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
Does 'African mathematics' facilitate access to mathematics?: towards an ongoing critical analysis of ethnomathematics in a South African context
- Horsthemke, Kai, Schäfer, Marc
- Authors: Horsthemke, Kai , Schäfer, Marc
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141004 , vital:37936 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20885
- Description: Mosibudi Mangena, the Minister of Science and Technology, said in an address to the Annual Congress of the South African Mathematical Society at the University of the Potchefstroom, November 2, 2004: "There is one thing we need to address before anything else. We need to increase the number of young people, particularly blacks and women, who are able to successfully complete the first course in Mathematics at our universities." How is this to be achieved? A popular trend involves a call for the introduction and incorporation of so-called ethnomathematics, and more particularly 'African mathematics', into secondary and tertiary curricula. Although acknowledging the obvious benefits of so-called ethnomathematics, this paper critically analyses three aspects of ethnomathematics that have been neglected in past critiques. Our focus is not on the relationship as such between ethnomathematics and mathematics education. Our critique involves (1) epistemological and logical misgivings, (2) a new look at practices and skills, (3) concerns about embracing 'African mathematics' as valid and valuable - just because it is African.
- Full Text:
- Date Issued: 2007
- Authors: Horsthemke, Kai , Schäfer, Marc
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/141004 , vital:37936 , https://0-hdl.handle.net.wam.seals.ac.za/10520/EJC20885
- Description: Mosibudi Mangena, the Minister of Science and Technology, said in an address to the Annual Congress of the South African Mathematical Society at the University of the Potchefstroom, November 2, 2004: "There is one thing we need to address before anything else. We need to increase the number of young people, particularly blacks and women, who are able to successfully complete the first course in Mathematics at our universities." How is this to be achieved? A popular trend involves a call for the introduction and incorporation of so-called ethnomathematics, and more particularly 'African mathematics', into secondary and tertiary curricula. Although acknowledging the obvious benefits of so-called ethnomathematics, this paper critically analyses three aspects of ethnomathematics that have been neglected in past critiques. Our focus is not on the relationship as such between ethnomathematics and mathematics education. Our critique involves (1) epistemological and logical misgivings, (2) a new look at practices and skills, (3) concerns about embracing 'African mathematics' as valid and valuable - just because it is African.
- Full Text:
- Date Issued: 2007
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