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
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