of the study was to investigate the mathematical discourses of grade eleven learners related to the worded, numerical, tabular, and graphic asymptotes of the hyperbola and exponential functions. The theory of commognition was referred to, with particular emphasis on the characteristics of the mathematical discourse; that is, word use, visual mediators, endorsed narratives, and routines.
The study has fundamentally adopted an interview-based qualitative research design approach, with descriptive and interpretative elements complementing its data analysis processes. In addition, some quantitative aspects were administered by means of test-based activities. The study was conducted in four schools in the rural Mthatha district of the Eastern Cape Province of South Africa. Data was collected by means of a test administered to 112 respondents, and task-based interviews with 12 pairs of grade eleven students in those schools. In each school, about 30 learners participated in the test, and six from each school took part in the interviews. Data was analysed by means of the Discourse Profile of the Hyperbola and Exponential Function adapted from the Arithmetic Discourse Profile propounded by Ben-Yahuda and others.
The findings revealed that learners have learnt functions in class, and were all familiar with the asymptotes of the hyperbola and the exponential function. While learners could answer questions on functions, a rephrasing of the question changed their response. There were also challenges of linking different representations of a function to each other. Students would also work efficiently on procedure tasks, but struggled on action-oriented tasks.. The theory of commognition was referred to, with particular emphasis on the characteristics of the mathematical discourse; that is, word use, visual mediators, endorsed narratives, and routines.
The study has fundamentally adopted an interview-based qualitative research design approach, with descriptive and interpretative elements complementing its data analysis processes. In addition, some quantitative aspects were administered by means of test-based activities. The study was conducted in four schools in the rural Mthatha district of the Eastern Cape Province of South Africa. Data was collected by means of a test administered to 112 respondents, and task-based interviews with 12 pairs of grade eleven students in those schools. In each school, about 30 learners participated in the test, and six from each school took part in the interviews. Data was analysed by means of the Discourse Profile of the Hyperbola and Exponential Function adapted from the Arithmetic Discourse Profile propounded by Ben-Yahuda and others.
The findings revealed that learners have learnt functions in class, and were all familiar with the asymptotes of the hyperbola and the exponential function. While learners could answer questions on functions, a rephrasing of the question changed their response. There were also challenges of linking different representations of a function to each other. Students would also work efficiently on procedure tasks, but struggled on action-oriented tasks.
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Degree of Doctor of philosophy (mathematics education) university of KwaZulu- Natal Durban,2018.