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An exploration of folding back in improving grade 10 students’ reasoning in geometry

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dc.contributor.advisor Chuene, K. M.
dc.contributor.advisor Maoto, R. S.
dc.contributor.author Mabotja, Koena Samuel
dc.date.accessioned 2017-06-14T08:57:26Z
dc.date.available 2017-06-14T08:57:26Z
dc.date.issued 2017
dc.identifier.uri http://hdl.handle.net/10386/1805
dc.description Thesis (M. Ed. (Mathematics Education)) -- University of Limpopo, 2017 en_US
dc.description.abstract The purpose of this study was to explore the role of folding back in enriching grade 10 students’ reasoning in geometry. Although various attempts are made in teaching and learning geometry, evidence from several research studies shows that most learners struggle with geometric reasoning. Hence, this study came as a result of such learners’ struggles as shown in the literature as well as personal experiences. The study was a constructivist teaching experiment methodology that sought to answer the following research questions: How does folding back support learners’ interaction with geometric reasoning tasks during the lessons? How does a Grade 10 mathematics teacher use folding back to enrich student reasoning in geometry? The teaching experiment as a research design in this study was found useful in studying learners’ geometric reasoning as a result of mathematical interactions in their learning of geometry. Therefore, it should be noted that the teaching experiments were not conducted as an attempt to implement a particular way of teaching, but rather to understand the role of folding back in enriching learners’ reasoning in geometry. As a referent to the teaching experiment methodology, the participants in this study were 7 grade 10 mathematics learners’ sampled from a classroom of 54 learners. These seven learners did not necessarily represent the whole class in accordance with the purpose of the study. This requirement was not necessary in determining rigour in teaching experiments. Instead interest was on “organising and guiding [teacher-researchers] experience of learners doing mathematics” (Steffe & Thompson, 2000, p. 300). Furthermore, the participants were divided into two groups while working on the learning activities. Participants were further encouraged to share ideas with each other as they solved the learning activities. Data was collected through video recording while learners were working on mathematical learning activities. The focus was on the researcher-teacher – learners and learners-learners interactions while working on geometric reasoning learning activities. Learning activities and observations served as subsets of the video data. Learners were encouraged to share ideas with each other as they v solved the learning activities as recommended by Steffe and Thompson (2000). Likewise, in order to learn the learners’ mathematics, the researcher could teach and interact with learners in a way that encourage them to improve their current thinking (Steffe & Thompson, 2000). In analysing data, the study adopted narrative analysis. The researcher performed verbatim transcription of the video recordings. Subsequently, information-rich interaction for each mathematical learning activity, where folding back was observed was selected. The selections of such information-rich interactions were guided by Martin’s (2008) framework for describing folding back. The main findings of the study revealed that in a learning environment where folding back takes place, learners’ reasoning in geometry is enriched. The researcher-teacher’s instructional decisions such as discouraging, questioning, modelling and guiding were found to be effective sources through which learners fold back. The findings also revealed that learners operating at different layers of mathematical understanding are able to share their geometry knowledge with their peers. Moreover, the findings indicated that in a learning environment where folding back takes place, learners questioning ability is enriched. Based on the findings of the study, the recommendations were that Mathematics teachers should create a learning environment where learners are afforded the opportunity to interact with each other during geometry problem solving; such is a powerful quest for folding back to take place. en_US
dc.description.sponsorship Research Chair Developmental Grant at the University of Limpopo en_US
dc.format.extent x, 150 leaves en_US
dc.language.iso en en_US
dc.relation.requires Adobe Acrobat Reader en_US
dc.subject Folding back en_US
dc.subject Growth of mathematical understanding en_US
dc.subject Geometry en_US
dc.subject Geometric reasoning en_US
dc.subject.ddc 372.76044 en_US
dc.subject.lcsh Geometry -- Study and teaching(Secondary) en_US
dc.subject.lcsh Geometry -- Study and teaching en_US
dc.subject.lcsh Mathematics --Study and teaching(Secondary) en_US
dc.subject.lcsh Reasoning -- Study and teaching en_US
dc.title An exploration of folding back in improving grade 10 students’ reasoning in geometry en_US
dc.type Thesis en_US


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