Examining mathematical reasoning through enacted visualisation
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
- Authors: Dongwi, Beata Lididimikeni
- Date: 2019
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia , Mathematics -- Study and teaching -- Audio-visual aids , Geometry -- Study and teaching , Reasoning , Mathematical ability
- Language: English
- Type: text , Thesis , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/68192 , vital:29217
- Description: This study sets out to analyse the co-emergence of visualisation and reasoning processes when selected learners engaged in solving word problems. The study argues that visualisation processes and mathematical reasoning processes are closely interlinked in the process of engaging in any mathematical activity. This qualitative research project adopted a case study methodology embedded within a broader interpretative orientation. The research participants were a cohort of 17 mixedgender and mixed-ability Grade 11 learners from a private school in southern Namibia. Data was collected in three phases and comprised of one-on-one task-based interviews in the first phase, focus group task-based interviews in the second, and semi-structured reflective interviews in the third. The analytical framework was informed by elements of enactivism and consisted of a hybrid of observable visualisation and mathematical reasoning indicators. The study was framed by an enactivist perspective that served as a linking mediator to bring visualisation and reasoning processes together, and as a lens through which the coemergence of these processes was observed and analysed. The key enactivist concepts of structural coupling and co-emergence were the two mediating ideas that enabled me to discuss the links between visualisation and reasoning that emerged whilst my participants solved the set word problems. The study argues that the visualisation processes enacted by the participants when solving these problems are inseparable from the reasoning processes that the participants brought to bear; that is, they co-emerged.
- Full Text:
- Date Issued: 2019
Observing and evaluating creative mathematical reasoning through selected VITALmaths video clips and collaborative argumentation
- Authors: Kellen, Matthew Earl
- Date: 2017
- Subjects: Mathematics Study and teaching (Secondary) South Africa Grahamstown , Mathematics Study and teaching (Secondary) Audio-visual aids , Reasoning , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6107 , vital:21032
- Description: Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.
- Full Text:
- Date Issued: 2017
- Authors: Kellen, Matthew Earl
- Date: 2017
- Subjects: Mathematics Study and teaching (Secondary) South Africa Grahamstown , Mathematics Study and teaching (Secondary) Audio-visual aids , Reasoning , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6107 , vital:21032
- Description: Creative mathematical reasoning is a definition that the NCS policies allude to when they indicate the necessity for students to, “identify and solve problems and make decisions using critical and creative thinking.”(NCS, 2011: 9). Silver (1997) and Lithner (2008) focus on creativity of reasoning in terms of the flexibility, fluency and novelty in which one approaches a mathematical problem. Learners who can creatively select appropriate strategies that are mathematically founded, and justify their answers use creative mathematical reasoning. This research uses Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips that pose mathematics problems to stimulate articulated reasoning among small multi-age, multi-ability Grade 9 peer groups. Using VITALmaths clips that pose visual and open-ended task, set the stage for collaborative argumentation between peers. This study observes creative mathematical reasoning in two ways: Firstly by observing the interaction between peers in the process of arriving at an answer, and secondly by examining the end product of the peer group’s justification of their solution. (Ball & Bass, 2003) Six grade 8 and 9 learners from no-fee public schools in the township of Grahamstown, South Africa were selected for this case study. Participants were a mixed ability, mixed gendered, sample group from an after-school programme which focused on creating a space for autonomous learning. The six participants were split into two groups and audio and video recorded as they solved selected VITALmaths tasks and presented their evidence and solutions to the tasks. Audio and video recordings and written work were used to translate, transcribe, and code participant interactions according to a framework adapted from Krummheuer (2007) and Lithner (2008) and Silver (1997) and Toulmin (1954). This constituted the analysis of the process of creative mathematical reasoning. Group presentations of evidence and solutions to the VITALmaths tasks, were used in conjunction with an evaluation framework adapted from Lithner (2008) and Campos (2010). This was the product analysis of creative mathematical reasoning. This research found that there was significant evidence of creative mathematical reasoning in the process and product evaluation of group interactions and solutions. Process analysis showed that participants were very active, engaged, and creative in their participation, but struggled to integrate and implement ideas cohesively. Product analysis similarly showed that depth and concentration of strategies implemented are key to correct and exhaustive mathematically grounded solutions.
- Full Text:
- Date Issued: 2017
An investigation into an afterschool intervention programme aimed at improving learners' mental computation skills
- Authors: Moyo, Kwethemba Michael
- Date: 2015
- Subjects: After-school programs -- Namibia , Mental arithmetic , Mental arithmetic -- Study and teaching (Secondary) , Mental arithmetic -- Study and teaching (Secondary) -- Activity programs , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2041 , http://hdl.handle.net/10962/d1017352
- Description: This case study centres round an afterschool intervention programme aimed at enhancing mental computation skills of Grade 8 learners at a secondary school in the Erongo educational region of Namibia. Nine research participants took part in the study, and the mental computational strategies exhibited by these participants constitutes the unit of analysis. The study is anchored within an interpretive paradigm and is theoretically underpinned by constructivist epistemology. Kilpatrick, Swafford and Findell’s (2001) model of mathematical proficiency provides the conceptual framework supporting the study. The research was carried out in four sequential phases – an initial pre-test, the intervention itself, a follow-up post-test, and a focus group discussion. The study highlights the underdevelopment of mental computation skills and the associated lack of appropriate mental computational strategies in secondary school learners. It is recommended that appropriate time within the school curriculum be allocated for the development of learners’ mental computation skills.
- Full Text:
- Date Issued: 2015
- Authors: Moyo, Kwethemba Michael
- Date: 2015
- Subjects: After-school programs -- Namibia , Mental arithmetic , Mental arithmetic -- Study and teaching (Secondary) , Mental arithmetic -- Study and teaching (Secondary) -- Activity programs , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2041 , http://hdl.handle.net/10962/d1017352
- Description: This case study centres round an afterschool intervention programme aimed at enhancing mental computation skills of Grade 8 learners at a secondary school in the Erongo educational region of Namibia. Nine research participants took part in the study, and the mental computational strategies exhibited by these participants constitutes the unit of analysis. The study is anchored within an interpretive paradigm and is theoretically underpinned by constructivist epistemology. Kilpatrick, Swafford and Findell’s (2001) model of mathematical proficiency provides the conceptual framework supporting the study. The research was carried out in four sequential phases – an initial pre-test, the intervention itself, a follow-up post-test, and a focus group discussion. The study highlights the underdevelopment of mental computation skills and the associated lack of appropriate mental computational strategies in secondary school learners. It is recommended that appropriate time within the school curriculum be allocated for the development of learners’ mental computation skills.
- Full Text:
- Date Issued: 2015
An investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms : a case study
- Authors: Mbelani, Xoliswa Lydia
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown , Boredom , Mathematics -- Study and teaching (Secondary) -- Evaluation , Mathematical ability , Teaching -- Aids and devices , Creative teaching -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2040 , http://hdl.handle.net/10962/d1017351
- Description: This research report focuses on an investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms in the Grahamstown region, South Africa. Boredom seems to be strongly evident in our classrooms. Quantitative data was derived from an initial survey questionnaire while semi-structured interviews were used to elicit qualitative data. The data from the survey was analysed quantitatively using descriptive statistics. The quantitative data was categorised according to the structure of the survey. The data was represented in bar graphs and then discussed accordingly. In the final narrative I infused extracts from the interviews with my quantitative analysis. The qualitative data was analysed and coded according to different categories and themes that emerged through repeated engagement with the interview transcripts. The findings revealed that boredom is a common problem in the 8 Grade 10 Mathematics schools in the Grahamstown region and this finding answered my first research question. To answer my second research question, the results showed that learners were bored due to many factors, such as; lack of understanding, repetition and the teacher’s actions and many more. My findings align with what is highlighted by Nett, Goetz, & Hall. (2011) that many learners from particularly the senior secondary schools frequently report episodes of boredom. The study recommends that teachers make their teaching more interesting, much use of concrete teaching materials and make mathematics tasks to be relevant and real.
- Full Text:
- Date Issued: 2015
- Authors: Mbelani, Xoliswa Lydia
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa -- Grahamstown , Boredom , Mathematics -- Study and teaching (Secondary) -- Evaluation , Mathematical ability , Teaching -- Aids and devices , Creative teaching -- South Africa -- Grahamstown
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2040 , http://hdl.handle.net/10962/d1017351
- Description: This research report focuses on an investigation into the prevalence and nature of boredom in Grade 10 Mathematics classrooms in the Grahamstown region, South Africa. Boredom seems to be strongly evident in our classrooms. Quantitative data was derived from an initial survey questionnaire while semi-structured interviews were used to elicit qualitative data. The data from the survey was analysed quantitatively using descriptive statistics. The quantitative data was categorised according to the structure of the survey. The data was represented in bar graphs and then discussed accordingly. In the final narrative I infused extracts from the interviews with my quantitative analysis. The qualitative data was analysed and coded according to different categories and themes that emerged through repeated engagement with the interview transcripts. The findings revealed that boredom is a common problem in the 8 Grade 10 Mathematics schools in the Grahamstown region and this finding answered my first research question. To answer my second research question, the results showed that learners were bored due to many factors, such as; lack of understanding, repetition and the teacher’s actions and many more. My findings align with what is highlighted by Nett, Goetz, & Hall. (2011) that many learners from particularly the senior secondary schools frequently report episodes of boredom. The study recommends that teachers make their teaching more interesting, much use of concrete teaching materials and make mathematics tasks to be relevant and real.
- Full Text:
- Date Issued: 2015
Investigating how a peer teaching programme could shape the mathematical experience of the participating tutors
- Authors: Lubasi, Justin Mwandamena
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) , Peer teaching , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2039 , http://hdl.handle.net/10962/d1017350
- Description: This case study, involving six Grade 10 learners, investigates how a peer tutoring programme could shape the mathematical experience and disposition of the participating tutors. The study is grounded in an interpretive paradigm and data was collected in four sequential phases. The Mathematics Dispositional Functions Inventory (MDFI) instrument was completed by the tutors prior to commencement of the tutoring programme. The tutoring sessions then took place over a three week period during which time each tutor kept a reflective journal. Semi-structured interviews were then conducted, after which each tutor completed the MDFI instrument again in order to track any potential changes in their mathematical disposition. The study found that the participating tutors showed an improved mathematics disposition after the peer tutoring experience. Not only was the peer tutoring programme an empowering experience for the tutors, it also had a positive influence on both the tutors’ self-confidence as well as their perceived mathematical ability.
- Full Text:
- Date Issued: 2015
- Authors: Lubasi, Justin Mwandamena
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) , Peer teaching , Mathematical ability
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2039 , http://hdl.handle.net/10962/d1017350
- Description: This case study, involving six Grade 10 learners, investigates how a peer tutoring programme could shape the mathematical experience and disposition of the participating tutors. The study is grounded in an interpretive paradigm and data was collected in four sequential phases. The Mathematics Dispositional Functions Inventory (MDFI) instrument was completed by the tutors prior to commencement of the tutoring programme. The tutoring sessions then took place over a three week period during which time each tutor kept a reflective journal. Semi-structured interviews were then conducted, after which each tutor completed the MDFI instrument again in order to track any potential changes in their mathematical disposition. The study found that the participating tutors showed an improved mathematics disposition after the peer tutoring experience. Not only was the peer tutoring programme an empowering experience for the tutors, it also had a positive influence on both the tutors’ self-confidence as well as their perceived mathematical ability.
- Full Text:
- Date Issued: 2015
An investigation into the possible causes of the difference between the boys' and girls' drop-out rate in mathematics at the end of the junior secondary phase of education
- Authors: Oberholster, E J
- Date: 1986
- Subjects: Mathematical ability , Gender , Mathematics teaching , Drop-out rate , Junior secondary
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1351 , http://hdl.handle.net/10962/d1001417
- Description: In the past two decades much research in the field of Mathematics in Education has dealt with boy- girl differences. In the 1960's sex differences in mathematical achievement played an important role in research. The results of more recent and better controlled studies seem to indicate that overall boy-girl differences in mathematical achievement are probably negligible at the Primary stage and exist at the Secondary stage principally in areas involving spatial visualization and problem solving.
- Full Text:
- Date Issued: 1986
- Authors: Oberholster, E J
- Date: 1986
- Subjects: Mathematical ability , Gender , Mathematics teaching , Drop-out rate , Junior secondary
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: vital:1351 , http://hdl.handle.net/10962/d1001417
- Description: In the past two decades much research in the field of Mathematics in Education has dealt with boy- girl differences. In the 1960's sex differences in mathematical achievement played an important role in research. The results of more recent and better controlled studies seem to indicate that overall boy-girl differences in mathematical achievement are probably negligible at the Primary stage and exist at the Secondary stage principally in areas involving spatial visualization and problem solving.
- Full Text:
- Date Issued: 1986
- «
- ‹
- 1
- ›
- »