Gamification technology in teaching: Exploring how mathematics teachers make use of Kahoot! Gamification to facilitate learning of probability in classrooms
- Authors: Mbete, Ayanda
- Date: 2022-10-14
- Subjects: Gamification , Kahoot! , Mathematics Study and teaching (Elementary) South Africa Eastern Cape , Probabilities , Educational technology , Rural schools South Africa Eastern Cape , Technological Pedagogical Content Knowledge , Cultural-historical activity theory
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/405311 , vital:70160
- Description: This study seeks to examine the use of Kahoot! as a gamification technology in practice with Grade six teachers to explore its use in supporting the learning of Probability in Mathematics in rural primary schools. Purposive sampling was adopted wherein nine Grade six mathematics teachers from four rural primary schools in Amathole East district were selected as participants of the study. In addition, to inform this qualitative case study, an interpretive paradigm was adopted. Data was collected using semi-questionnaires, semi-structured interviews, non-participant observations, workshop discussions and reflective journals. The TPACK by Mishra & Koehler (2009) and Vygotsky’s (1978) socio-cultural theory were employed as the lenses through which all the proceedings of the study were based. The key findings indicate that integrating Kahoot! gamification technology, in the ‘Probability’ lesson, has positive consequences such as bringing fun into the classroom, enhancing learner participation, prompt feedback and offering a learner-driven approach to learning as opposed to the conventional teaching strategies. The findings also revealed that enabling and constraining factors are associated with using Kahoot! in teaching: the ICT infrastructure, teachers’ competency levels and the environment in which teaching and learning occurs. This study concluded that the use of Kahoot enhances the learning of probability in rural under-resourced primary schools. This study recommended the integration of Kahoot gamification into the mathematics curriculum. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Mbete, Ayanda
- Date: 2022-10-14
- Subjects: Gamification , Kahoot! , Mathematics Study and teaching (Elementary) South Africa Eastern Cape , Probabilities , Educational technology , Rural schools South Africa Eastern Cape , Technological Pedagogical Content Knowledge , Cultural-historical activity theory
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/405311 , vital:70160
- Description: This study seeks to examine the use of Kahoot! as a gamification technology in practice with Grade six teachers to explore its use in supporting the learning of Probability in Mathematics in rural primary schools. Purposive sampling was adopted wherein nine Grade six mathematics teachers from four rural primary schools in Amathole East district were selected as participants of the study. In addition, to inform this qualitative case study, an interpretive paradigm was adopted. Data was collected using semi-questionnaires, semi-structured interviews, non-participant observations, workshop discussions and reflective journals. The TPACK by Mishra & Koehler (2009) and Vygotsky’s (1978) socio-cultural theory were employed as the lenses through which all the proceedings of the study were based. The key findings indicate that integrating Kahoot! gamification technology, in the ‘Probability’ lesson, has positive consequences such as bringing fun into the classroom, enhancing learner participation, prompt feedback and offering a learner-driven approach to learning as opposed to the conventional teaching strategies. The findings also revealed that enabling and constraining factors are associated with using Kahoot! in teaching: the ICT infrastructure, teachers’ competency levels and the environment in which teaching and learning occurs. This study concluded that the use of Kahoot enhances the learning of probability in rural under-resourced primary schools. This study recommended the integration of Kahoot gamification into the mathematics curriculum. , Thesis (MEd) -- Faculty of Education, Education, 2022
- Full Text:
- Date Issued: 2022-10-14
Exploring visual probability teaching strategies for enhancing mathematical thinking in grade 11 classrooms
- Nghidinwa, Lavinia Tangi-Jehova
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Nghidinwa, Lavinia Tangi-Jehova
- Date: 2021-10-29
- Subjects: Mathematics Study and teaching (Secondary) Namibia , Probabilities , Visualization , Learning models (Stochastic processes) , VIPROMaths project
- Language: English
- Type: Master's theses , text
- Identifier: http://hdl.handle.net/10962/192002 , vital:45187
- Description: This Namibian case study aimed to explore the use of visualisation tools associated with different teaching strategies in the teaching of probability concepts in Grade 11 by selected teachers, to promote mathematical thinking. This research project is an integral component of the VIPROMaths project whose goal is to research the effective use of visualisation strategies in the mathematics classroom in the Southern African region. As a mathematics teacher, I have observed that mathematics teaching practices in our classrooms have relatively little connection with actual mathematics and as a result, teaching misses opportunities to promote mathematical thinking. This qualitative case study is underpinned by an interpretive paradigm and it is informed by the dual coding theory. Data was collected through survey questionnaires, reflective journals, field notes, observation schedules and stimulus-recall interviews. Firstly, I piloted my study by conducting a survey with the Grade 10-12 mathematics teachers in the Khomas region. The aim of this survey was to understand and explore how teachers in the Khomas region taught probability prior to the intervention programme. The data was analysed quantitatively using descriptive statistics such as tables and bar graphs. The findings from the survey necessitated the need for an intervention programme with some teachers in the region, focused on the use of visual tools to promote mathematical thinking. Lastly, three schools were selected from which three Grade 11 mathematics teachers were chosen to take part in an intervention programme. The goal was to observe how these three teachers use visual probability teaching strategies to enhance mathematical thinking after participating in an intervention programme. Lesson observations showed that all observed teachers used visual models to generate images and used models to develop a probability idea as well as to create platforms for classroom discussions. Interviews revealed that teachers’ views towards probability have shifted from that of being the centre of knowledge to that of a facilitator. As a result, teachers used different models to build on learners’ prior knowledge, to assess whether they grasped the probability concept and extend their teaching to real-life situations. This study concluded that the teachers need to consider using mathematical models for creating a platform for discussion to ensure that their verbal explanations are in line with the visuals incorporated. Coupled with that, the teachers’ correct use of visual probability teaching strategies has the potential of enhancing learners’ mathematical thinking. Therefore, teachers need to teach the learners how to create visuals for enhancing maximise understanding of probability concepts in mathematics. Furthermore, it is hoped that the findings will be useful to mathematics teachers, scholars and educators to improve the teaching of probability. , Thesis (MEd) -- Faculty of Education, Education, 2021
- Full Text:
- Date Issued: 2021-10-29
Reliability analysis: assessment of hardware and human reliability
- Authors: Mafu, Masakheke
- Date: 2017
- Subjects: Bayesian statistical decision theory , Reliability (Engineering) , Human machine systems , Probabilities , Markov processes
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/6280 , vital:21077
- Description: Most reliability analyses involve the analysis of binary data. Practitioners in the field of reliability place great emphasis on analysing the time periods over which items or systems function (failure time analyses), which make use of different statistical models. This study intends to introduce, review and investigate four statistical models for modeling failure times of non-repairable items, and to utilise a Bayesian methodology to achieve this. The exponential, Rayleigh, gamma and Weibull distributions will be considered. The performance of the two non-informative priors will be investigated. An application of two failure time distributions will be carried out. To meet these objectives, the failure rate and the reliability functions of failure time distributions are calculated. Two non-informative priors, the Jeffreys prior and the general divergence prior, and the corresponding posteriors are derived for each distribution. Simulation studies for each distribution are carried out, where the coverage rates and credible intervals lengths are calculated and the results of these are discussed. The gamma distribution and the Weibull distribution are applied to failure time data.The Jeffreys prior is found to have better coverage rate than the general divergence prior. The general divergence shows undercoverage when used with the Rayleigh distribution. The Jeffreys prior produces coverage rates that are conservative when used with the exponential distribution. These priors give, on average, the same average interval lengths and increase as the value of the parameter increases. Both priors perform similar when used with the gamma distribution and the Weibull distribution. A thorough discussion and review of human reliability analysis (HRA) techniques will be considered. Twenty human reliability analysis (HRA) techniques are discussed; providing a background, description and advantages and disadvantages for each. Case studies in the nuclear industry, railway industry, and aviation industry are presented to show the importance and applications of HRA. Human error has been shown to be the major contributor to system failure.
- Full Text:
- Date Issued: 2017
- Authors: Mafu, Masakheke
- Date: 2017
- Subjects: Bayesian statistical decision theory , Reliability (Engineering) , Human machine systems , Probabilities , Markov processes
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/6280 , vital:21077
- Description: Most reliability analyses involve the analysis of binary data. Practitioners in the field of reliability place great emphasis on analysing the time periods over which items or systems function (failure time analyses), which make use of different statistical models. This study intends to introduce, review and investigate four statistical models for modeling failure times of non-repairable items, and to utilise a Bayesian methodology to achieve this. The exponential, Rayleigh, gamma and Weibull distributions will be considered. The performance of the two non-informative priors will be investigated. An application of two failure time distributions will be carried out. To meet these objectives, the failure rate and the reliability functions of failure time distributions are calculated. Two non-informative priors, the Jeffreys prior and the general divergence prior, and the corresponding posteriors are derived for each distribution. Simulation studies for each distribution are carried out, where the coverage rates and credible intervals lengths are calculated and the results of these are discussed. The gamma distribution and the Weibull distribution are applied to failure time data.The Jeffreys prior is found to have better coverage rate than the general divergence prior. The general divergence shows undercoverage when used with the Rayleigh distribution. The Jeffreys prior produces coverage rates that are conservative when used with the exponential distribution. These priors give, on average, the same average interval lengths and increase as the value of the parameter increases. Both priors perform similar when used with the gamma distribution and the Weibull distribution. A thorough discussion and review of human reliability analysis (HRA) techniques will be considered. Twenty human reliability analysis (HRA) techniques are discussed; providing a background, description and advantages and disadvantages for each. Case studies in the nuclear industry, railway industry, and aviation industry are presented to show the importance and applications of HRA. Human error has been shown to be the major contributor to system failure.
- Full Text:
- Date Issued: 2017
Intelligent design and biology
- Authors: Ramsden, Sean
- Date: 2003
- Subjects: Hume, David, 1711-1776 , Darwin, Charles, 1809-1882 , Paley, William, 1743-1805 , Dembski, William A., 1960- , Behe, Michael J., 1952- , Evolution (Biology) , Probabilities , Naturalism , Intelligent design (Teleology)
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2739 , http://hdl.handle.net/10962/d1007561 , Hume, David, 1711-1776 , Darwin, Charles, 1809-1882 , Paley, William, 1743-1805 , Dembski, William A., 1960- , Behe, Michael J., 1952- , Evolution (Biology) , Probabilities , Naturalism , Intelligent design (Teleology)
- Description: The thesis is that contrary to the received popular wisdom, the combination of David Hume's sceptical enquiry and Charles Darwin's provision of an alternative theoretical framework to the then current paradigm of natural theology did not succeed in defeating the design argument. I argue that William Paley's work best represented the status quo in the philosophy of biology circa 1800 and that with the logical mechanisms provided us by William Dembski in his seminal work on probability, there is a strong argument for thr work of Michael Behe to stand in a similar position today to that of Paley two centuries ago. The argument runs as follows: In Sections 1 and 2 of Chapter 1 I introduce the issues. In Section 3 I argue that William Paley's exposition of the design argument was archetypical of the natural theology school and that given Hume's already published criticism of the argument, Paley for one did not feel the design argument to be done for. I further argue in Section 4 that Hume in fact did no such thing and that neither did he see himself as having done so, but that the design argument was weak rather than fallacious. In Section 5 I outline the demise of natural theology as the dominant school of thought in the philosophy of biology, ascribing this to the rise of Darwinism and subsequently neo-Darwinism. I argue that design arguments were again not defeated but went into abeyance with the rise of a new paradigm associated with Darwinism, namely methodological naturalism. In Chapter 2 I advance the project by a discussion of William Dembski's formulation of design inferences, demonstrating their value in both everyday and technical usage. This is stated in Section 1. In Sections 2 and 3 I discuss Dembski's treatment of probability, whilst in Section 4 I examine Dembski's tying of different levels of probability to different mechanisms of explanation used in explicating the world. Section 5 is my analysis of the logic of the formal statement of the design argument according to Dembski. In Section 6 I encapsulate objections to Dembski. I conclude the chapter (with Section 7) by claiming that Dembski forwards a coherent model of design inferences that can be used in demonstrating that there is little difference between the way that Paley came to his conclusions two centuries ago and how modem philosophers of biology (such as I take Michael Behe to be, albeit that by profession he is a scientist) come to theirs when offering design explanations. Inference to the best explanation is demonstrated as lying at the crux of design arguments. In Chapter 3 I draw together the work of Michael Behe and Paley, showing through the mechanism of Dembski's work that they are closely related in many respects and that neither position is to be lightly dismissed. Section 1 introduces this. In Section 2 I introduce Behe's concept of irreducible complexity in the light of (functional) explanation. Section 3 is a detailed analysis of irreducible complexity. Section 4 raises and covers objections to Behe with the general theme being that (neo-) Darwinians beg the question against him. In Section 4 I apply the Dembskian mechanic directly to Behe's work. I argue that Behe does not quite meet the Dembskian criteria he needs to in order for his argument to stand as anything other than defeasible. However, in Section 5 I conclude by arguing that this is exactly what we are to expect from Behe's and similar theories, even within competing paradigms, in the philosophy of biology, given that inference to the best explanation is the logical lever therein at work. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2003
- Authors: Ramsden, Sean
- Date: 2003
- Subjects: Hume, David, 1711-1776 , Darwin, Charles, 1809-1882 , Paley, William, 1743-1805 , Dembski, William A., 1960- , Behe, Michael J., 1952- , Evolution (Biology) , Probabilities , Naturalism , Intelligent design (Teleology)
- Language: English
- Type: Thesis , Masters , MA
- Identifier: vital:2739 , http://hdl.handle.net/10962/d1007561 , Hume, David, 1711-1776 , Darwin, Charles, 1809-1882 , Paley, William, 1743-1805 , Dembski, William A., 1960- , Behe, Michael J., 1952- , Evolution (Biology) , Probabilities , Naturalism , Intelligent design (Teleology)
- Description: The thesis is that contrary to the received popular wisdom, the combination of David Hume's sceptical enquiry and Charles Darwin's provision of an alternative theoretical framework to the then current paradigm of natural theology did not succeed in defeating the design argument. I argue that William Paley's work best represented the status quo in the philosophy of biology circa 1800 and that with the logical mechanisms provided us by William Dembski in his seminal work on probability, there is a strong argument for thr work of Michael Behe to stand in a similar position today to that of Paley two centuries ago. The argument runs as follows: In Sections 1 and 2 of Chapter 1 I introduce the issues. In Section 3 I argue that William Paley's exposition of the design argument was archetypical of the natural theology school and that given Hume's already published criticism of the argument, Paley for one did not feel the design argument to be done for. I further argue in Section 4 that Hume in fact did no such thing and that neither did he see himself as having done so, but that the design argument was weak rather than fallacious. In Section 5 I outline the demise of natural theology as the dominant school of thought in the philosophy of biology, ascribing this to the rise of Darwinism and subsequently neo-Darwinism. I argue that design arguments were again not defeated but went into abeyance with the rise of a new paradigm associated with Darwinism, namely methodological naturalism. In Chapter 2 I advance the project by a discussion of William Dembski's formulation of design inferences, demonstrating their value in both everyday and technical usage. This is stated in Section 1. In Sections 2 and 3 I discuss Dembski's treatment of probability, whilst in Section 4 I examine Dembski's tying of different levels of probability to different mechanisms of explanation used in explicating the world. Section 5 is my analysis of the logic of the formal statement of the design argument according to Dembski. In Section 6 I encapsulate objections to Dembski. I conclude the chapter (with Section 7) by claiming that Dembski forwards a coherent model of design inferences that can be used in demonstrating that there is little difference between the way that Paley came to his conclusions two centuries ago and how modem philosophers of biology (such as I take Michael Behe to be, albeit that by profession he is a scientist) come to theirs when offering design explanations. Inference to the best explanation is demonstrated as lying at the crux of design arguments. In Chapter 3 I draw together the work of Michael Behe and Paley, showing through the mechanism of Dembski's work that they are closely related in many respects and that neither position is to be lightly dismissed. Section 1 introduces this. In Section 2 I introduce Behe's concept of irreducible complexity in the light of (functional) explanation. Section 3 is a detailed analysis of irreducible complexity. Section 4 raises and covers objections to Behe with the general theme being that (neo-) Darwinians beg the question against him. In Section 4 I apply the Dembskian mechanic directly to Behe's work. I argue that Behe does not quite meet the Dembskian criteria he needs to in order for his argument to stand as anything other than defeasible. However, in Section 5 I conclude by arguing that this is exactly what we are to expect from Behe's and similar theories, even within competing paradigms, in the philosophy of biology, given that inference to the best explanation is the logical lever therein at work. , KMBT_363 , Adobe Acrobat 9.54 Paper Capture Plug-in
- Full Text:
- Date Issued: 2003
A probability operator
- Authors: Sinclair, Allan M
- Date: 1965
- Subjects: Mathematics , Probabilities
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5423 , http://hdl.handle.net/10962/d1007702 , Mathematics , Probabilities
- Description: From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.
- Full Text:
- Date Issued: 1965
- Authors: Sinclair, Allan M
- Date: 1965
- Subjects: Mathematics , Probabilities
- Language: English
- Type: Thesis , Masters , MSc
- Identifier: vital:5423 , http://hdl.handle.net/10962/d1007702 , Mathematics , Probabilities
- Description: From Introduction: In probability theory it is often convenient to represent laws by characteristic functions, these being particularly suited to classical analysis. Trotter has suggest ted that probability laws can also be represented by probability operators. These operators are easily handled since they are continuous, and hence bounded, positive linear operators on a normed linear space. This representation arises because distribution functions and their complete convergence correspond to probability operators and their complete convergence. Hence the relations between distribution functions and probability operators will be discussed before the introduction of probability laws.
- Full Text:
- Date Issued: 1965
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