A critical analysis of how the potential of Dynamic Geometry Software as a visualisation tool may enhance the teaching of Mathematics
- Authors: Mavani, Beena Deepak
- Date: 2021-04
- Subjects: Mathematics -- Computer-assisted instruction , Geometry -- Study and teaching (Secondary) -- South Africa -- Mthatha , Manipulatives (Education) -- South Africa -- Mthatha , Information visualization , Mathematics teachers -- Training of -- South Africa -- Mthatha , GeoGebra Literacy Initiative Project (GLIP) , Dynamic Geometry Software (DGS)
- Language: English
- Type: thesis , text , Doctoral , PhD
- Identifier: http://hdl.handle.net/10962/177192 , vital:42798 , 10.21504/10962/177192
- Description: Visualisation in the mathematics classroom has its own pedagogical value and plays a significant role in developing mathematical intuition, thought and ideas. Dynamic visualisation possibilities of current digital technologies afford new ways of teaching and learning mathematics. The freely available GeoGebra software package is highly interactive and makes use of powerful features to create objects that are dynamic, and which can be moved around on the computer screen for mathematical exploration. This research study was conceptualised within the GeoGebra Literacy Initiative Project (GLIP) – an ICT teacher development project in Mthatha in the Eastern Cape, South Africa. The focus of this study was on how GeoGebra could be used as a teaching tool by harnessing its powerful visualisation capacity. In the study, selected GLIP teachers collaboratively developed GeoGebra applets, then implemented and evaluated them. The research methodology took the form of action research cycles in which the design, implementation and evaluation of successive applets determined the data gathering and analysis process. My data consisted mainly of recorded observations and reflective interviews. The underlying theoretical foundation of this study lies in constructivism, which aligned well with the conceptual and analytical framework of Kilpatrick et al.’s (2001) description of teaching proficiency. An in-depth analysis of my classroom observations resulted in multiple narratives that illuminated how teachers harnessed the visualisation capabilities inherent in the software. My findings showed that dynamic visualisation and interactivity afforded by the use of technology are key enabling factors for teachers to enhance the visualisation of mathematical concepts. My analysis across participants also showed that technical difficulties often compromised the use of technology in the teaching of mathematics. The significance of this research is its contribution to the ongoing deliberations of visualisation and utilisation of technological resources, particularly through the empowerment of a community of teachers. The findings recognised that the integration of technology required appropriate training, proper planning and continuous support and resources for the teaching of mathematics. This action research provided insightful information on integrating Dynamic Geometry Software (DGS) tools in mathematics classrooms that could be useful to teachers and curriculum planners. , Thesis (PhD) -- Education, Education, 2021
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- Date Issued: 2021-04
A comparison of Grade 10 Mathematics classroom-based test items and the end-of-year national examinations, using Stein's framework of cognitive demands : a Namibian case study
- Authors: Ihonya, Saima Namupa
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Ohangwena , Educational tests and measurements -- Namibia -- Ohangwena , Cognitive learning , Critical thinking , Examinations -- Namibia -- Ohangwena
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2032 , http://hdl.handle.net/10962/d1017343
- Description: This study researched the nature of tasks used in Grade 10 mathematics tests and end-of-year national examinations. The study was carried out in three, purposively selected, Grade 10 schools in the Ohangwena region in Northern Namibia. For the purpose of this study, a mixed method approach was employed to analyse a combination of both quantitative and qualitative data. A sample of three tests per mathematics teacher from the three participating schools and national examinations question papers for the past three consecutive years (2011-2013) were analysed using Stein, Smith, Henningsen, & Silver’s (2000) framework of cognitive demand. The study was divided into two phases. Phase 1 was the analysis of teacher test items and national examination items in terms of their cognitive demand. Phase 2 involved semi-structured interviews with three selected teachers to probe their views and find out their basis for selecting test items. The findings of this study revealed that there was no substantial difference in the distribution of the levels of cognitive demand in both tests and national examinations items. The study, however, showed that mainly tasks requiring only procedures without connections dominated the tests and the examinations. The number of higher level tasks in both tests and examinations analysed was low. There was no single task coded at level 4 in any of the teachers’ tests. Only 2% of tasks could be classified at level 4 in the examination items. The study also revealed that since tests and examinations assess the same learning objectives from the syllabus, most of the test items set by teachers were extracted from the national examinations question papers. The paper recommends that more tasks at a higher level category need to be included in assessment tasks to promote critical thinking amongst learners.
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- Date Issued: 2015
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.
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- Date Issued: 2015
An investigation into the nature of mathematics connections used by selected Grade 11 teachers when teaching algebra : a case study
- Authors: Kanyanda, Ester Ndahekomwenyo
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Tsumeb , Algebra -- Study and teaching (Secondary) -- Namibia -- Tsumeb , Connections (Mathematics) , Teacher effectiveness -- Namibia -- Tsumeb
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2036 , http://hdl.handle.net/10962/d1017347
- Description: The purpose of this study was to investigate the nature of mathematical connections used by selected teachers when teaching the topic of algebra and to investigate their perceptions of their use of connections. The participants were selected on the basis of teaching experience as well as their willingness to share their ideas. An interpretive paradigm was used to collect and analyse data. The data was collected from three participating teachers. These participants were selected from the three secondary schools in the town of Tsumeb in Namibia. I used video recordings of two lessons per teacher as well as semi-structured interviews as my tools to gather data. After the two lessons were video recorded, I conducted a workshop with the teachers to introduce them to the 5 types of mathematical connections pertinent to this study. We analysed the videos together using Businskas' framework as a basis for analysis. This then formed part of the stimulated recall interviews. It was found that, even though teachers were not aware of the concept of mathematical connections before our interactions, there was strong evidence of connections being made and used in their lessons. The two types of connections that were used most frequently (24.1 percent each) were procedural and instruction-oriented connections respectively. Part-whole relationships connections were used the least with a frequency of 12 percent. All three teachers agreed that they needed to make more connections when teaching and that they would think more about connections in future, particularly when preparing their lessons. The study makes recommendations to encourage the continuous use of connections in teaching mathematics.
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- 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.
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- Date Issued: 2015
An investigation into the types of classroom tasks senior secondary school (grade 11 and 12) mathematics teachers give to their learners : a case study
- Authors: Shapange, Ismael
- Date: 2015
- Subjects: Mathematics -- Study and teaching (Secondary) -- Namibia -- Omusati , Task analysis in education -- Namibia -- Omusati , Student-centered learning -- Namibia -- Omusati , High school teaching -- Namibia -- Omusati
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2045 , http://hdl.handle.net/10962/d1017356
- Description: This interpretive case study was undertaken to investigate the nature of classroom tasks that teachers give to their learners and to gain insights into how they choose these tasks. It was carried out at two secondary schools in the Okahao circuit of the Omusati region in Namibia. The schools range from Grade 8 to Grade 12. This study focused mainly on teachers who teach Mathematics at senior secondary phase (Grade 11 and 12). The research participants were of four mathematics teachers – two from each school. The study was designed around two phases. Phase one consisted of video-recording of lessons, and phase two consisted of interviewing the teachers. The main purpose of the study was to ascertain the types and nature of tasks that teachers give to their learners and to gain insights into how they chose these tasks. The research adopted a combination of both qualitative and quantitative approaches. The study revealed that the participating teachers provided a near equal amount of lower level cognitive tasks and higher level cognitive tasks. It further revealed several factors that influence teachers when selecting the types of tasks they give to their learners. These factors include curriculum requirements, types of learners and their experiences, and learners’ contexts.
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- Date Issued: 2015
Developing and using an assessment instrument for spatial skills in Grade 10 geometry learners
- Authors: Cowley, Jane
- Date: 2015
- Subjects: Geometry -- Study and teaching (Secondary) -- South Africa -- Eastern Cape , Geometry -- Evaluation. , Mathematics -- Study and teaching (Secondary)
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2025 , http://hdl.handle.net/10962/d1017336
- Description: This qualitative investigation took the form of a case study and fell within the interpretive research paradigm. The Mathematics Chair at the Education Department of Rhodes University launched the Mathematics Teacher Enrichment Programme (MTEP) in 2010 in order to combat poor Mathematics performance of learners in the lower Albany district of the Eastern Cape. The challenge that the participating MTEP teachers faced was a lack of time available to implement new teaching ideas. This was because most of their time was spent catching up “lost” or untaught concepts in the classroom. To address this problem, the Catch-Up Project was launched, whereby selected Mathematics teachers in the area taught lost concepts to Grade Ten learners during afternoon classes in an attempt to improve their fundamental Mathematics knowledge. In order to establish which sections of Mathematics were more difficult for the learners in this programme, bench mark tests were administered biannually. Whilst these tests certainly identified deficient areas within their Mathematics knowledge, the poorest performance areas were the sections of the syllabus which were spatial in nature, such as Space and Shape and Geometry. However, a more in depth assessment tool was required to establish which specific spatial skills the learners were not able to employ when doing these Geometry tasks. To this end, the Spatial Skills Assessment Tasks (SSAT) was developed. It consisted of traditional text book type Geometry tasks and real-world context tasks, both of which were used to assess six spatial skills deemed crucial to successfully facilitate learning Geometry. The case study took place in two of the schools which participated in the Grade Ten Catch-Up project. The case was focused on Grade Ten learners and the unit of analysis was their responses to the SSAT instrument. The learners that participated all did so on a strictly voluntary basis and great care was taken to protect their wellbeing and anonymity at all times. The results of the SSAT instrument revealed that the real world context tasks were in general far more successfully answered than the traditional text book type questions. Important trends in learner responses were noted and highlighted. For example, geometric terminology remains a huge challenge for learners, especially as they study Mathematics in their second language. The ability of the learners to differentiate between such concepts as congruency and similarity is severely compromised, partly due to a lack of terminological understanding but also due to a perceived lack of exposure to the material. Concepts such as verticality and horizontality also remain a huge challenge, possibly for the same reasons. They are poorly understood and yet vital to achievement in Geometry. Recommendations for the development and strengthening of spatial skills support the constructivist approach to learning. Hands on activities and intensive sustained practice over a period of a few months, in which both teachers and learners are actively involved in the learning process, would be considered most beneficial to the long term enhancement of these vital spatial skills and to the learning of Geometry in general.
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- Date Issued: 2015