An analysis of how the use of geoboards as visualisation tools can be utilised in the teaching of quadrilaterals
- Authors: Matengu, Given Kahale
- Date: 2019
- Subjects: Manipulatives (Education) , Information visualization , Visualization , Mathematics -- Study and teaching , Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96724 , vital:31312
- Description: The relationship between visualisation processes and using manipulatives in the teaching and learning of mathematics is apparent and yet not so vocal in the literature. This could be because of the common mistaken understanding that because manipulatives are visual in nature, then visualisation processes should be obvious. Literature warns that just because something is visual therefore it is transparent, is incorrect. This study argues that the effective use of manipulatives in the teaching of mathematics helps learners to effectively understand mathematical concepts. Research on the teaching and learning of mathematics suggests that physical manipulation experiences, especially of concrete materials concerning shapes, is an important process in learning at all ages. One such teaching tool, the Geoboard, a physical manipulative that employs visualisation processes when correctly used, is explored in this study. The aim of this interpretive case study was to investigate and analyse the use of Geoboards as a visualisation tool in the teaching of the properties of quadrilaterals. The study focused on visualisation processes and the use of Geoboards through a teaching framework that was informed by the Van Hiele phases of teaching geometry. The study was conducted in the Opuwo circuit of the Kunene region, Namibia, and it involved three selected Grade 7 mathematics teachers, each from a different primary school. It was underpinned by a constructivist theory using the Van Hiele phases of teaching geometry and framed within visualisation processes. The study employed the use of qualitative data collection techniques such as observations and interviews. The analysis of the findings of this study revealed that Geoboards were very useful in demonstrating the visual representations of the properties of quadrilaterals in a cheap and yet novel way in the selected teachers’ classes. Moreover, the use of Geoboards by the selected teachers effectively fostered visualisation processes such as concrete pictorial imagery, dynamic imagery, perceptual apprehension, sequential apprehension, discursive apprehension and operative apprehension. It was also revealed that Geoboards enabled the selected teachers to structure and teach their lessons in a well-planned manner according to the Van Hiele phases, although it was difficult for them to adhere strictly to the hierarchy of the phases.
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- Date Issued: 2019
Factors affecting grade 6 learners’ performance in Mathematics in the East London Education District
- Authors: Kwateng, Jesse
- Date: 2019
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10353/15935 , vital:40565
- Description: Mathematics is one of the most important subjects rooted in many fields of study but has also been one of the greatest challenges for learners in every country, most especially in the Republic of South Africa. There have been attempts to curb the challenges that have bedeviled the success of mathematics education by governments, the Department of Education and many other stakeholders who have not enjoyed positive results in mathematics in the district of East London. Therefore, this study examines factors affecting grade 6 learners’ performance in mathematics in selected schools within the East London education district. There were three hundred and forty-five (345) grade 6 learners and 12 teachers drawn through a parallel mixed methods sampling. Stratified random sampling was used to select participants for the quantitative strand while purposive sampling was used for selecting 60 learners and 12 teachers for the qualitative strand. The researcher used the mixed method research approach. The instruments used in collecting data were structured questionnaire and semi-structured interviews to elicit information from grade 6 learners and teachers. Information gathered from the learners and teachers included: biographical information, factors affecting teaching and learning of mathematics and suggestions. The quantitative data were analyzed by using descriptive statistics of percentage from the responses of learners. The quantitative analysis was done by using excel 2010 to formulate data into percentages and qualitatively, voice recordings from the respondents semi-structured interviews were reduced through thematic analysis. The findings of the study revealed that some of the qualified mathematics educators preferred to work in another profession. Quality of teaching and learning were less effective due to overcrowded classrooms, inadequate teaching and learning resources, poor monitoring of educators, some of the learners were not adequately motivated and many others. For performance in mathematics to improve in the primary schools in East London Education District, the study made some recommendations from the findings to the stakeholders in education such as the Department of Education, principals, the government, educators and learners. These recommendations might virtually assist in finding lasting solutions to grade 6 learners with mathematics challenges.
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- Date Issued: 2019
An investigation of teachers' mathematical task selection in the Zambia context
- Authors: Kangwa, Evaristo
- Date: 2013
- Subjects: Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1384 , http://hdl.handle.net/10962/d1001512
- Description: This research sought to investigate the sources and type of tasks used in the teaching of trigonometry in Zambia’s secondary schools, and to investigate the criteria used and decisions made by teachers in their selection and implementation of tasks. The study was conducted in three different school types located in high cost, medium cost and low cost respectively. One participant was chosen from each of the different categories of schools. The research was located within an interpretive paradigm. Data were collected through semi-structured interviews, lesson observations and document analysis which include: lesson plans for five consecutive days, pupils’ activity books and three textbooks predominantly used by the teachers. Document analysis was informed by the task analysis guide and essential themes which were used to tease out teachers’ task practice with regard to criteria used and decisions made in the selection and implementation of tasks. Essential themes that were qualitatively established were validated and explicated by the qualitative analysis. The findings of the study indicate that teachers picked tasks from prescribed textbooks. The study further suggests that teachers selected a mix of low and high level tasks, procedures without connections and procedures with connections tasks to be specific. There were no memorisations and doing mathematics tasks. Their choice of tasks was based on the purpose for which the task was intended. Some tasks were selected for the purpose of practicing the procedures and skills, other tasks for the promotion conceptual development. Most of high level tasks decline to low level tasks during implementation. The findings also indicate that teachers selected and implemented a variety of tasks and concepts. Furthermore, teachers presented tasks in various forms of representations and in a variety of ways. However, the results of this study could not be generalized because of the small sample involved. The results presented reflect the views and task practices of the target group. A possibility for future study would be to consider a large population, drawn across the country.
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- Date Issued: 2013
Case study : using visual representations to enhance conceptual knowledge of division in mathematics
- Authors: Joel, Linea Beautty
- Date: 2013
- Subjects: Mathematics -- Study and teaching , Visual learning , Division -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:1992 , http://hdl.handle.net/10962/d1013356
- Description: Literature emphasizes how important it is that procedural and conceptual knowledge of mathematics should be learned in integration. Yet, generally, the learning and teaching in mathematics classrooms relies heavily on isolated procedures. This study aims to improve teaching and learning of partitive and quotitive division, moving away from isolated procedural knowledge to that of procedures with their underlying concepts through the use of manipulatives, visual representation and questioning. Learning and teaching lessons were designed to teach partitive and quotitive division both procedurally and conceptually. The study explored the roles these manipulatives, visual representations and questioning played toward the conceptual learning of partitive and quotitive division. It was found that manipulatives and iconic visualization enhanced learning, and this could be achieved through scaffolding using a questioning approach. It was concluded that manipulatives and iconic visualization need to be properly planned and used, and integrated with questioning to achieve success in the learning of procedural and conceptual knowledge.
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- Date Issued: 2013
Multiple representations and cognitive load: words, arrows, and colours when solving algebraic problems
- Authors: Brey, Amina
- Date: 2013
- Subjects: Algebraic logic , Mathematical analysis , Mathematics -- Study and teaching
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9580 , http://hdl.handle.net/10948/d1020392
- Description: This study investigates the possible effects that access to selected multiple representations (words, arrows and colours) have in terms of cognitive load and learner achievement when presented with algebraic problems at grade nine level. The presentation of multiple representations (the intervention) was intended to decrease extraneous cognitive load, manage the intrinsic cognitive load (algebraic problems) and optimise germane cognition (schema acquisition and automation). An explanatory sequential mixed-method design was employed with six hundred and seventy three learners in four secondary schools. Quantitative data were generated via pre-, intervention and post-tests/questionnaires, while qualitative data were obtained from open-ended questions in the pre-, intervention, and post-tests/questionnaires, eight learner focus group interviews (n = 32), and four semi-structured, open-ended teacher interviews. Statistically and practically significant improvement in mean test scores from the pre- to intervention test scores in all schools was noted. No statistically and practically significant improvement was noted in further post-tests except for post-test 2 which employed more challenging problems (statistically significant decrease with a small practical effect). Learners expressed their preference for arrows, followed by colours and then words as effective representations. Teacher generated qualitative data suggests that they realise the importance of using multiple representations as an instructional strategy and implicitly understand the notion of cognitive load. The findings, when considered in the light of literature on cognitive load, suggest that a reduction in extraneous cognitive load by using a more effective instructional design (multiple representations) frees working memory capacity which can then be devoted to the intrinsic cognitive load (algebraic problems) and thereby increase germane cognition (schema acquisition and automation).
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- Date Issued: 2013
Teachers' and learners' experiences and perceptions concerning the use of English as a language of learning and teaching in bi/multilingual mathematical literarcy classrooms
- Authors: Pillai, Saloshni
- Date: 2013
- Subjects: Education, Bilingual , Mathematics -- Study and teaching , English language -- Usage
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:9440 , http://hdl.handle.net/10948/d1021022
- Description: In South Africa, there is concern about the poor achievement by first additional language (FAL) English learners in mathematics, and this is a consequence not solely of the apartheid era but more appropriately, the existing current situation in the classroom. Since 2006, the Department of Basic Education in South Africa introduced mathematical literacy (ML) as another learning area for the Further Education and Training (FET) band. ML, as an alternative choice to mathematics, is envisaged as a key to the understanding of our everyday world filled with numbers. Mathematical literacy FAL English learners and teachers are exposed to a ML curriculum that demands high linguistic skills in English in order to engage with the mathematical concepts through the medium of English which is not their home language. While the Language-in-Education Policy (DoE, 1997) recommends that school language policies promote additive bilingualism and the use of learners’ home languages as languages of learning and teaching (LoLT), there has been little implementation of these recommendations by schools, for the reason that all assessments and learner and teacher support materials (LTSM) are only available in English. Thus it appears that ML creates a language gap when FAL English learners and teachers have to possess a high level of communication and language proficiency of the LoLT English to successfully engage with the mathematical context and content of the ML curriculum since the language itself carries all the meaning. The majority of FAL English learners and teachers struggle with the necessary English language proficiency to successfully interact with the ML curriculum and are often required to use their own home language (code switching) to bring about understanding. In this study, I explore how teachers and learners who are dominantly FAL English speakers, engage in teaching and learning of ML in bi/multilingual classrooms. The main aim of the study is to investigate the FAL English learners’ and teachers’ experiences and perceptions concerning the use of English as the LoLT in bi/multilingual ML classrooms. Qualitative measures were generated through personal interviews (teachers [n=15] and learners [n=25]) from five different secondary schools situated in the rural areas of the Midlands in KwaZulu-Natal. This study is framed by Wenger’s (1991) model of situated learning and Vygotsky’s socio-cultural perspectives, which propose that learning involves a process of engagement in a community of practice and reflects the learners’ sociocultural relationship to school mathematics respectively. The study also describes Cummins’ quadrants and explores the benefits of Cummins’ notion of language use (Cummins, 1984). Analysis of the semi-structured interviews revealed that, despite both teachers’ and learners’ difficulty with the language, English is the more popular language to be used in teaching and learning in bi/multilingual mathematical literacy classrooms since English is accepted as a global language. Worldwide emphasis and dominance of English as a powerful language that gives access to goods and social mobility were also highlighted. However, overall results in this study showed that most participants did express their preference for using their home language isiZulu alongside English through the extensive practice of code switching for the teaching and learning of ML.
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- Date Issued: 2013