Developing Namibian Grade 8 Learners’ Conceptions of Fractions Using Visual Models
- Albin, Simon, Brown, Bruce J L
- Authors: Albin, Simon , Brown, Bruce J L
- Date: 2019
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/483706 , vital:78788 , https://doi.org/10.1080/18117295.2019.1658443
- Description: Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to deepen learners’ understanding of fractions as a means to represent rational quantities. The initial benchmark test indicated a number of ways of working with fraction representations, many of which were inappropriate to the rational quantity presented. Although most learners were able to use a fraction to appropriately describe a part–whole area diagram with a single whole, few were able to appropriately label a similar diagram with multiple wholes, or a quantity greater than 1 on the number line. In the learning programme learners worked with visual models that incorporated multiple reference wholes, to explicitly identify the reference whole, to quantify the size of appropriately subdivided units using unit fraction names and to use these units in a measurement process to quantify the quantities these models indicated. A final test showed a sound conceptualisation of the use of fractions to represent rational quantities less than and greater than 1, in such models.
- Full Text:
- Date Issued: 2019
- Authors: Albin, Simon , Brown, Bruce J L
- Date: 2019
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/483706 , vital:78788 , https://doi.org/10.1080/18117295.2019.1658443
- Description: Learning rational number concepts is acknowledged as an important task but many learners find it difficult to make sense of them. This paper reports on a case study of the learning in a short (nine-lesson) learning programme for Grade 8 learners in a Namibian school, which sought to use visual models (circle area, bar area and number line) to deepen learners’ understanding of fractions as a means to represent rational quantities. The initial benchmark test indicated a number of ways of working with fraction representations, many of which were inappropriate to the rational quantity presented. Although most learners were able to use a fraction to appropriately describe a part–whole area diagram with a single whole, few were able to appropriately label a similar diagram with multiple wholes, or a quantity greater than 1 on the number line. In the learning programme learners worked with visual models that incorporated multiple reference wholes, to explicitly identify the reference whole, to quantify the size of appropriately subdivided units using unit fraction names and to use these units in a measurement process to quantify the quantities these models indicated. A final test showed a sound conceptualisation of the use of fractions to represent rational quantities less than and greater than 1, in such models.
- Full Text:
- Date Issued: 2019
Identifying Systems of Interaction in Mathematical Engagement
- Authors: Brown, Bruce J L
- Date: 2014
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/483717 , vital:78789 , https://doi.org/10.1080/10288457.2014.953293
- Description: Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed analysis of the process of mathematical engagement by two postgraduate education students working together to solve a number of mathematical puzzles. A process model of mathematical engagement was developed, identifying coherent systems of ‘thinking in action’. Both mathematical and everyday systems were identified, as well as systems that mediated the interaction between the two. Four fundamental subsystems relate to the mathematical system: subsystems oriented to mathematical objects; mathematical actions; mathematical representations; and mathematical patterns and relationships. A further four functional subsystems relate to the interaction between the mathematical and everyday: subsystems relating to linking; orientation; evaluation; and strategic control. These subsystems are detailed through the analysis of a particular episode in the engagement data.
- Full Text:
- Date Issued: 2014
- Authors: Brown, Bruce J L
- Date: 2014
- Subjects: To be catalogued
- Language: English
- Type: text , article
- Identifier: http://hdl.handle.net/10962/483717 , vital:78789 , https://doi.org/10.1080/10288457.2014.953293
- Description: Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed analysis of the process of mathematical engagement by two postgraduate education students working together to solve a number of mathematical puzzles. A process model of mathematical engagement was developed, identifying coherent systems of ‘thinking in action’. Both mathematical and everyday systems were identified, as well as systems that mediated the interaction between the two. Four fundamental subsystems relate to the mathematical system: subsystems oriented to mathematical objects; mathematical actions; mathematical representations; and mathematical patterns and relationships. A further four functional subsystems relate to the interaction between the mathematical and everyday: subsystems relating to linking; orientation; evaluation; and strategic control. These subsystems are detailed through the analysis of a particular episode in the engagement data.
- Full Text:
- Date Issued: 2014
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
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