A Case Study of Two Selected Teachers as they Integrated Dynamic Geometry Software as a Visualisation Tool in Teaching Geometry:
- Mavani, Deepak, Mavani, Beena, Schäfer, Marc
- Authors: Mavani, Deepak , Mavani, Beena , Schäfer, Marc
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141076 , vital:37942 , https://doi.org/10.1080/18117295.2018.1522716
- Description: This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick’s framework of teaching proficiency.
- Full Text:
- Date Issued: 2018
- Authors: Mavani, Deepak , Mavani, Beena , Schäfer, Marc
- Date: 2018
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141076 , vital:37942 , https://doi.org/10.1080/18117295.2018.1522716
- Description: This paper reports on an aspect of a larger research study conceptualised within a teacher development project in Mthatha, Eastern Cape Province. The project was initiated with the objective to develop appropriate skills to use dynamic geometry software (DGS) effectively and strategically as a teaching and learning tool for mathematics. The study reported in this paper aims specifically to ascertain how selected mathematics teachers integrated co-developed technologically aided visualisation tools in the observed lessons. The case study involved two teachers from different schools. The data sources were the classroom observations followed by stimulated reflective interviews with the teachers. The data were analysed to study the use of DGS visualisation tools in relation to Kilpatrick’s framework of teaching proficiency.
- Full Text:
- Date Issued: 2018
Enactivism as a powerful theoretical framework for research and tool to reflect on my own role as a supervisor:
- Authors: Schäfer, Marc
- Date: 2016
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141102 , vital:37944 , DOI: 10.1080/18117295.2016.1243938
- Description: Enactivism, as an interesting and useful theoretical underpinning is gaining traction in Mathematics Education research. It forms the central theme of this paper whose aim is two-fold: first to describe and engage with how elements of enactivism informed a PhD study, both on a theoretical and analytical level, and second to reflect on the enacted role of the supervisor of this study. Despite the inevitable embodied relationship between the supervisor and the supervised PhD project, it is not often written about. This paper thus attempts to address this. The PhD study in question used constructs of enactivism such as autonomy, sense-making, emergence, embodiment and experience to design a pre-service mathematics education programme and then explored the growth of student teachers’ mathematical identity and disposition in their development of becoming mathematics teachers. The PhD supervision process was framed by the enactivist notion that learning and the construction of meaning and knowledge is co-created by the lecturer, the student and the particular context.
- Full Text:
- Date Issued: 2016
- Authors: Schäfer, Marc
- Date: 2016
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141102 , vital:37944 , DOI: 10.1080/18117295.2016.1243938
- Description: Enactivism, as an interesting and useful theoretical underpinning is gaining traction in Mathematics Education research. It forms the central theme of this paper whose aim is two-fold: first to describe and engage with how elements of enactivism informed a PhD study, both on a theoretical and analytical level, and second to reflect on the enacted role of the supervisor of this study. Despite the inevitable embodied relationship between the supervisor and the supervised PhD project, it is not often written about. This paper thus attempts to address this. The PhD study in question used constructs of enactivism such as autonomy, sense-making, emergence, embodiment and experience to design a pre-service mathematics education programme and then explored the growth of student teachers’ mathematical identity and disposition in their development of becoming mathematics teachers. The PhD supervision process was framed by the enactivist notion that learning and the construction of meaning and knowledge is co-created by the lecturer, the student and the particular context.
- Full Text:
- Date Issued: 2016
Teacher code switching consistency and precision in a multilingual mathematics classroom:
- Chikiwa, Clemence, Schäfer, Marc
- Authors: Chikiwa, Clemence , Schäfer, Marc
- Date: 2016
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141087 , vital:37943 , https://doi.org/10.1080/18117295.2016.1228823
- Description: This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape Province. Elements of Gumperz and Mercer’s work on lesson categories and Dowling’s Domains of Mathematical Practice were used to analyse data. Results showed that code switching frequency in general was inconsistent across different lessons for the same teacher.
- Full Text:
- Date Issued: 2016
- Authors: Chikiwa, Clemence , Schäfer, Marc
- Date: 2016
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141087 , vital:37943 , https://doi.org/10.1080/18117295.2016.1228823
- Description: This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape Province. Elements of Gumperz and Mercer’s work on lesson categories and Dowling’s Domains of Mathematical Practice were used to analyse data. Results showed that code switching frequency in general was inconsistent across different lessons for the same teacher.
- Full Text:
- Date Issued: 2016
'The Area of a Triangle is 1800C’: an analysis of Learners' Idiosyncratic Geometry Responses through the Lenses of Vygotsky's Theory of Concept Formation
- Mhlolo, Michael K, Schäfer, Marc
- Authors: Mhlolo, Michael K , Schäfer, Marc
- Date: 2013
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141127 , vital:37946 , DOI: 10.1080/10288457.2013.826973
- Description: In this paper, we focus specifically on Vygotsky's theory of concept formation to gain initial insights into seemingly garbled and incoherent connections we observed in learners' responses to a geometry task. While acknowledging research that is supportive of the van Hiele model as being useful when analysing concept formation in geometry, in this paper we use empirical evidence to argue that today's geometry requires learners to reason with many tools which the van Hiele model does not seem to accommodate. Working with 470 written responses of 12–14-year-old learners to a geometry task, we then explored the potential of Vygotsky's theory of concept formation as an alternative framework. We conclude by discussing the paper's contribution both to theory and to classroom practice.
- Full Text:
- Date Issued: 2013
- Authors: Mhlolo, Michael K , Schäfer, Marc
- Date: 2013
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141127 , vital:37946 , DOI: 10.1080/10288457.2013.826973
- Description: In this paper, we focus specifically on Vygotsky's theory of concept formation to gain initial insights into seemingly garbled and incoherent connections we observed in learners' responses to a geometry task. While acknowledging research that is supportive of the van Hiele model as being useful when analysing concept formation in geometry, in this paper we use empirical evidence to argue that today's geometry requires learners to reason with many tools which the van Hiele model does not seem to accommodate. Working with 470 written responses of 12–14-year-old learners to a geometry task, we then explored the potential of Vygotsky's theory of concept formation as an alternative framework. We conclude by discussing the paper's contribution both to theory and to classroom practice.
- Full Text:
- Date Issued: 2013
Teacher education for Mathematical Literacy: a modelling approach
- Brown, Bruce J L, Schäfer, Marc
- Authors: Brown, Bruce J L , Schäfer, Marc
- Date: 2006
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141040 , vital:37939 , DOI: 10.4102/pythagoras.v0i64.98
- Description: This paper reports on a study of the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil-and-paper exercises based on linear generalisation tasks set in both numeric and two-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was analysed and classified into one of seven categories. In addition, a meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The results of this study strongly support the notion that question design can play a critical role in influencing learners' choice of strategy and level of attainment when solving pattern generalisation tasks. An understanding of the importance of appropriate question design has direct pedagogical application within the context of the mathematics classroom.
- Full Text:
- Date Issued: 2006
- Authors: Brown, Bruce J L , Schäfer, Marc
- Date: 2006
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141040 , vital:37939 , DOI: 10.4102/pythagoras.v0i64.98
- Description: This paper reports on a study of the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil-and-paper exercises based on linear generalisation tasks set in both numeric and two-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was analysed and classified into one of seven categories. In addition, a meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The results of this study strongly support the notion that question design can play a critical role in influencing learners' choice of strategy and level of attainment when solving pattern generalisation tasks. An understanding of the importance of appropriate question design has direct pedagogical application within the context of the mathematics classroom.
- Full Text:
- Date Issued: 2006
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