The nature and quality of the mathematical connections teachers make:
- Mhlolo, Michael K, Schäfer, Marc, Venkat, Hamsa
- Authors: Mhlolo, Michael K , Schäfer, Marc , Venkat, Hamsa
- Date: 2012
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140893 , vital:37927 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC120887
- Description: Current reforms in mathematics education emphasise the need for pedagogy because it offers learners opportunities to develop their proficiency with complex high-level cognitive processes. One has always associated the ability to make mathematical connections, together with the teacher's role in teaching them, with deep mathematical understanding. This article examines the nature and quality of the mathematical connections that the teachers' representations of those connections enabled or constrained. The researchers made video recordings of four Grade 11 teachers as they taught a series of five lessons on algebra-related topics. The results showed that the teachers' representations of mathematical connections were either faulty or superficial in most cases. It compromised the learners' opportunities for making meaningful mathematical connections. The researchers concluded by suggesting that helping teachers to build their representation repertoires could increase the effectiveness of their instructional practices.
- Full Text:
- Date Issued: 2012
- Authors: Mhlolo, Michael K , Schäfer, Marc , Venkat, Hamsa
- Date: 2012
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140893 , vital:37927 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC120887
- Description: Current reforms in mathematics education emphasise the need for pedagogy because it offers learners opportunities to develop their proficiency with complex high-level cognitive processes. One has always associated the ability to make mathematical connections, together with the teacher's role in teaching them, with deep mathematical understanding. This article examines the nature and quality of the mathematical connections that the teachers' representations of those connections enabled or constrained. The researchers made video recordings of four Grade 11 teachers as they taught a series of five lessons on algebra-related topics. The results showed that the teachers' representations of mathematical connections were either faulty or superficial in most cases. It compromised the learners' opportunities for making meaningful mathematical connections. The researchers concluded by suggesting that helping teachers to build their representation repertoires could increase the effectiveness of their instructional practices.
- Full Text:
- Date Issued: 2012
Towards empowering learners in a democratic mathematics classroom: to what extent are teachers' listening orientations conducive to and respectful of learners' thinking?
- Mhlolo, Michael K, Schäfer, Marc
- Authors: Mhlolo, Michael K , Schäfer, Marc
- Date: 2012
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140882 , vital:37926 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC129235
- Description: In an effort to make education accessible, to 'heal the divisions of the past and establish a society based on democratic values', the South African Department of Education claims that a series of mathematics reforms that has so far been introduced is underpinned by the principles of 'social justice, fundamental human rights and inclusivity'. Critics however argue that the system has remained 'undemocratic' in that those groups of learners who were supposed to be 'healed' continue to underperform and hence be disempowered. In this study, we conceptualised a democratic and mathematically empowering classroom as one that is consistent with the principle of inclusivity and in which a hermeneutic listening orientation towards teaching promotes such a democratic and mathematically empowering learning environment. We then worked with three different orientations teachers might have towards listening in the mathematics classroom: evaluative, interpretive and hermeneutic. We then used these orientations to analyse 20 video-recorded lessons with a specific focus on learners' unexpected contributions and how teachers listened and responded to such contributions. The results were consistent with the literature, which shows that teachers tend to dismiss learners' ways of thinking by imposing their own formalised constructions.
- Full Text:
- Date Issued: 2012
- Authors: Mhlolo, Michael K , Schäfer, Marc
- Date: 2012
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140882 , vital:37926 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC129235
- Description: In an effort to make education accessible, to 'heal the divisions of the past and establish a society based on democratic values', the South African Department of Education claims that a series of mathematics reforms that has so far been introduced is underpinned by the principles of 'social justice, fundamental human rights and inclusivity'. Critics however argue that the system has remained 'undemocratic' in that those groups of learners who were supposed to be 'healed' continue to underperform and hence be disempowered. In this study, we conceptualised a democratic and mathematically empowering classroom as one that is consistent with the principle of inclusivity and in which a hermeneutic listening orientation towards teaching promotes such a democratic and mathematically empowering learning environment. We then worked with three different orientations teachers might have towards listening in the mathematics classroom: evaluative, interpretive and hermeneutic. We then used these orientations to analyse 20 video-recorded lessons with a specific focus on learners' unexpected contributions and how teachers listened and responded to such contributions. The results were consistent with the literature, which shows that teachers tend to dismiss learners' ways of thinking by imposing their own formalised constructions.
- Full Text:
- Date Issued: 2012
Visual technology for the autonomous learning of mathematics:
- Linneweber-Lammerskitten, Helmut, Schäfer, Marc, Samson, Duncan
- Authors: Linneweber-Lammerskitten, Helmut , Schäfer, Marc , Samson, Duncan
- Date: 2010
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140949 , vital:37931 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20930
- Description: This paper describes a collaborative research and development project between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa. The project seeks to establish, disseminate and research the efficacy and use of short video clips designed specifically for the autonomous learning of mathematics. Specific to the South African context is our interest in capitalising on the ubiquity of cellphone technology and the autonomous affordances offered by mobile learning. This paper engages with a number of theoretical and pedagogical issues relating to the design, production and use of these video clips. Although the focus is specific to the contexts of South Africa and Switzerland, the discussion is of broad applicability.
- Full Text:
- Date Issued: 2010
- Authors: Linneweber-Lammerskitten, Helmut , Schäfer, Marc , Samson, Duncan
- Date: 2010
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/140949 , vital:37931 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20930
- Description: This paper describes a collaborative research and development project between the University of Applied Sciences Northwestern Switzerland and Rhodes University in South Africa. The project seeks to establish, disseminate and research the efficacy and use of short video clips designed specifically for the autonomous learning of mathematics. Specific to the South African context is our interest in capitalising on the ubiquity of cellphone technology and the autonomous affordances offered by mobile learning. This paper engages with a number of theoretical and pedagogical issues relating to the design, production and use of these video clips. Although the focus is specific to the contexts of South Africa and Switzerland, the discussion is of broad applicability.
- Full Text:
- Date Issued: 2010
An analysis of the influence of question design on learners' approaches to number pattern generalisation tasks:
- Samson, Duncan, Schäfer, Marc
- Authors: Samson, Duncan , Schäfer, Marc
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141026 , vital:37938 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20890
- 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: 2007
- Authors: Samson, Duncan , Schäfer, Marc
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141026 , vital:37938 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20890
- 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: 2007
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