Assessering van wiskunde in graad 10
- Authors: Spangenberg, Erica Dorethea
- Date: 2008-07-07T09:40:01Z
- Subjects: Mathematics study and teaching (Secondary) , Competency based education , Training of mathematics teachers , Intelligence tests research
- Type: Thesis
- Identifier: uj:10382 , http://hdl.handle.net/10210/776
- Description: The research study focuses on assessment in Mathematics in Grade 10. The purpose is to identify problems which educators are experiencing in the assessment of Mathematics and to find possible solutions for the problems. This will enable the researcher to develop guidelines for facilitators at District Offices which in turn will contribute to more effective guidance and support for educators regarding assessment in Mathematics. The implementation of the National Curriculum Statement (“NCS”) in Grade 10 with a focus on outcomes-based assessment necessitates changes in the assessment practices in Mathematics. The literature examined views at the nature of Mathematics, constructivism and approaches to learning in Mathematics over the past century, outcomes-based education in the “NCS” and outcomes-based assessment in Mathematics. A pragmatic philosophy was followed. Both quantitative and qualitative methods of data collection were used in the study. Questionnaires were used to collect quantitative information and interviews made it possible to collect qualitative information. Questionnaires and interviews were administered, analysed and interpreted. From the analyses of the questionnaires, it was found that there is the perception that Mathematics is a subject with fixed knowledge, procedures and formulae. The educator still plays the dominant role in assessment and learners are passive in the construction of knowledge. The findings of the study revealed that the recording of outcomes-based assessment is too much and is time consuming. From the interviews it was found that the biggest changes that occurred in the Mathematics classroom because of the “NCS” were the assessment forms, - instruments and - methods. Factors that influence the assessment results in Mathematics are language, time, background and attitude of the learner and the training and experience of the educator. The recommendations of the researcher, based on the findings of the study, focus on the development of guidelines for assessment in Mathematics. The guidelines and recommendations are in the following areas: · Cognitive levels for the development of assessment tasks in Mathematics; · Outcomes in the determining of assessment strategies; · Daily assessment and formal assessment; · The development of assessment strategies; · The process of assessment; · Practical steps in the preparation of the assessment techniques; and · Guidance and support with regard to assessment to the teacher. Though the educators in this study could not solve many problems in assessment, bad planning and time-management created some of the problems. Furthermore, educators received guidelines for assessment from facilitators at District Offices, but they did not make it their own. Some educators did not take the responsibility to do research themselves and failed to adjust their assessment strategies. However, District Officials can still play a crucial role in initiating in-service training and projects that will focus on assessment. Furthermore, if facilitators at District Offices have good insight into the problems which educators are experiencing in Mathematics, they can guide and support educators effectively in the assessment processes in their classrooms. Good application of assessment in the Mathematics classroom, definitely contributes to improved quality of teaching of the subject and consequently a more skillful learner in the community. , Prof. J. Strauss
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- Authors: Spangenberg, Erica Dorethea
- Date: 2008-07-07T09:40:01Z
- Subjects: Mathematics study and teaching (Secondary) , Competency based education , Training of mathematics teachers , Intelligence tests research
- Type: Thesis
- Identifier: uj:10382 , http://hdl.handle.net/10210/776
- Description: The research study focuses on assessment in Mathematics in Grade 10. The purpose is to identify problems which educators are experiencing in the assessment of Mathematics and to find possible solutions for the problems. This will enable the researcher to develop guidelines for facilitators at District Offices which in turn will contribute to more effective guidance and support for educators regarding assessment in Mathematics. The implementation of the National Curriculum Statement (“NCS”) in Grade 10 with a focus on outcomes-based assessment necessitates changes in the assessment practices in Mathematics. The literature examined views at the nature of Mathematics, constructivism and approaches to learning in Mathematics over the past century, outcomes-based education in the “NCS” and outcomes-based assessment in Mathematics. A pragmatic philosophy was followed. Both quantitative and qualitative methods of data collection were used in the study. Questionnaires were used to collect quantitative information and interviews made it possible to collect qualitative information. Questionnaires and interviews were administered, analysed and interpreted. From the analyses of the questionnaires, it was found that there is the perception that Mathematics is a subject with fixed knowledge, procedures and formulae. The educator still plays the dominant role in assessment and learners are passive in the construction of knowledge. The findings of the study revealed that the recording of outcomes-based assessment is too much and is time consuming. From the interviews it was found that the biggest changes that occurred in the Mathematics classroom because of the “NCS” were the assessment forms, - instruments and - methods. Factors that influence the assessment results in Mathematics are language, time, background and attitude of the learner and the training and experience of the educator. The recommendations of the researcher, based on the findings of the study, focus on the development of guidelines for assessment in Mathematics. The guidelines and recommendations are in the following areas: · Cognitive levels for the development of assessment tasks in Mathematics; · Outcomes in the determining of assessment strategies; · Daily assessment and formal assessment; · The development of assessment strategies; · The process of assessment; · Practical steps in the preparation of the assessment techniques; and · Guidance and support with regard to assessment to the teacher. Though the educators in this study could not solve many problems in assessment, bad planning and time-management created some of the problems. Furthermore, educators received guidelines for assessment from facilitators at District Offices, but they did not make it their own. Some educators did not take the responsibility to do research themselves and failed to adjust their assessment strategies. However, District Officials can still play a crucial role in initiating in-service training and projects that will focus on assessment. Furthermore, if facilitators at District Offices have good insight into the problems which educators are experiencing in Mathematics, they can guide and support educators effectively in the assessment processes in their classrooms. Good application of assessment in the Mathematics classroom, definitely contributes to improved quality of teaching of the subject and consequently a more skillful learner in the community. , Prof. J. Strauss
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Comparing the achievement goal orientation of mathematics learners with and without attention-deficit hyperactivity disorder
- Authors: Spangenberg, Erica Dorethea
- Date: 2017
- Subjects: Achievement goal orientation , Attention-deficit hyperactivity disorder (ADHD) , Learners
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/249097 , uj:25915 , Citation: Spangenberg, E.D. 2017. Comparing the achievement goal orientation of mathematics learners with and without attention-deficit hyperactivity disorder. South African Journal of Education, 37(3):1-10. https://doi.org/10.15700/saje.v37n3a1419.
- Description: Abstract: Many learners with different learning challenges are accommodated in the same classroom in South Africa, which could result in poor performance in mathematics. By reinforcing or disregarding certain goals, a teacher can influence the way in which learners learn mathematics. This study compared the achievement goal orientation of Grade Nine mathematics learners in a conventional classroom. The two groups studied were learners experiencing attention-deficit hyperactivity disorder (ADHD) and learners without ADHD. A quantitative, exploratory research design was used. Twenty Grade Nine learners, of whom 10 experienced ADHD, were purposefully selected from one school in Ekurhuleni-East, South Africa. Data was collected with an existing questionnaire. The results revealed that while learners without ADHD compare themselves against their peers’ behavioural and cognitive engagement, as well as the level of their mastery goal orientation, learners with ADHD rely more on their personal performance-avoidance goal orientation and the goal orientation of their parents. Differences between the achievement goal orientation of mathematics learners with or without ADHD could assist teachers in recognising methods to direct learners’ goals for better engagement with and improved results in mathematics, which could support learners to develop to their full potential in the subject.
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- Authors: Spangenberg, Erica Dorethea
- Date: 2017
- Subjects: Achievement goal orientation , Attention-deficit hyperactivity disorder (ADHD) , Learners
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/249097 , uj:25915 , Citation: Spangenberg, E.D. 2017. Comparing the achievement goal orientation of mathematics learners with and without attention-deficit hyperactivity disorder. South African Journal of Education, 37(3):1-10. https://doi.org/10.15700/saje.v37n3a1419.
- Description: Abstract: Many learners with different learning challenges are accommodated in the same classroom in South Africa, which could result in poor performance in mathematics. By reinforcing or disregarding certain goals, a teacher can influence the way in which learners learn mathematics. This study compared the achievement goal orientation of Grade Nine mathematics learners in a conventional classroom. The two groups studied were learners experiencing attention-deficit hyperactivity disorder (ADHD) and learners without ADHD. A quantitative, exploratory research design was used. Twenty Grade Nine learners, of whom 10 experienced ADHD, were purposefully selected from one school in Ekurhuleni-East, South Africa. Data was collected with an existing questionnaire. The results revealed that while learners without ADHD compare themselves against their peers’ behavioural and cognitive engagement, as well as the level of their mastery goal orientation, learners with ADHD rely more on their personal performance-avoidance goal orientation and the goal orientation of their parents. Differences between the achievement goal orientation of mathematics learners with or without ADHD could assist teachers in recognising methods to direct learners’ goals for better engagement with and improved results in mathematics, which could support learners to develop to their full potential in the subject.
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Grade 9 mathematics learners’ strategies in solving number-pattern problems
- Spangenberg, Erica Dorethea, Pithmajor, Aphane Koko
- Authors: Spangenberg, Erica Dorethea , Pithmajor, Aphane Koko
- Date: 2020
- Subjects: Learners , Mathematics , Number-pattern
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/422232 , uj:36023 , Citation: Spangenberg, E.D. & Pithmajor, A.K. 2020. Grade 9 mathematics learners’ strategies in solving number-pattern problems. EURASIA Journal of Mathematics, Science and Technology Education, 16(7), em1862. https://doi.org/10.29333/ejmste/8252
- Description: Abstract: Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners’ strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer and Voica (2013) highlighting four indicators, namely decoding, representing, processing and implementing, underpinned the study. Ninety Grade 9 learners were purposively selected from three rural schools (30 from each school) to participate. Qualitative data were collected through a written activity and semi-structured one-on-one interviews. The study found that learners utilise four main strategies to solve number-pattern problems, namely (1) direct counting; (2) direct proportion; (3) recursive strategy; and (4) mental image representation. Knowledge about learners’ strategies can assist teachers in their pedagogies to teach number-pattern problems. The study adds to the research on problem solving, specifically pertaining to number patterns.
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- Authors: Spangenberg, Erica Dorethea , Pithmajor, Aphane Koko
- Date: 2020
- Subjects: Learners , Mathematics , Number-pattern
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/422232 , uj:36023 , Citation: Spangenberg, E.D. & Pithmajor, A.K. 2020. Grade 9 mathematics learners’ strategies in solving number-pattern problems. EURASIA Journal of Mathematics, Science and Technology Education, 16(7), em1862. https://doi.org/10.29333/ejmste/8252
- Description: Abstract: Many Grade 9 mathematics learners face difficulties in solving number-pattern problems due to insufficient exposure to strategies in solving such problems. The aim of this exploratory qualitative study was to investigate Grade 9 mathematics learners’ strategies in solving number-pattern problems. The problem-solving conceptual framework of Singer and Voica (2013) highlighting four indicators, namely decoding, representing, processing and implementing, underpinned the study. Ninety Grade 9 learners were purposively selected from three rural schools (30 from each school) to participate. Qualitative data were collected through a written activity and semi-structured one-on-one interviews. The study found that learners utilise four main strategies to solve number-pattern problems, namely (1) direct counting; (2) direct proportion; (3) recursive strategy; and (4) mental image representation. Knowledge about learners’ strategies can assist teachers in their pedagogies to teach number-pattern problems. The study adds to the research on problem solving, specifically pertaining to number patterns.
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Riglyne vir die plasing van leerders in Wiskunde of Wiskunde Geletterdheid
- Authors: Spangenberg, Erica Dorethea
- Date: 2010-07-12T07:48:16Z
- Subjects: Mathematics study and teaching , Choice of subjects
- Type: Thesis
- Identifier: http://ujcontent.uj.ac.za8080/10210/389022 , uj:6884 , http://hdl.handle.net/10210/3332
- Description: D.Ed. , The study focused on the placement of Grade 10 learners in either Mathematics or Mathematical Literacy. The purpose was to develop guidelines to assist Grade 10 learners to make a proper choice, which would render their placement more justifiable and objective and, in turn, enhance their results. A central theme of the National Curriculum Statement (NCS) is the importance that secondary schools will shape learners to become responsible citizens in a fast-developing, scientific and technological society. South Africa has an urgent need for more scientists, engineers, high-level economists and technicians, which can only be satisfied if learners with potential for science-related studies are identified. Due to the fact that learners need skills to interact critically with the world outside the school environment, more learners should be encouraged to take Mathematics. A good foundation of Mathematics and Mathematical Literacy necessitates the development of guidelines to add value to assessment. Therefore, this study examined the nature of Mathematics and Mathematical Literacy, the historical background of Mathematics education in South Africa, constructivism and its approaches to learning and teaching, as well as cognitive and non-cognitive factors associated with achievement and general test evaluations. A pragmatic philosophy was followed. National Curriculum Statement (NCS) documents were analysed to distinguish between Mathematics and Mathematical Literacy in terms of subject content. Qualitative and quantitative information was collected by means of interviews and questionnaires respectively.The analyses of the NCS documents showed content similarities and differences between Mathematics and Mathematical Literacy and identified the gaps in learners’ learning experiences that could contribute to non-achievement in either subject.
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- Authors: Spangenberg, Erica Dorethea
- Date: 2010-07-12T07:48:16Z
- Subjects: Mathematics study and teaching , Choice of subjects
- Type: Thesis
- Identifier: http://ujcontent.uj.ac.za8080/10210/389022 , uj:6884 , http://hdl.handle.net/10210/3332
- Description: D.Ed. , The study focused on the placement of Grade 10 learners in either Mathematics or Mathematical Literacy. The purpose was to develop guidelines to assist Grade 10 learners to make a proper choice, which would render their placement more justifiable and objective and, in turn, enhance their results. A central theme of the National Curriculum Statement (NCS) is the importance that secondary schools will shape learners to become responsible citizens in a fast-developing, scientific and technological society. South Africa has an urgent need for more scientists, engineers, high-level economists and technicians, which can only be satisfied if learners with potential for science-related studies are identified. Due to the fact that learners need skills to interact critically with the world outside the school environment, more learners should be encouraged to take Mathematics. A good foundation of Mathematics and Mathematical Literacy necessitates the development of guidelines to add value to assessment. Therefore, this study examined the nature of Mathematics and Mathematical Literacy, the historical background of Mathematics education in South Africa, constructivism and its approaches to learning and teaching, as well as cognitive and non-cognitive factors associated with achievement and general test evaluations. A pragmatic philosophy was followed. National Curriculum Statement (NCS) documents were analysed to distinguish between Mathematics and Mathematical Literacy in terms of subject content. Qualitative and quantitative information was collected by means of interviews and questionnaires respectively.The analyses of the NCS documents showed content similarities and differences between Mathematics and Mathematical Literacy and identified the gaps in learners’ learning experiences that could contribute to non-achievement in either subject.
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The values learners consider as important in the learning of mathematics
- Madosi, Tendai, Spangenberg, Erica Dorethea, Ramdhany, Viren
- Authors: Madosi, Tendai , Spangenberg, Erica Dorethea , Ramdhany, Viren
- Date: 2020
- Subjects: Learners , Values , Mathematics
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/424275 , uj:36278 , Madosi, T., Spangenberg, E.D., Ramdhan, V.: The values learners consider as important in the learning of mathematics. DOI: http://dx.doi. org/10.18820/2519593X/pie. v38i1.13
- Description: Abstract: Learners have different values that could affect their learning and eventually their performance in mathematics. However, many teachers are unaware of these values. Therefore, this paper reports on a study that established the values learners consider as important in the learning of mathematics. The participants were 274 Grade 9 learners, selected purposively from one school in Gauteng, South Africa. An exploratory quantitative research method was adopted and data were collected with a standardised questionnaire developed by Seah (2011b). The results revealed that learners value 1) Hard work and effort when doing mathematics; 2) Numerous different methods to obtain the answer to a mathematics problem; 3) Authentic examples of shapes to understand their properties; 4) Demonstration and explanation of mathematics concepts and proofs; and 5) Teaching and explaining mathematical concepts. This paper highlights the values teachers should consider in the teaching and learning of mathematics in order to ensure better learner performance in mathematics. Furthermore, the paper adds to research on values in Mathematics Education within a South African context.
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- Authors: Madosi, Tendai , Spangenberg, Erica Dorethea , Ramdhany, Viren
- Date: 2020
- Subjects: Learners , Values , Mathematics
- Language: English
- Type: Article
- Identifier: http://hdl.handle.net/10210/424275 , uj:36278 , Madosi, T., Spangenberg, E.D., Ramdhan, V.: The values learners consider as important in the learning of mathematics. DOI: http://dx.doi. org/10.18820/2519593X/pie. v38i1.13
- Description: Abstract: Learners have different values that could affect their learning and eventually their performance in mathematics. However, many teachers are unaware of these values. Therefore, this paper reports on a study that established the values learners consider as important in the learning of mathematics. The participants were 274 Grade 9 learners, selected purposively from one school in Gauteng, South Africa. An exploratory quantitative research method was adopted and data were collected with a standardised questionnaire developed by Seah (2011b). The results revealed that learners value 1) Hard work and effort when doing mathematics; 2) Numerous different methods to obtain the answer to a mathematics problem; 3) Authentic examples of shapes to understand their properties; 4) Demonstration and explanation of mathematics concepts and proofs; and 5) Teaching and explaining mathematical concepts. This paper highlights the values teachers should consider in the teaching and learning of mathematics in order to ensure better learner performance in mathematics. Furthermore, the paper adds to research on values in Mathematics Education within a South African context.
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