An investigation into the use of visualisation processes as a teaching strategy to enhance number sense
- Authors: Griqua, Ronald Max
- Date: 2020
- Subjects: Mathematics -- Study and teaching -- South Africa , Mathematics -- Study and teaching -- Psychological aspects , Visualization , Number concept , RUMEP (Rhodes University Mathematics Education Project)
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/147226 , vital:38606
- Description: The literature agrees that in order to improve learning outcomes, instruction in classrooms should be improved first. Mathematics educationists therefore advocate that schools should make extensive and deep efforts to rethink their instructional programmes. Research furthermore suggests that increasingly, indicators on school performance and teaching reveal largely unacknowledged problematic teaching of mathematics in the great majority of South African schools. This research study is therefore a contribution towards rethinking the teaching strategies within mathematics classrooms. The study examined the use of visualisation processes in order to understand how these interact with the pedagogy of selected mathematics teachers when they teach number sense after participating in an intervention programme. This study argues that the effective use of visualisation processes enhanced the teaching of number sense. The research study was framed as a case study that was grounded within the interpretive paradigm. The study was located in classrooms where the participating teachers promoted active learning after taking part in an intervention programme. A constructivist theoretical underpinning was therefore adopted. At the heart of the study was the Visualisation Intervention Programme (VIP), which involved seven Rhodes University Mathematics Education Project (RUMEP) teachers within the John Taolo Gaetsewe District of the Northern Cape Province. The content of the VIP was informed by initially working with five teachers of well-resourced schools within the Northern Cape who made interesting use of visualisation processes and manipulatives to teach number sense. With the assistance of these five teachers, the VIP was then implemented by seven selected RUMEP teachers to investigate the role of visualisation processes in the teaching of number sense understandings. The study employed a mixed method approach. Qualitative data was collected through observations and interviews, while quantitative data was collected with a series of pre- and post-tests. The analysis of the findings of this research study revealed that the effective use of visualisation processes was instrumental in enhancing the teaching of number sense understandings. Furthermore, the use of visualisation processes by the selected teachers fostered independent thought and conceptual understanding of number sense topics on the part of their learners.
- Full Text:
Investigating conceptual teaching of word problems through visualisation processes: a case of selected Grad 9 mathematics teachers
- Authors: John, Ssennyomo Bernard
- Date: 2020
- Subjects: Mathematics -- Study and teaching (Secondary) -- South Africa , Pythagorean theorem -- Study and teaching (Secondary) , Mathematics teachers -- South Africa , Visualization
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/167497 , vital:41486
- Description: This study investigated how selected grade 9 mathematics teachers used visualisation strategies to conceptually teach Pythagoras' theorem word problems as a result of an intervention program. 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. This case study of mathematics teachers in the John Taolo Gaetsewe (JTG) District in the Northern Cape Province, used a social constructivist theory. The study is grounded within an interpretive paradigm and used an explanatory sequential mixed methods design. It surveyed eighty-seven mathematics teachers from all the secondary schools in the JTG District, focusing on their experiences when using visualisation approaches to teach Pythagoras’ theorem word problems. After the survey, three teachers purposively selected from three different schools in the district took part in the intervention programme. I used a survey questionnaire, classroom observations and interviews to collect the data from the study participants. The data were analysed quantitatively and qualitatively. The findings from survey data revealed that while teachers in the JTG District acknowledge the importance and value of visualisation strategies in the teaching of Pythagoras’ theorem word problems, many of them are either using visuals minimally or not using them at all. Challenges such as lack of resources in schools, time constrains, a lack of support from subject advisers, among others were noted. This thus necessitated a need for an intervention with some teachers in the district, specifically focusing on the use of visualisation tools and skills to teach Pythagoras’ theorem word problems for conceptual understanding. Lessons observations showed that all observed teachers used visual models to generate images and used the models to develop mathematical ideas. The teachers used the images to create platforms for classroom discussions. The discussions were driven by questions which teachers asked both for ascertaining learners’ prior knowledge and for finding out if they understood what the teachers were teaching. Interviews revealed that teachers’ perceptions had changed because they now know how to make and use different models to build on learners’ prior knowledge, extend what they are teaching to real life and make sense of Pythagoras’ proposition in multiple ways and to establish connections among a rich set of mathematics concepts when teaching Pythagoras’ theorem word problems. This study concludes that the use of visual strategies has the potential of enhancing conceptual teaching of Pythagoras’ theorem word problems. The implications for teachers are that learners need to be taught how to create visual representations (both internally and externally) of the relations between objects in a word problem as this will help them in maximising understanding. Furthermore, it is hoped that the results of this study could be used by various stake holders who include inter alia, mathematics subject advisers and teacher training institutions to improve the teaching of Pythagoras’ theorem word problems.
- Full Text:
A critical analysis of selected teachers’ perceptions and experiences of the role that visualisation processes play in their Van Hiele level 1 teaching to migrate their learners to the next Van Hiele level
- Authors: Munichinga, Ben Muyambango
- Date: 2019
- Subjects: Hiele, Pierre M. van. Structure and insight , Visualization , Mathematics -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia , Mathematics -- Study and teaching (Secondary) -- Activity programs -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96735 , vital:31313
- Description: Learning is a process that involves building on prior knowledge, enriching and exchanging existing understanding where learners’ knowledge base is scaffolded in the construction of knowledge. Research on the teaching and learning of geometry in mathematics suggests that physical manipulation experiences, especially of shapes, is an important process in learning at all ages. The focus of the study was the migration of Grade 8 learners from one Van Hiele level to the next as a result of teachers incorporating visualisation processes and Van Hiele phases of instructions in their teaching. The study underpinned by the social constructivist’s theory, therefore aimed at teachers developing visual materials and using Van Hiele’s phases of instruction to teach two dimensional figures in Geometry. The study was carried out in Namibia, Zambezi region in Bukalo circuit. It involved four schools, with 93 learners and three teacher participants. The research is an interpretive case study of a planned intervention programme, which took a four weeks to complete. Participating learners wrote a Van Hiele Geometric test prior and post the intervention programme to determine their geometric level of thought. Participating teachers all received training on visualisation in mathematics and the Van Hiele theory before the intervention. During the intervention, teacher planned and each taught three lessons on two-dimensional figures. Qualitative data was collected from classroom observation, stimulus recall interviews and focus group interviews. Quantitative data came from the pre and post-test of learners. This study found that on average, Grade 8 learners who participated in the study were operating at levels lower than expected of pupils at their stage of schooling. This study also found that, visualisation processes and the Van Hiele phases are effective when used in geometry lessons to migrate learners from lower Van Hiele levels to higher. For teachers in the same circuit, partnership and planning of difficult topics on an agreed regular basis is recommended. When planning lessons teachers are encouraged to take advantage of the Van Hiele phases of instructions. This study thus recommends the incorporation of visualisation strategies of teaching geometry in particular at primary and lower secondary levels. Mathematics teachers are further encouraged to design visual materials such as Geoboards to use for every topic in geometry. Such visual materials should be carefully developed and evaluated to ensure that their use in the classroom is effectively linked to concepts under discussion in a given lesson.
- Full Text:
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.
- Full Text:
An analysis of the roles and functions of teachers’ gestures as visualisation tools in the teaching of mathematics at the junior primary phase (Grades 0 –3)
- Authors: Namakalu, Dietlinde Nelao
- Date: 2019
- Subjects: Gesture , Gesture in mathematics education , Visual learning , Visualization , Education, Elementary -- Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/96713 , vital:31311
- Description: There is ample evidence in the literature that gestures are important hand and bodily actions that play vital roles during interactions between learners and teachers in the mathematics classroom. These gestures enable both the teacher and the learner to visualise mathematical concepts and ideas. The aim of this Namibian interpretive case study, located in enactivist theory, was to analyse the types of gestures that three selected teachers at the junior primary phase (Grades 0–3) used in their teaching of mathematics. The study also interrogated the roles that these gestures played in the teaching process of the three teachers. As I intended to analyse the types of gestures the selected teachers used and understand their views and perceptions of the roles and functions their gestures played as visualisation tools in the teaching of mathematics, I observed ten lessons of each teacher and video recorded them. I then interviewed them (one-on-one stimulus-recall interviews) and interpreted the gestures they used and utterances they made about using these gestures. The types of gestures that the participating teachers used are classified according to McNeill‘s (1992) framework, namely pointing (deictic) gestures, iconic (illustrators) gestures, metaphoric gestures, beat (motor) gestures and symbolic (emblems) gestures. The study found that the participating teachers incorporated a variety of gestures into their lessons and used them strategically. According to the teachers, gestures made the lessons interesting and encouraged active participation of the learners in the lessons. The teachers also revealed that gestures assist in explaining mathematical concepts and thus affected the learners‘ understanding positively. This study strongly suggests that the usefulness and efficacy of employing gestures as visualisation tools in mathematics education should be strategically harnessed.
- Full Text:
An analysis of how visualisation processes can be used by teachers participating in an intervention programme to teach for conceptual understanding of geometry
- Authors: Muhembo, Gottfried Mbundu
- Date: 2018
- Subjects: Geometry -- Study and teaching (Secondary) -- Namibia -- Kavango East , Visualization , Mathematics teachers -- Namibia -- Kavango East , Effective teaching -- Namibia -- Kavango East , Mathematics -- Study and teaching -- Activity programs
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62439 , vital:28190
- Description: Visualisation in general and visualisation processes in particular have received much attention in the mathematics education research literature. Literature suggests that the appropriate use of visualisation helps learners to develop their conceptual understanding and skills of geometry as it allows them to visually interpret and understand fundamental mathematical and geometrical concepts. It is claimed that visual tools play an important role in communicating mathematical ideas through diagrams, gestures, images, sketches or drawings. Learning mathematics through visualisation can be a powerful tool to explore mathematical problems and give meaning to mathematical concepts and relationships between them. This interpretive case study focused on how selected teachers taught concepts in geometry through visualisation processes for conceptual understanding as a result of an intervention programme. The study was conducted at four high schools by four mathematics teachers in the Kavango East Region in Northern Namibia. The participants were involved in a three-week intervention programme and afterwards taught three lessons each on the topic of geometry. The data collection method of this research was: focus group and stimulus recall interviews, classroom observations and recorded videos. This research is located in constructivism. I used vertical and horizontal analysis strategies to analyse the data. My analytical instrument consisted of an observation schedule which I used in each lesson to identify how each of the visualisation processes was evident in each of the observed lessons. This study revealed that the participant teachers used visualisation processes in most of their lessons and these processes were used accurately in line with the requirements of the grade 8 mathematics syllabi. The visualisation processes were used through designed visual materials, posters and through the use of geometrical objects such as chalkboard ruler, protractor and compass. The results from this study also confirmed that visualisation processes can be a powerful instructional tool for enhancing learners’ conceptual understanding of geometry.
- Full Text:
An investigation into teaching mathematics using a visualisation approach to recontextualise indigenous knowledge
- Authors: Tshithigona, Gaus
- Date: 2018
- Subjects: Ethnoscience Namibia , Mathematics Study and teaching (Elementary) Namibia , Visual learning , Visualization , Interdisciplinary approach to knowledge , Teacher effectiveness Namibia , Traditional ecological knowledge Namibia
- Language: English
- Type: text , Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/62461 , vital:28195
- Description: It can be argued that the Namibian curriculum is largely influenced by a Western epistemology. However, many studies suggest that learners make powerful meanings of mathematical concepts they are learning if they visualise these and experience them in relation to what they already know from their own cultural backgrounds. According to the Namibian National Curriculum for Basic Education (NNCBE, 2010), it is not only important for learners to acquire mathematical knowledge and skills, but also to develop and grow their identities, cultures and values as individuals. The aim of this study was to explore and investigate how selected mathematics teachers employ visualisation as a teaching approach to re-contextualise indigenous knowledge (IK). The study set out to explore how conceptual understanding is enhanced by participation in an intervention programme. The use of visualisation is considered an important mediating and pedagogical tool in the mathematics classroom to enhance the mathematics learning of learners. The research is informed by a socio-cultural theory of learning and is located within an interpretive paradigm. The study was conducted at four schools in the Oshana region of Namibia and involved four mathematics teachers who were purposefully selected due to their willingness to use visualisation-IK approaches in their teaching, based on their responses to the survey. The methodologies used are qualitative and quantitative case study. To gather data, document analysis, a survey, lesson observations and focus group interviews were used. The study found that most teachers in the Oshana region have an understanding of the effective use of visualisation-IK approaches. However, the study revealed that visualisation- IK approaches are mostly used in grades 4 to 7 mathematics classrooms. It also discovered that most of the visualisation approaches that teachers employed aligned well with the curriculum and promoted conceptual understanding in the teaching of mathematics. The results of the study showed that teachers have experience of the enabling and constraining factors in using a visualisation-IK approach to teaching mathematics.
- Full Text:
An analysis of selected grade 11 learners’ interactions with geometry tasks using visualization processes: a case study in Namibia
- Authors: Kabuku, Brian S
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Activity programs , Geometry -- Study and teaching (Secondary) -- Namibia , Geometry -- Study and teaching (Secondary) -- Namibia -- Cast studies , Visualization
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/5949 , vital:20997
- Description: This case study was conducted at a secondary school where I teach, situated in the semi-rural setting of Bukalo village in Namibia, and sought to gain insights into the nature and role of visualisation processes employed when selected grade 11 learners interacted with selected geometry problems. According to Mariotti and Pensci (1994), visualisation takes place when "thinking is spontaneously accompanied and supported by images”, and helps students to understand the problem at hand. Visualisation is regarded as "making the unseen visible and imagery as the power to imagine the possible and the impossible” (Mason 1992). The study is located within an interpretive research paradigm in order to obtain in-depth understanding of the participants’ visualisation processes. Within this paradigm, both quantitative and qualitative approaches were adopted. The eight Grade 11 participants engaged with 12 items of the Geometry Visualisation Tasks (GVT) worksheets. Data was collected using video-recorded learners’ interactions with the GVT, observations, stimulated recall interviews and post-GVT interviews with the learners. During the data analysis stage, I used inductive analysis to determine patterns evident in learners ‘thinking processes’. My analytical framework consisted of indicators that were used to identify and classify visualisation processes for each task of the GVT for each participant. I adapted this framework from Ho (2010) and Ho, Ramful and Lowrie’s (2015) clarification of the representations. The findings from this study revealed that the use of visualisations facilitated meaningful learning when learners made use of these to develop and scaffold their conceptual understanding. The findings revealed that most learners used visualisation processes fairly to very accurately when solving geometry problems. They used visualisation processes by using sketches and diagrams that transformed a mathematical problem pictorially, connected their thinking to previous knowledge and experience, clarified the algebraic task and assisted them to understand the spatial relationships within each task.
- Full Text:
An analysis of visualization processes used by selected Grade 11 and 12 learners when solving algebraic problems: a Namibian case study
- Authors: Josef, Joseane
- Date: 2017
- Subjects: Visualization , Mathematics -- Study and teaching -- Namibia -- Case studies , Mathematics -- Study and teaching (Secondary) -- Activity programs , Algebra -- Study and teaching (Secondary) -- Namibia -- Case studies
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/7843 , vital:21309
- Description: Visualisation is gaining visibility in mathematics education research. It is a powerful tool for solving different types of problems in many areas of mathematics, including Algebra - the mathematical domain of this study. The aim of this case study was to analyse the visualisation processes that selected senior secondary school learners used to solve a set of ten algebraic problems.The research was conducted at a secondary school in the Erongo region of Namibia. This is the school where the researcher is teaching. The sample consisted of six selected learners, three from Grade 11 and three from Grade 12. The learners were purposefully selected to participate in this study based on their mathematics performance in class and their willingness to participate. The participants were video recorded as they worked through the ten items of an Algebraic Visualisation Tasks (AVT) worksheet. They were also interviewed about the visualisation processes they employed when solving each of the tasks. The AVT, the videos and the interviews were analysed with the aid of an adapted visualisation template. The findings of the study show that learners used visualisations in all their problem-solving processes. These visualisations were used for different purposes such as starting points, for illustrative purposes, as organizational tools and as simplification tools. Visualisations as starting points were used when the problem was wordy and had lengthy descriptions and explanations. Illustrative visualisations enabled learners to articulate in their own way mathematical notations, mathematical equations and expressions that they then used to solve the problem. Organizational pictures provided a useful structural framework for solving the problems.This research suggests that the selected participants indeed used visualisation processes to solve algebraic problems. It is thus important for teachers to harness this aid and make the most use of these visualisation processes when teaching Algebra.
- Full Text:
An investigation of how Visual Technology for the Autonomous Learning of Mathematics (VITALmaths) video clips on mobile phones can be used by student teachers as a visualisation tool in the teaching of Number Sense: a case study
- Authors: Kangwa, Lemmy
- Date: 2017
- Subjects: Mathematics -- Study and teaching -- Zambia -- Case studies , Visualization , Number concept , Mobile communication systems in education , Mathematics -- Study and teaching -- Software , Telecommunications in education , Educational innovations , VITALmaths
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: http://hdl.handle.net/10962/6930 , vital:21201
- Description: Visualisation is increasingly being recognised as having a significant role in the learning of mathematics especially when students are solving mathematical problems (Thornton, 2001). It is argued that visualisation is a powerful tool for learners to construct mental and physical representations that correctly mirror mathematical relationships and concepts. To gain a thorough understanding of the scope of visualisation, three Visual Technology for Autonomous Learning of Mathematics (VITALmaths) (www.vitalmaths.com) video clips were uploaded on mobile phones of each of the eleven participating student teachers who used them in their teaching practice. This is in cognisance of the educational potential offered by mobile phones and their current pervasiveness in the daily lives of both teachers and learners in Zambia (Zambia. Ministry of Education [M.O.E], 2013]). This study sought to investigate how VITALmaths video clips on mobile phones could be used by student teachers as a visualisation tool in the teaching of Number Sense. The videos of the lessons formed the core of my analysis. The study was conducted at four primary schools by eleven student teachers of a public university in Zambia. The study is framed as a case study and is grounded within the interpretive paradigm. The findings revealed that the student teachers’ use of the video clips in the classrooms for teaching was generally approached from two perspectives: at the beginning of the lesson or at the end. The videos were used at the beginning of the lesson as a means to introduce a topic or an idea, and at the end of the lesson to consolidate what was taught. The videos were also used to enhance the conceptual understanding of Number Sense. The findings also revealed that students encountered both enabling and constraining factors in their use of mobile phones to teach number sense. The overall findings revealed that, if well utilised, mobile phones as visualisation tools had the potential to enhance the teaching of Mathematics in general and Number Sense in particular, and therefore teachers should be encouraged to use them in their teaching.
- Full Text: