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
The inducement of a contract by duress of goods - a reappraisal
- Authors: Glover, Graham B
- Date: 2006
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/70734 , vital:29722 , https://hdl.handle.net/10520/EJC54192
- Full Text: false
- Date Issued: 2006
- Authors: Glover, Graham B
- Date: 2006
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/70734 , vital:29722 , https://hdl.handle.net/10520/EJC54192
- Full Text: false
- Date Issued: 2006
Biogeographic and nearshore–offshore trends in isotope ratios of intertidal mussels and their food sources around the coast of southern Africa
- Hill, Jaclyn M, McQuaid, Christopher D, Kaehler, Sven
- Authors: Hill, Jaclyn M , McQuaid, Christopher D , Kaehler, Sven
- Date: 2006
- Language: English
- Type: text , Article
- Identifier: vital:6878 , http://hdl.handle.net/10962/d1011633
- Description: There are broad differences in oceanography and primary production around the southern African coast that are likely to give rise to major differences in trophic pathways. Stable isotope ratios provide integrated information on trophic relationships, yet there has been limited research on geographic variation in isotopic composition of marine consumers and their food. In this study, δ13C and δ15N of suspended particulate matter (SPM), intertidal mussels and common macroalgae along the southern African coastline were explored. Nearshore–offshore isotope trends as well as biogeographic and temporal patterns in isotopic ratios of mussel tissue, macroalgae and SPM were investigated at 12 sites along the coast from Namibia to the Mozambique border. SPM exhibited overall trends of nearshore 13C depletion from south-west to north-east along the coastline and from nearshore (0 km) to offshore (10 km) waters, in both cases suggesting a shift from a nearshore signature strongly influenced by macroalgal detritus to one more representative of oceanic phytoplankton. With one exception it was possible, using discriminant analysis, to categorize mussel populations into 4 geographic groups, on the basis of both carbon and nitrogen signatures: the east coast, the south-east coast, the south-west coast and the west coast. Macroalgae showed no consistent biogeographic trends and need to be examined in greater detail to relate nearshore SPM values to living macroalgal signatures. A linear mixing model indicated that mussels along the entire coastline generally demonstrated more than 50% dependence on nearshore carbon and nitrogen, emphasizing the importance of nearshore primary production to intertidal consumers.
- Full Text:
- Date Issued: 2006
- Authors: Hill, Jaclyn M , McQuaid, Christopher D , Kaehler, Sven
- Date: 2006
- Language: English
- Type: text , Article
- Identifier: vital:6878 , http://hdl.handle.net/10962/d1011633
- Description: There are broad differences in oceanography and primary production around the southern African coast that are likely to give rise to major differences in trophic pathways. Stable isotope ratios provide integrated information on trophic relationships, yet there has been limited research on geographic variation in isotopic composition of marine consumers and their food. In this study, δ13C and δ15N of suspended particulate matter (SPM), intertidal mussels and common macroalgae along the southern African coastline were explored. Nearshore–offshore isotope trends as well as biogeographic and temporal patterns in isotopic ratios of mussel tissue, macroalgae and SPM were investigated at 12 sites along the coast from Namibia to the Mozambique border. SPM exhibited overall trends of nearshore 13C depletion from south-west to north-east along the coastline and from nearshore (0 km) to offshore (10 km) waters, in both cases suggesting a shift from a nearshore signature strongly influenced by macroalgal detritus to one more representative of oceanic phytoplankton. With one exception it was possible, using discriminant analysis, to categorize mussel populations into 4 geographic groups, on the basis of both carbon and nitrogen signatures: the east coast, the south-east coast, the south-west coast and the west coast. Macroalgae showed no consistent biogeographic trends and need to be examined in greater detail to relate nearshore SPM values to living macroalgal signatures. A linear mixing model indicated that mussels along the entire coastline generally demonstrated more than 50% dependence on nearshore carbon and nitrogen, emphasizing the importance of nearshore primary production to intertidal consumers.
- Full Text:
- Date Issued: 2006
Determining the daily spawning cycle of the chokka squid, Loligo reynaudii off the South African Coast
- Authors: Melo, Y , Sauer, Warwick H H
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/124275 , vital:35588 , https://doi.10.1007/s11160-006-9034-6
- Description: The study investigated the duration and peak of the daily spawning cycle of the chokka squid Loligo reynaudii, and the possibility of estimating the spawning frequency by means of classification and grouping (by age) of postovulatory follicles. Post-ovulatory follicles were classified into three types: new, intermediate or old, based in part on the degree of resorption of the follicles determined from histological sections. Ovulation in this species appears to be a rapid process, seen by the occurrence of both mature oocytes and post-ovulatory follicles in partially spent ovaries. Results suggest that chokka squid present a diel timing of spawning, with successive periods of egg accumulation at night, interrupted by periods of active spawning during the day. The ovarian cycle for this species appears typical of serial spawners. During the spawning phase ovaries go through ripe, partially spent and recovering stages by undergoing a process of maturation, ovulation and redeveloping, where a new batch of advanced oocytes is recruited. The cycle typically appears to last between 24 and 36 h, and may depend on a number of factors such as environmental conditions and the presence of predators. The short-lived (about 14 h) nature of the post-ovulatory follicles precludes the calculation of the exact spawning interval and does not allow us to accurately predict the spawning frequency. Together with the degree of oviduct fullness they do however give a good indication of imminent or recent spawning.
- Full Text:
- Date Issued: 2007
- Authors: Melo, Y , Sauer, Warwick H H
- Date: 2007
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/124275 , vital:35588 , https://doi.10.1007/s11160-006-9034-6
- Description: The study investigated the duration and peak of the daily spawning cycle of the chokka squid Loligo reynaudii, and the possibility of estimating the spawning frequency by means of classification and grouping (by age) of postovulatory follicles. Post-ovulatory follicles were classified into three types: new, intermediate or old, based in part on the degree of resorption of the follicles determined from histological sections. Ovulation in this species appears to be a rapid process, seen by the occurrence of both mature oocytes and post-ovulatory follicles in partially spent ovaries. Results suggest that chokka squid present a diel timing of spawning, with successive periods of egg accumulation at night, interrupted by periods of active spawning during the day. The ovarian cycle for this species appears typical of serial spawners. During the spawning phase ovaries go through ripe, partially spent and recovering stages by undergoing a process of maturation, ovulation and redeveloping, where a new batch of advanced oocytes is recruited. The cycle typically appears to last between 24 and 36 h, and may depend on a number of factors such as environmental conditions and the presence of predators. The short-lived (about 14 h) nature of the post-ovulatory follicles precludes the calculation of the exact spawning interval and does not allow us to accurately predict the spawning frequency. Together with the degree of oviduct fullness they do however give a good indication of imminent or recent spawning.
- Full Text:
- Date Issued: 2007
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