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The purpose of this research was to explore South African Grade 11 learners' conceptual understanding of 'image formation by lenses'. The participants for this study were 70 Grade 11 learners from a selected senior secondary school in Mthatha, Eastern Cape Province, South Africa. The qualitative approach employed in the study made use of a two-tier open-ended questionnaire as the data collection instrument. The study explored several alternative conceptions the learners had held in terms of the roles that the lens and the screen play in the image formation and the characteristics of the image formed when a lens with a larger diameter is used and when a portion of the lens is covered. Most of the participants could not respond correctly in the situations presented in the questionnaire. However, almost all of them were found to have adequate conceptual understanding about the role of a lens in the image formation.

The study explored learners' experiences with the mobile learning technology-based instruction module (MLTBIM) in learning Functions and related concepts. A sample of thirty-nine participants was purposefully drawn from the Grade 10 Mathematics classes in a selected historically disadvantaged rural senior secondary school. Adopting a case study research design, an attitude test was used in the collection of data. Microsoft Excel was used in presenting and analysing the data. The first finding of the study was that most respondents viewed the Mobile Learning Technology-Based application as very useful in the teaching and learning of Functions and related concepts. Secondly, most respondents upheld the view that Mobile Learning Technology-Based Instruction (MLTBI) was an effective method to learn Mathematics. Lastly, most of the respondents advocated that the application used in MLTBI enhanced their conceptual understanding of linear, quadratic and exponential functions. To conclude, the participants were convinced that cell phone devices and the Math4Mobile software were very useful and effective in the teaching and learning of Functions and related concepts regardless of the fact that there were some shortcomings involved.

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