Pre-service education students’ application of visualisation strategies to solve mathematical word-problems
- Authors: Shaw , Peter
- Date: 2018
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: http://hdl.handle.net/10353/12941 , vital:39406
- Description: This classroom-based action research dissertation examined visualisation strategies used by pre-service Intermediate Phase PGCE education students to solve mathematical word-problems. The setting was an Eastern Cape university. Previous literature indicated a positive correlation between the use of visual scaffolds and success in solving word problems. However, a gap was found insofar as little research had been published on the application of visualisation to word-problems by student teachers in South Africa. This thesis advances our understanding of the role visualisation may play in assisting student teachers to solve word-problems. The theoretic framework was informed by Bruner’s theory of learning. The research was grounded in the hermeneutic tradition. An interpretivist research paradigm was expedited by using an inductive, naturalistic perspective and relativist ontology. Thirtyeight student-teachers participated in the study. Parallel and convergent qualitative and quantitative data gathering instruments were used, thereby facilitating triangulation and examination for microgenesis. It was found that vestiges of past teaching practices initially limited the participants’ knowledge to a deeply-flawed, banking model of routines and an instrumental perception of mathematics. Disruptive calls for social justice impeded progress. Albeit visualisation strategies liberated understanding, many foundational concepts and skills had to be reconstructed. The confluence of time and rehearsal culminated in some measure of expertise. Sustained effort enabled new knowledge to be compressed and consigned to long-term memory. Salient visual representations assisted participants to conceptualise relational mathematical metaconcepts and reduced the cognitive demands imposed by word-problems but that achievement was a hard-won prize.
- Full Text:
- Date Issued: 2018
- Authors: Shaw , Peter
- Date: 2018
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Doctoral , PhD (Education)
- Identifier: http://hdl.handle.net/10353/12941 , vital:39406
- Description: This classroom-based action research dissertation examined visualisation strategies used by pre-service Intermediate Phase PGCE education students to solve mathematical word-problems. The setting was an Eastern Cape university. Previous literature indicated a positive correlation between the use of visual scaffolds and success in solving word problems. However, a gap was found insofar as little research had been published on the application of visualisation to word-problems by student teachers in South Africa. This thesis advances our understanding of the role visualisation may play in assisting student teachers to solve word-problems. The theoretic framework was informed by Bruner’s theory of learning. The research was grounded in the hermeneutic tradition. An interpretivist research paradigm was expedited by using an inductive, naturalistic perspective and relativist ontology. Thirtyeight student-teachers participated in the study. Parallel and convergent qualitative and quantitative data gathering instruments were used, thereby facilitating triangulation and examination for microgenesis. It was found that vestiges of past teaching practices initially limited the participants’ knowledge to a deeply-flawed, banking model of routines and an instrumental perception of mathematics. Disruptive calls for social justice impeded progress. Albeit visualisation strategies liberated understanding, many foundational concepts and skills had to be reconstructed. The confluence of time and rehearsal culminated in some measure of expertise. Sustained effort enabled new knowledge to be compressed and consigned to long-term memory. Salient visual representations assisted participants to conceptualise relational mathematical metaconcepts and reduced the cognitive demands imposed by word-problems but that achievement was a hard-won prize.
- Full Text:
- Date Issued: 2018
Cointegration in equity markets: a comparison between South African and major developed and emerging markets
- Authors: Petrov, Pavel
- Date: 2011
- Subjects: Cointegration Stock exchanges -- South Africa Stock exchanges -- Developing countries Stock exchanges -- Developed countries South Africa -- Economic conditions Portfolio management -- South Africa Econometrics Autoregression (Statistics)
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: vital:5575 , http://hdl.handle.net/10962/d1005539
- Description: Cointegration has important implications for portfolio diversification. One of these is that in order to spread risk it is advisable to invest in markets that are not cointegrated. Over the last several decades communication technology has made the world a smaller place and hence cointegration in equity markets has become more prevalent. The bulk of research into cointegration focuses on developed and Asian markets, with little research been done on African markets. This study compares the Engle-Granger and Johansen tests for cointegration and uses them to calculate the level of cointegration between South African and other global equity markets. Each market is compared pair-wise with South Africa and the results have been that in general South Africa is cointegrated with other emerging markets but not really with African nor developed markets. Short-run analysis with the error correction was carried out and showed that in general markets respond slowly to any disequilibrium. Innovation accounting methods showed that the country placed first in Cholesky ordering dominates the other one. Multivariate cointegration was carried out using three selections of 4, 6 and 8 market portfolios. One of the markets was SA and the others were all chosen based on the criteria that they are not pair-wise cointegrated with SA. The level of cointegration varied depending on the portfolios, as did the error correction rates, impulse responses and variance decomposition. The one constant was that the USA dominated any portfolio where it was introduced. Recommendations were finally made about which market portfolio an investor should consider as most favourable.
- Full Text:
- Date Issued: 2011
- Authors: Petrov, Pavel
- Date: 2011
- Subjects: Cointegration Stock exchanges -- South Africa Stock exchanges -- Developing countries Stock exchanges -- Developed countries South Africa -- Economic conditions Portfolio management -- South Africa Econometrics Autoregression (Statistics)
- Language: English
- Type: Thesis , Masters , MCom
- Identifier: vital:5575 , http://hdl.handle.net/10962/d1005539
- Description: Cointegration has important implications for portfolio diversification. One of these is that in order to spread risk it is advisable to invest in markets that are not cointegrated. Over the last several decades communication technology has made the world a smaller place and hence cointegration in equity markets has become more prevalent. The bulk of research into cointegration focuses on developed and Asian markets, with little research been done on African markets. This study compares the Engle-Granger and Johansen tests for cointegration and uses them to calculate the level of cointegration between South African and other global equity markets. Each market is compared pair-wise with South Africa and the results have been that in general South Africa is cointegrated with other emerging markets but not really with African nor developed markets. Short-run analysis with the error correction was carried out and showed that in general markets respond slowly to any disequilibrium. Innovation accounting methods showed that the country placed first in Cholesky ordering dominates the other one. Multivariate cointegration was carried out using three selections of 4, 6 and 8 market portfolios. One of the markets was SA and the others were all chosen based on the criteria that they are not pair-wise cointegrated with SA. The level of cointegration varied depending on the portfolios, as did the error correction rates, impulse responses and variance decomposition. The one constant was that the USA dominated any portfolio where it was introduced. Recommendations were finally made about which market portfolio an investor should consider as most favourable.
- Full Text:
- Date Issued: 2011
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