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Mandikonza, Caleb. "Relating indigenous knowledge practices and science concepts : an exploratory case study in a secondary school teacher-training programme." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1007321.
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This study reports research on how student teachers in Science at Mutare Teachers' College in Zimbabwe worked with indigenous knowledge practices in relation to science concepts in the secondary school syllabus. The study was conducted among first-year science students and involved them in developing science learning activities for a peer-teaching process that was part of their course. The research was undertaken during a review ofthe college syllabus and as a study to inform the Secondary Teacher Training Environmental Education Programme (ST²EEP). The research design involved the researcher in participant observations and interviews with rural people to document indigenous knowledge practices and to develop materials for the students to work with in the lessons design part of the study. The student teachers used the documented practices to generate learning activities and lesson plans to teach the science concepts they had identified. A peer review session and focus group interviews followed the lesson presentations. Findings from the research point to the rural community being a repository of diverse indigenous knowledge practices. Student teachers showed that they had prior knowledge of both indigenous knowledge practices and science concepts when they come to class. Student teachers were able to relate indigenous knowledge practices and science concepts in ways that have the potential to enhance the learning of science in rural school contexts that lack laboratories and science equipment. The scope of the study does not allow for anything beyond tentative conclusions that point to the need for further work to be undertaken with student teachers and for the research to be extended to teaching and learning interactions in schools. Recommendations are also made for further resource-based work to be undertaken within the forthcoming St²eep implementation phase in 2007.
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Mlambo, Watson. "Information and communication technology in A-level physics teaching and learning at secondary schools in Manicaland Zimbabwe: multiple case studies." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1003458.
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As personal computers (PCs) and related ICTs become more and more omnipresent than ever before in institutions of education, teachers are faced with the challenge of having to teach in ICT rich environments. Some syllabuses increase this pressure by stipulating where ICT may be applied. While past research efforts have focused on presence of and/or effectiveness of ICTs on achieving various didactic goals, there is limited literature on the extent to which actual practice occurred naturally. It was the aim of this study to determine the extent to which Physics teachers and students used ICT in their usual teaching/learning ambience, referred to as natural settings in this study. Using activity theory as a theoretical lens, multiple case studies were chosen as a strategy using 10 schools, 15 Physics teachers, 20 A-level Physics students and 10 ICT teachers (computer specialists). Questionnaires, observations and informal and focus group interviews were used to elicit responses from students, teachers and computer specialists. It emerged from the case studies that despite the presence of apt ICT infrastructure in the schools and although the teachers had a positive attitude towards the use of ICT for teaching and learning of Physics, teachers were apathetic when it came to the actual use. Some of the reasons militating against use were lack of an ICT policy, school authority, and monopoly of computers enjoyed by computer studies teachers. However among students there were ‘early starters’ who used ICTs outside of school, a situation that tended to change the Physics learning environment. These findings led to a proposal for a post of Computer Specialist (CS) in the schools. The need for developing ICT policy at all levels namely national, Ministry of Education and the school was also proposed. Lastly staff development in the use ICT for Physics teachers was proposed as indispensable.
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Lau, Yin-har, and 劉燕霞. "Values teaching in Hong Kong junior secondary mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31958734.
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Chitepo, Thokozile 1961. "Cognitive processes in the acquisition of knowledge from science instruction in Zimbabwe." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66075.
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Chitepo, Thokozile 1961. "Students' ability to apply their knowledge and reason from science instruction in Zimbabwe." Thesis, McGill University, 1997. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=34515.
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The goal of this research was to investigate the knowledge high school students acquire from science instruction in Zimbabwe, and their ability to reason from and apply their knowledge based on previous learning. Science educators in Zimbabwe are concerned with improving the quality of student's achievement and that students develop a conceptual understanding of basic science rather than a rote memorisation of facts and that students become better prepared to acquire science content on their own. The research reported here utilises the discourse comprehension analysis model and methods developed by Frederiksen (1975, 1986) to investigate students' learning. Based on these methods, it is possible to examine: (a) how students acquire knowledge and understanding, and (b) how they apply what they learn to reason using their conceptual knowledge.The design of the study involved the use of three texts each of which represented different information types within a science domain, 'gas pressure'. The content of the texts was presented by the same teacher during natural classroom instruction to classes at two levels (higher and lower) of a high school grade. The first text concerned Basic Knowledge (concepts and principles) in the domain, and the second and third texts described Familiar and Unfamiliar experiments respectively within the same science domain. In addition, for both of these experiments, several types of information were presented: Procedures, Observations and Explanations. Students' responses to comprehension questions were subjected to a conceptual (propositional) analysis and coded against an 'expert' model of the content of the texts used by the teacher during instruction to the students. The study focused on identifying the extent to which the students' responses directly matched the 'expert' model or consisted of modifications (inferences) that indicated alternative (true or false) conceptual knowledge frameworks that the students may have possessed.
The major findings of this research were as follows: Students' answers to questions about their knowledge of basic concepts comprised a large number of responses that directly matched (i.e., literally recalled) the information presented by the teacher during instruction and also included a high number of incorrect inferences. Students' comprehension of the Familiar and Unfamiliar experiments was also characterised by a high degree of 'literal learning' as shown in the generally high amounts of recall of propositional information compared to inferences. Students' responses to these questions consisted mostly of Observation information, and least of Explanations. This suggests that they were more likely to recall observed events that they were to interpret. Students' reasoning was generally poor relative to their comprehension of both experiments, and their responses consisted of more recall responses than inferences. In addition, students' reasoning about the Unfamiliar experiment was characterised by a high number negative higher-order inferences. Finally, students in the higher level displayed higher levels of competence than those in the lower level, particularly in their knowledge of Procedures and Observations in contrast to Explanation information, for both experiments.
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Ceasar, Reginald Raymon. "Investigating an integrated teaching methodology as a means to prepare students for university studies in mathematics." Thesis, University of the Western Cape, 2005. http://etd.uwc.ac.za/index.php?module=etd&.
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A key issue for the success of students entering a first year mathematics course at tertiary level is whether or not they have an integrated understanding and view of the mathematical concepts acquired at school. Various integrated applications from first year mathematics suggest that a compartmentalised view of mathematics would be detrimental to any student's chances of passing mathematics at this level. This study tried to assess whether learners do have an integrated understanding of mathematics at grade 12 level.
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Luwango, Luiya. "Critical reflective teaching practice in three mathematics teachers." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1003366.
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This qualitative study reports on critical reflective teaching by three mathematics teachers and how it shapes their classroom practice. The study was carried out in three secondary schools in Rundu in northern Namibia. The study employed a case study method. The selection of teachers was based on their rich practical professional knowledge and exemplary teaching practices. Data collection and analysis was done through an interpretive approach. Interviews and document analyses were the two research tools used, not only for the collection of data but for triangulation also. Interpretations of the findings were validated through member checking. Critical reflective teaching involves thought and action, and it raises teachers’ consciousness of what they do. Through critical reflective practice, teachers scrutinize their beliefs and knowledge of the subject and their practice. Furthermore critical reflective practice may get teachers into a disposition to find alternatives to improve their teaching. In this study, the findings are that participants reflect extensively on their classroom practice. The teachers pointed out that reflection on practice enables them to analyse and evaluate their teaching in line with effective mathematics teaching. They emphasised that critical reflection leads to the identification of weaknesses in teachers’ classroom practice. This culminates in better planning whereby alternative approaches to teaching are exercised. Because of its potential to improve teaching and enhance professional development it is therefore recommended that mathematics teachers be exposed to skills that enhance critical reflective teaching practice. Teachers need to familiarise themselves with the concept of critical reflective teaching in mathematics to meet the demands of superior quality teaching.
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Mudyahoto, Tapiwa. "The implementation of the inclusive education policy in sport: a case study of four secondary schools in Masvingo District, Zimbabwe." Thesis, University of Fort Hare, 2016. http://hdl.handle.net/10353/2116.
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The purpose of the present study was to explore the implementation of the inclusive education policy in sport in four secondary schools in Masvingo District, Zimbabwe. The case study research design was employed; interviews, focus groups, document analysis and observations were used to collect data. Four school Heads, 4 sports masters, 4 team trainers, 4 team captains, 2 learners with disabilities and a district education officer were purposively selected to take part in this study. Data were presented, analysed/discussed, starting with demographic data in the first section followed by emerging themes. It emerged from the study that all the participants were not knowledgeable about inclusive education and the aspect of including learners with disabilities in mainstream sport. The major barriers identified include inadequate policy dialogue, unavailability of sporting equipment and attitudes. Further findings revealed that there is dire need for knowledge and skills in inclusive sport among teachers in regular schools. Findings also confirmed unavailability of policy circulars in schools. Most teachers were not afforded opportunities to attend workshops and seminars. Findings also revealed that teachers faced major challenges such as funding to undertake courses in SNE and inclusive sport. Teachers were reeled in with a lot of pressure due to congested timetables and large classes. Participants believed that the challenges they faced could be resolved through some proposed intervention strategies. The researcher concluded that teachers in regular schools were not equipped to teach sport to learners with special education needs in the mainstream. The MoPSE was not doing much in preparing teachers to be effective in including learners with disabilities in regular school sport. The study recommended that the MoPSE should put in place provisions to meet the inclusive needs of both teachers and learners. It also recommended that school Heads should be taught about SNE and inclusive sport for them to be able to guide teachers properly. Besides the national policy, schools should design inclusive policies specifically for their respective schools in line with the national policy. The study also recommended that the MoPSE should come up with a comprehensive framework in sport to counter some of these challenges.
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Nyika, Mugove Walter. "Permaculture as an aspect of environmental learning: an investigation into secondary school communities in Zimbabwe." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1008447.
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The Schools and Colleges Permaculture (SCOPE) Programme in Zimbabwe has developed a process for use by schools in planning for the sustainable management of their land. The process is called Integrated Land-Use Design (ILUD) and is based on Permaculture principles. The ILUD process has so far been implemented in 54 pilot schools where it has been used to facilitate the re-design of the school grounds through the active participation of the students, staff and parents. The aim of this research was to investigate what environmental learning takes place during the implementation of the ILUD process and related activities, with a view to informing the improvement of the process. The research was conducted within the interpretive paradigm with particular use being made of the Symbolic Interactionist theoretical framework to explore the social situations in which the ILUD process has been applied. A purposive sample of two schools and five form 4 (grade 11) pupils from each school was selected for the study. The main data collection method was the structured interview. Other data were collected from nonparticipant observations and the analysis of documents, particularly photographs. The data was analysed using the constant comparative method. The findings point towards a significant contribution from the Permaculture activities to the environmental knowledge, environmental management skills and the positive environmental attitudes of the pupils. The work done at the two schools indicates the usefulness of the ILUD process as a tool for environmental action in the schools but its application in the communities was found to be limited by constraints such as lack of resources and the limited capacity of teachers to work in the field of adult education and training. It is recommended that Permaculture should be integrated into the secondary school curriculum if the momentum of the progress made so far is to be maintained. The SCOPE Programme itself needs to be strengthened for its work with communities. There is, for example, a need for adult education and training methods if the introduction of ILUD to the communities is to be successful.
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Alleyn, Suzanne. "Learning the language of mathematics." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81477.
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In this thesis, I describe how interactive journal writing was used to improve the understanding of mathematics, and to foster communication with two groups of remedial grade ten students. Mathematics is a gatekeeper course in high school, and students who are not successful with this subject are at a distinct disadvantage, both in terms of their education and in their future careers. A persistent source of difficulty for these students is related to language; students often struggle both to understand what is being taught, and how to explain concepts or problem solutions in their own words. Interactive journal writing was initiated as a means of addressing this situation, and of meeting the objectives proposed by the Quebec Education Plan, which specifies three closely related competencies: (1) solve situational problems; (2) use mathematical reasoning; (3) and communicate by using mathematical language. There is ample proof in the research literature that communication plays an important role in supporting learners by helping them clarify, refine and consolidate their thinking.This study demonstrates the importance of allowing and encouraging students to use writing as part of their learning processes. By writing about what they are being taught, students are forced to slow down, examine and reflect on the steps they use to solve problems. Sharing what they write promotes meaningful dialogue and personal engagement, essential ingredients of successful learning.
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Ng, Yui-kin, and 吳銳堅. "Computers, Gödel's incompleteness theorems and mathematics education: a study of the implications of artificialintelligence for secondary school mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31957419.
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Tang, Cham-wing, and 鄧湛榮. "The attitudes of secondary school mathematics teachers towards the teaching of mathematics by using computers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1996. http://hub.hku.hk/bib/B31958886.
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Stephanus, Gervasius Hivengwa. "Exploring teaching proficiency in geometry of selected effective mathematics teachers in Namibia." Thesis, Rhodes University, 2014. http://hdl.handle.net/10962/d1013012.
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Quality mathematics education relies on effective pedagogy which offers students appropriate and rich opportunities to develop their mathematical proficiency (MP) and intellectual autonomy in learning mathematics. This qualitative case study aimed to explore and analyse selected effective mathematics teachers' proficiency in the area of geometry in five secondary schools in five different Namibia educational regions. The sample was purposefully selected and comprised five mathematics teachers, identified locally as being effective practitioners by their peers, Education Ministry officials and the staff of the University of Namibia (UNAM). The schools where the selected teachers taught were all high performing Namibian schools in terms of students' mathematics performance in the annual national examinations. The general picture of students' poor performance in mathematics in Namibia is no different to other sub-Saharan countries and it is the teachers who unfortunately bear the brunt of the criticism. There are, however, beacons of excellence in Namibia and these often go unnoticed and are seldom written about. It is the purpose of this study to focus on these high achievers and analyse the practices of these teachers so that the rest of Namibia can learn from their practices and experience what is possible in the Namibian context. The mathematical content and context focus of this study was geometry. This qualitative study adopted a multiple case study approach and was framed within an interpretive paradigm. The data were collected through individual questionnaires, classroom lesson observations and in-depth open-ended and semi-structured interviews with the participating teachers. These interviews took the form of post lesson reflective and stimulated recall analysis sessions. An adapted framework based on the Kilpatrick, Swafford and Findell's (2001) five strands of teaching for MP was developed as a conceptual and analytical lens to analyse the selected teachers' practice. The developed coding and the descriptive narrative vignettes of their teaching enabled a qualitative analysis of what teachers said contributed to their effectiveness and how they developed MP in students. An enactivist theoretical lens was used to complement the Kilpatrick et al.'s (2001) analytical framework. This enabled a deeper analysis of teacher teaching practice in terms of their embodied mathematical knowledge, actions and interactions with students. procedural fluency (PF) and productive disposition (PD), were addressed regularly by all five participating teachers. Evidence of addressing either the development of students' strategic competence (SC) or adaptive reasoning (AR) appeared rarely. Of particular interest in this study was that the strand of PD was the glue that held the other four strands of MP together. PD was manifested in many different ways in varying degrees. PD was characterised by a high level of content knowledge, rich personal experience, sustained commitment, effective and careful preparation for lessons, high expectations of themselves and learners, collegiality, passion for mathematics and an excellent work ethic. In addition, the teachers' geometry teaching practices were characterised by making use of real-world connections, manipulatives and representations, encouraging a collaborative approach and working together to show that geometry constituted a bridge between the concrete and abstract. The findings of the study have led me, the author, to suggest a ten (10) principles framework and seven (7) key interrelated factors for effective teaching, as a practical guide for teachers. This study argues that the instructional practices enacted by the participating teachers, who were perceived to be effective, aligned well with practices informed by the five strands of the Kilpatrick et al.'s (2001) model and the four concepts of autopoesis, co-emergence, structural determinism and embodiment of the enactivist approach. The study concludes with recommendations for effective pedagogical practices in the teaching of geometry, and opportunities for further research.
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袁東璇 and Tung-shuen Yuen. "Using ICT in learning and teaching mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31256570.
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Fisher, Diana Marie. "Introducing Complex Systems Analysis in High School Mathematics Using System Dynamics Modeling: A Potential Game-Changer for Mathematics Instruction." PDXScholar, 2016. http://pdxscholar.library.pdx.edu/open_access_etds/2950.
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Complex systems abound on this planet, in the composition of the human body, in ecosystems, in social interaction, in political decision-making, and more. Analytical methods allowing us to better understand how these systems operate and, consequently, to have a chance to intervene and change the undesirable behavior of some of the more pernicious systems have developed and continue to be enhanced via quickly changing technology. Some of these analytical methods are accessible by pre-college students, but have not been widely used at that level of education. Jay Forrester, the founder of one of the methodologies, System Dynamics (SD), used to study complex system behavior involving feedback, laments the lack of understanding of complex systems evident in short-sited decisions made by legislators -- global climate change and fiscal policies being cases in point.
In order to better prepare future decision makers with tools that could allow them to make more informed decisions about issues involving complex systems efforts have been underway to increase pre-college teacher understanding of the SD method. The research described in this dissertation introduces the mathematics education community to the value of System Dynamics modeling in pre-college algebra classes, indicates a path by which a traditional mathematics curriculum could be enhanced to include small SD models as a new representation for elementary functions studied in algebra classes, and provides an empirical study regarding conceptual understanding of functions by students.
Chapter 2 indicates the numerous beneficial learning outcomes that empirical studies have shown accompany model-building activities. Chapter 3 indicates the need for students to become familiar with complex systems analysis, how SD modeling (one method of complex systems analysis) aligns with the Common Core State Standards in Mathematics, and the work that has transpired over the past two decades using SD in K-12. Chapter 4 focuses on the importance of the concept of function in high school mathematics, some limitations of exclusive reliance on the closed form equation representation for mathematizing problems and the SD stock/flow representations of some of the elementary functions that are studied in algebra classes. Chapter 5 looks at the issues affecting two traditional teachers and the challenges they faced when trying to reintroduce SD modeling into their algebra classes. Chapter 6 explains the student component of the classroom experiment that was conducted by the teachers who are highlighted in Chapter 5.
The analysis of the results of student model-building activities in the two classroom studies that are part of the third paper did not indicate a statistical difference between the two experimental groups and the two control groups. Many environmental and scheduling issues conspired to adversely affect the experiment. However, positive outcomes were evident from the two pairs of students who were videotaped while they built the final multi-function drug model, the final student lesson in the experiment. Research focused on student outcomes is needed to further assess the strengths and weakness of the SD approach for student learning in mathematics.
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Matsolo, Matjala Lydia. "Perceived experiences that grade seven learners have in learning algebra." Thesis, University of the Western Cape, 2006. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_9454_1181559574.
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This thesis investigates grade seven learners perceived experiences in learning algebra.Things that learners do and say during algebra lessons and about algebra were investigated. The study was done at one of the previously disadvantaged schools in Cape Town, South Africa.The data were collected through observations, a questionnaire and interviews. Observations were made from the day the topic was started in two grade seven classes. Two different teachers taught the two classes. Focus group interviews were conducted, two group of learners, ten learners from each of the two classes were interviewed. Learners devised a number of strategies for solving problems related to sums and differences. The principal learning difficulties experienced by learners in algebra related to the transition from arithmetic conventions to those of algebra, the meaning of literal symbols and the recoginition of structures. It became obvious then that developing algebraic thinking is not necessarily dependent upon algebraic notation and that the presence of algebraic notation says little about the level of problem solving.
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Cheung, Pak-hong, and 張百康. "Statistical analysis of secondary school teachers' attitudes towards mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31976517.
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Spence, Alan Peter. "The primary - secondary transition : a study of teaching strategies and children's attitudes towards mathematics." Thesis, University of Brighton, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361056.
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McAskill, Donald Bruce. "A program evaluation of applications of Mathematics 10 in British Columbia public schools." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape3/PQDD_0011/NQ52765.pdf.
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Crespo, Luna Sandra M. "Mathematics achievement in the Dominican Republic : grade 12." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29585.
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The general goal of the present study was to assess mathematics achievement at the end of Grade 12 in the Dominican Republic, with particular attention to school and regional differences, as well as gender differences. Also, gains in achievement were examined by comparing the achievement of students in Grade 12 to that of students finishing Grade 11. In addition, the performance of Grade 12 students was compared to that of Grade 8 students as assessed in the Teaching and Learning of Mathematics in the Dominican Republic (TLMDR) study and to that of students from other countries in the Second International Mathematics Study (SIMS).
The sample included 1271 students in Grade 12 and 1413 in Grade 11, distributed over 49 schools. Three types of schools were sampled, public schools, and two kinds of private schools. They were urban schools located in the twelve largest cities of the country. These cities were grouped into three regions of similar size.
The mathematics test consisted of 70 multiple-choice items distributed over two test forms. Students' scores were analyzed to assess how much mathematics students in Grade 12 know. Grade 11 data were used as a surrogate for pre-test scores to estimate gains in achievement. School means were used in an analysis of variance designed to examine the effect of school type and region on mathematics achievement. Males' and females' scores were used to analyze gender differences in achievement at the item level, and within each of the school types and regions in the sample. Grade 12 students' responses to 14 items were compared to those of Grade 8 students. Finally, Grade 12 students' responses to 10 items were compared to those of students from other countries in SIMS.
Among the findings of this study were:
1. Students in Grade 12 scored poorly on the mathematics test. Grade 11 and Grade 12 students obtained similar achievement levels which indicated that the achievement gains between the two grades were very small.
2. School type and region were found to significantly affect mathematics achievement, but no interaction effect was found.
3. The comparison of school type means showed that only one type of private school significantly outperformed public schools. This type of school also outperformed the other type of private school.
4. The comparison of region means did not produce the predicted outcome. The pairwise comparisons showed that none of the regions was significantly different from the other, despite the fact that the region factor was significant.
5. The analysis of gender differences in mathematics achievement showed that males performed significantly better than females. At the item level, males outperformed females on only 19 items. Most of these items dealt with geometry, or were at the application level.
6. Gender differences favoring males were found to be independent of school type and region.
7. Comparison between Dominican Grade 12 and Grade 8 students revealed that mathematics achievement improved between the grades for most items.
8. Dominican performance was very poor on the SIMS items and it was far behind that of other countries.Education, Faculty of
Graduate
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Van, Ongevalle J. "The significance of participation in capacity development and project sustainability: a case study of the Zimbabwe Secondary Teacher Training Environmental Education Project (St²eep)." Thesis, Rhodes University, 2007. http://hdl.handle.net/10962/d1003651.
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This study uses a systems thinking perspective to explore the role and meaning of participation, capacity development and project sustainability in the Zimbabwe Secondary Teacher Training Environmental Education Project (St²eep). Since there was no consistent critical reflection upon the different assumptions that underpin these important aspects of St²eep in the original project design, this study aims to articulate a theoretical framework for guiding the project. St2eep is a donorfunded project, located in the Ministry of Higher and Tertiary Education in Zimbabwe that seeks to integrate environmental education across the curriculum of secondary teacher education. The study first develops a theoretical framework drawing on systems thinking. In particular it uses the holistic and constructivist perspectives embedded in systems thinking to describe a number of analytic frameworks that are used as a guide to investigate participation, capacity development and project sustainability in the St²eep case study. The research methodology comprises a qualitative case study approach, which contains elements of an instrumental, evaluative and critical case study. Data-collection methods include document analysis, focus group discussions, focus group interviews, semi-structured face-to-face interviews and participant observation. Data analysis follows the constant comparative method of coding and categorising data as outlined by Strauss and Corbin (1998). The outcomes of this research show that participation processes in St²eep evolve around the interactions between a political dimension and a learning dimension. The political dimension relates to giving the project stakeholders a critical voice, allowing them to shape the project and involving them in the decision-making process. This approach has fostered an ongoing learning process in a small team of committed stakeholders based on the principles of collaborative learning, team learning and action research. Participation was shown to enhance capacity-development processes at individual and institutional level by the provision of support through learning teams, and by the renegotiation of responsibilities and power relations between lecturers involved in St²eep, donor representatives and college administrations. The strong operational role of the donor organisation was seen as a serious threat towards individual and institutional capacity development since it creates a functional but artificial and independent project system within the college system and takes over any local institutional support structure that it might seek to develop. Fostering continuous learning and capacity development, St²eep’s participatory approach was shown to contribute to a better understanding of the interconnectedness of factors that influence future sustainability of the project and the implementation of environmental education. This has assisted in the development of different scenarios on the sustainability of the project. The research shows that the project-ustainability planning process draws directly from St²eep’s ongoing learning process, with individual and institutional capacity development featuring strongly in the different scenarios, and with the external context such as the economic situation and the low priority of environmental education being recognised as important factors that need to be considered. Drawing on the findings from the case study, this study makes a tentative recommendation that donor organisations should focus more on capacity-development initiatives and avoid taking on a strong operational role in project activities. The research also recommends that there is need for a deliberate focus on both the political and learning dimensions of the participation process in order to foster local ownership. Making the learning aspect much more central in St²eep is presented as a possible strategy for motivating a larger number of college lecturers to become involved in the project and the implementation of environmental education. The study also urges St²eep to combine the different scenarios that have emerged during the project sustainability planning process and to focus on the benefits that stakeholders want to see sustained.
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Lam, Mau-kwan, and 林謀坤. "Secondary three students' strategies in solving algebraic equations." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B3196025X.
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Young, Gerald E. "The Journey to Becoming Constructivist, Presidential Award for Excellence in Mathematics and Science Teaching, Secondary Mathematics Teacher." PDXScholar, 2014. http://pdxscholar.library.pdx.edu/open_access_etds/2065.
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The purpose of this research study is to describe and analyze the self-reported experiences of exemplary high school mathematics teachers who underwent personal and professional transformations in order to develop and use a standards-based, constructivist (SBC) teaching paradigm in their classrooms. These teachers were all past recipients of the Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST), an award that required them to demonstrate that their mathematics instruction was rigorous in the manner described by the NCTM standards.
The following research questions are addressed: (a) What are the paths SBC secondary mathematics teachers who received the PAEMST pursued to become highly effective?, (b) What obstacles and challenges did they encounter and how were these obstacles overcome?, and (c) What sustained them on their journeys? The research methodology used to be a narrative inquiry. Following a wide survey of PAEMST recipients, five volunteer participants were chosen for the study. Data were collected from each participant using a one-to-one interview and the written section of each participant's PAEMST application. A narrative was written for each participant describing the path they had followed to become a highly effective high school mathematics teacher. The narrative was sent to each participant, and a follow-up interview was conducted via telephone amending the narrative to reflect the participant's additions and deletions. From the five amended narratives, eight themes were identified: (a) influences; (b) education; (c) professional development; (d) NCTM standards; (e) teaching style: beginning, current, or end of a career; (f) obstacles; (g) personality traits and personal beliefs; and (h) student influence.
Several of the themes were supported by previous research. However, this research study discovered two new findings. First, the five participants had common characteristics and beliefs: (a) belief in their students, (b) persistence, (c) belief that professional development is vital for teacher growth, and (d) passion about mathematics and about conveying that passion to their students. The second research finding pertained to the influence that their own students had on all of the five participants. All the participants purposely sought out their students' thoughts about the classroom curriculum and about the instruction they received. The teachers considered their students part of the classroom learning community, and they honored and acted on their input.
Finally, in addition to describing the trajectory of five PAEMST winning teachers, this study offers recommendations for students studying to become high school mathematics teachers, teacher educators, and educational researchers. For these students, their teaching preparation courses need to be taught adhering to the four principles of learning: activity, reflection, collaboration and community. According to this research, the model of teacher preparation courses that emphasize the teaching of the above four principles using a traditional teacher-directed method does not prepare future mathematics teachers for the use of SBC teaching in their classrooms. Suggestions about further research are addressed.
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鄧國俊 and Kwok-chun Tang. "Stability and change in school mathematics: asocio-cultural case study of secondary mathematics in Macau." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B29797627.
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Sung, Edward William. "Using the concrete-representation-abstract instruction to teach algebra to students with learning disabilities." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3263.
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This project explored the Concrete to Representational to Abstract instruction (CRA instruction) as a strategy to teach abstract math concepts for secondary students with learning disabilities. Through the review of literature, multiple researchers suggested that students with learning disabilities need to be exposed to a variety of instructional strategies to develop problem solving skills in algebra concepts.
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Wong, Chung-shun, and 黃忠信. "Using a cognitive approach to assess achievement in secondary school mathematics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B42574274.
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Rawane, Mosima Gladys. "Exploring the embodiment of a secondary mathematics teacher." Thesis, University of Limpopo, 2016. http://hdl.handle.net/10386/1989.
Full textAbstract:
Thesis (M. Ed. (Mathematics Education)) --University of Limpopo, 2017Sarton (1936) stated that mathematics has grown so large for a single mind to grasp. Mack (1961) attributes that phenomenon by claiming that mathematics differs from science in that it keeps on adding new concepts to existing ones, whereas in science there is reduction of concepts. This continuing growth makes it impossible for an individual to study mathematics as a whole (Krantz, 2010). Van Bendegem (2009, p. 137) calls the mathematics world a “mad world”. Recently, Ellerton (2014) compared mathematics to a growing tree. A number of challenges arise out of the observations made above. Is the mathematics that is taught in secondary schools an appropriate reflection of the mathematics that is out there today? Is an individual an appropriate embodiment of a secondary mathematics teacher? In the mist of these and many other questions, this study locates itself in the second question and investigated the notion of an embodiment of a secondary mathematics teacher. The main research question that was pursued was ‘How adequate is an individual as an embodiment of a secondary mathematics teacher?’ This question should be understood and interrogated in the context of Festinger’s (1962) dissonance cognitive theory that also serves as the theoretical framework for the study. The expectations of a secondary mathematics teacher do not fit in with an individual’s capacity to embody those. Grounded theory (Glaser, Strauss & Beer, 1967) was used to generate and develop what Elliot and Higgins (2012) called a substantive theory. This was a desktop grounded theory study and data was collected from existing literature of published journals and books. Since the use of documents is recommended as one of the qualitative data collection methods in grounded theory (Strauss & Corbin, 1990), the documents served as primary data where only a few that were relevant to the issues discussed were selected (Breckenridge & Jones, 2009). Content and thematic analyses procedures were used. Content analysis assisted to organise data according to various eras, tracing the growth in mathematics education and mathematics content, comparing them to a mathematics teacher of different eras, which assisted in bringing the answer to the research question posed (Bowen, 2009). Thematic analysis was used to identify commonalities and differences with regard to the notion of a teacher in various eras (Fereday & Muir-Cochrane, 2006). The findings revealed that the notion of a secondary mathematics teacher of the current era is completely not a suitable embodiment of a secondary mathematics teacher. The current notion of an embodiment of a secondary mathematics teacher is seriously challenged by this ever growing subject. Secondary mathematics is so large for an individual to acclimatise with (Sarton, 1936), and there seems to be a need for more than an individual to ensure that mathematics is well taught and learned by learners. It is recommended that other studies should be undertaken to determine as to how many individuals can constitute a composite suitable to embody the requirements of an ideal secondary mathematics teacher.
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Wong, Man-on, and 黃萬安. "The effect of heuristics on mathematical problem solving." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31957523.
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Huang, Rongjin, and 黃榮金. "Mathematics teaching in Hong Kong and Shanghai: a classroom analysis from the perspective of variation." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B31244245.
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Odindo, Fredrick. "Introducing Learning Study approach to the teaching and learning of mathematics in Kenyan secondary schools." Thesis, University of East Anglia, 2019. https://ueaeprints.uea.ac.uk/69827/.
Full textAbstract:
Recent reports ([KNEC], 2014) have shown that students' performance in the national mathematics examinations in Kenya is weak and have expressed concerns about the pedagogical methods adopted by teachers. The Kenyan Government has made some interventions in the past, including the initiation of in-service training for mathematics and science teachers in secondary schools. However, performance has not improved significantly ([KNEC], 2014). The purpose of this study is to explore the effect of Learning Study (LS) approach in the teaching and learning of quadratic expressions and equations - one of the topics of concern ([KNEC], 2014). The LS approach promotes collaborative work between teachers. Firstly, they prepare a lesson together, then one of them teaches the lesson while the others observe, and they later meet to reflect on and revise the lesson. In this study and in tandem with the recommendations from the Kenyan Ministry of Education ([MoEST], 2012) for more student-centred learning, the lessons were organised with the students participating in small group discussions followed by a whole-class discussion. The participants of the study included three teachers teaching two Form 3 (16-18 years) classes, and 79 students. I applied a LS design (Lo, 2012) and collected qualitative data from students' pre-and post-lesson tests, classroom observations, individual interviews with the teachers, and a group interview of eight students. Lesson observation data was analysed using a Variation Theory framework (Lo, 2012) and interview data was analysed using thematic analysis (Braun and Clarke, 2006). The findings show that: students adequately learned the topic, experienced positive changes in their attitudes towards mathematics, improved participation and communication in mathematics lessons, and increased their confidence when solving mathematical problems. The teachers appreciated the LS approach, saying that teamwork improved their teaching of the topic and helped them learn from each other. KEY WORDS: Quadratic Expression and Equation, Learning Study, Variation Theory, Collaboration, Group work.
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Leung, Kung-shing, and 梁拱城. "The impact of teaching of analytical skills on the mathematics achievement of Form three students." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31955575.
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Mugore, Masawi Maireva Faustina. "Language learning and teaching in Zimbabwe : English as the sole language of instruction in schools : a study of students' use of English in Zimbabwe, their indigenous languages (Shona and Ndebele), and the schools' methods of instruction in secondary school classrooms." Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29090.
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This study focuses on the use of English as the sole medium of instruction in Zimbabwean schools and the effect of such a policy on the educational achievement of students, particularly in secondary schools. The role of Shona and Ndebele, two other Zimbabwean official languages, in schooling is also examined.Some of the findings reveal a learning and teaching environment that prevents strategies from addressing linguistic, social and cultural development with a coherent workable vision in the English classroom.
Because English is the working language of government, business, and industry in Zimbabwe, an English-only policy seems to be a practical means to prepare students for higher education and the workforce. The growing status of English as an international lingua franca provides additional support for such a policy.
This study reveals the need to rethink the imposition of an English-only policy. The findings indicate that current teaching approaches/methods and materials do not entirely support language development in English, largely because they do not take into account the economic, social, and linguistic situations of the students.
The study supports and calls for a multifaceted approach to the way language is currently taught in Zimbabwe, and sees this as one way secondary schools can produce, through the medium of English instruction, students and teachers who can adapt to rapid change, and relate to people from diverse socio-cultural and linguistic backgrounds.
The study emphasizes the integration and expectations of people's views on language and education, as heard and expressed by many respondents. This is considered central to any meaningful effort towards linguistic competence, a challenging but stimulating learning environment, and better communication among students and teachers.
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Kwong, Ka-to, and 鄺嘉圖. "An analysis of geometry in the junior secondary school (grade 7-9) mathematics textbooks from England, Hong Kong and Chinese Taipei." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/198864.
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This dissertation is intented to explore the similarities and differences of pedagogical characteristics in geometry though analyzing the contents of the junior Secondary school (grade 7-9) mathematics textbooks of England, Hong Kong and Taipei.
By studying the topic of “Relationships for angles at a point, angles on a line, vertically opposite angles, angles associated with a transversal cutting parallel lines and perpendicularity” of the textbooks, the textbooks of the three places have demonstrated how they organize the contents to achieve the various aims with different means and different emphasis. For English textbooks, their contents are characterized by using geometric intuition for verifying the properties of geometric objects and the theorems. On the contrary, for Taipei textbook, their contents are characterized by the extensive use of deductive reasoning and proof for verifying the properties of geometric objects and the theorems. Lastly, for Hong Kong textbooks, their contents are characterized by encouraging conjecturing through various explorative activities.
For developing students’ cognitive thinking in geometry, the progress of developing students’ level of sophistication in deductive reasoning is depended upon their age for England while Hong Kong and Taipei do not. Process of visualization is commonly used in the three countries for enhancing the reasoning process and various apprehensions of geometric objects. On the other hand, Hong Kong and Taipei textbooks tend to apply more on the process of reasoning in the teaching activities while English textbooks apply more on the process of construction.published_or_final_version
Education
Master
Master of Education
34
Govender, Vasuthavan Gopaul. "A multiple case study of parent involvement with grade 8 learners of mathematics." Thesis, Nelson Mandela Metropolitan University, 2007. http://hdl.handle.net/10948/511.
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The learning of mathematics is a worldwide concern. International studies over the last decade place South African learners amongst the lowest achievers. Although various initiatives have been tried there does not seem to be any improvement. In the USA and UK initiatives include the involvement of parents and these have been implemented with great success. One of the parent involvement programmes from the USA, the Family Maths Programme has been in South Africa since 1996. This programme has been successful in South Africa but is confined to parents of grades 4-7 children. However, there is no programme for parents of high school learners. As grade 8 is usually the first high school year in South Africa, this study focuses on parents of grade 8 children and their involvement in their children’s mathematics learning. It consists of an initial survey of grade 8 parents’ (from an urban school) mathematical backgrounds and experiences and their involvement in their children’s education. Using key points from the survey and elements from the literature review and other sources, the researcher designed a parent assistance programme for mathematics which was conducted with three groups of parents of grade 8 children from the same high school. Each group of parents was exclusive and the same set of procedures was applied to each group, making this study a qualitative multiple case study, within the interpretive research paradigm. The parent-assistance programme consists of a parents’ workshop and completion of journals over a 7-week period. Parents documented their interactions with their children in structured journals, a process known as participant journaling. After this journaling period, parents and children were surveyed on this interaction by means of follow-up questionnaires. This was followed later in interviews with the parents and mathematics teachers, separately. After the completion of all three case studies parents and children participated in focus group discussions to discuss and share experiences of the programme. The interrogation of the data, on two levels, suggests parents’ and children’s perceptions of mathematics were likely to be positively influenced. The data also suggest that children were likely to become more confident and to improve in mathematics.
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Alummoottil, Joseph Michael. "The spiral curriculum, integrated teaching and structured learning of mathematics at the secondary level." Thesis, Rhodes University, 1990. http://hdl.handle.net/10962/d1003654.
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The investigator's experience of teaching mathematics at a college of education since 1983 has reinforced his conviction that trainee students come to college with significant gaps, weaknesses and faults in their (mathematical) conceptual structures, probably as a result of shortcomings in the mathematics teaching to which they have been exposed. The theme of this investigation is thus a natural choice that appeared to be of immediate relevance to secondary school mathematics teaching. The analysis of the issue leads to a unified perspective: the problem is placed in a theoretical framework where Bruner [spiral curriculum], Ausubel [structured learning] and Skemp [relational understanding] are brought together. How the curriculum, textbooks and examination influence school mathematics teaching is examined in some depth and the consequences investigated. Two specific topics, viz. the generalised Pythagorean relation and absolute value are investigated in relation to published work, curriculum and textbooks, and each (topic) is presented as a unifying theme in secondary mathematics to standard 9 pupils. The classroom exercise is assessed to test the hypothesis that structured, integrated presentation around a spiral curriculum promotes "relational understanding". Analysis of results supports the hypothesis.
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Rathje, Ryan. "A Qualitative Case Study of Mathematics Teachers' Formative Assessment Feedback." ScholarWorks, 2018. https://scholarworks.waldenu.edu/dissertations/5934.
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Formative assessment is supported by research as a process to enhance student learning. A vital aspect in the process is the role of feedback which, based on its use, can support or hinder student learning. The problem addressed in this study was based on the concern of a high school administrator that teachers in the school were not using formative feedback in a manner that supported student learning. The purpose of this instrumental qualitative case study was to explore and understand the assessment and feedback practices of mathematics teachers in a private high school setting. The conceptual framework for this study was a model influenced by Black and Wiliam's theory of formative assessment and by Hattie and Timperley's model of feedback in which effective feedback is the supporting structure of the formative assessment process for promotion of student learning. The research questions were designed to explore the beliefs and practices of 3 mathematics teachers regarding the purpose of assessment and feedback. Qualitative data were collected from archival documents, observations, and a series of semistructured interviews. Data were analyzed by using multicycle descriptive coding and development of themes. Findings included teachers' beliefs, practices and misconceptions about the assessment and feedback cycle in relation to student learning in their classrooms. A recurring theme was that they lacked training in formative assessment practice. A 3-day professional development workshop that integrated and grounded formative assessment research into the daily practice of teachers was developed as a project. Teachers might bring about positive social change as their students develop self-regulatory learning strategies and transfer them into community life.
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McAninch, Melissa Joan. "A qualitative study of secondary mathematics teachers' questioning, responses, and perceived influences." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1691.
Full textAbstract:
The purpose of this study was to examine secondary mathematics teachers' questioning, responses, and perceived influences upon their instructional decisions regarding questioning and response to students' ideas. This study also compared the questioning practices, responses, and influences of beginning teachers to more experienced teachers. Previous studies on teacher quality in mathematics education have focused on general characteristics of mathematics teachers' instructional practice including a broad range of instructional strategies. Little is known about mathematics teachers' questioning practices and responses to students' ideas that research has repeatedly reported are critical to student mathematics learning in secondary classrooms. Furthermore, it is not clear how different novice teachers are in questioning and responding to students from experienced teachers. This understanding can provide significant insights into teacher education programs for mathematics teachers. With those issues in mind, this study was designed to answer the following questions: (1) What similarities and differences exist in questioning patterns between novice and experienced teachers when guiding a classroom mathematical discussion? (2) What similarities and differences exist in responses to students during pivotal teaching moments between novice and experienced teachers when guiding a classroom mathematical discussion? (3) What perceived factors impact the responses teachers give to students' ideas, and how are these factors of influence different among novice and experienced teachers?
This study employed a multiple case study research design to compare the questioning practices and responses of three beginning teachers and three experienced teachers. Multiple sources of data were collected, including two interviews (i.e., initial interview and follow-up interview) for each teacher, five days of classroom video footage for each teacher, and field notes by the researcher for each interview and observation. The researcher conducted initial interviews with each teacher to gain a general sense of the teacher's philosophy and use of questions in guiding classroom discussion. Five instructional days of observation followed the initial interview, and then the researcher conducted a follow-up interview by use of video-stimulated response. All interviews were transcribed verbatim for analysis. The data was analyzed mainly using the constant comparative method to identify regularities and patterns emerging from the data. Results showed differences between beginning and experienced teachers in the frequency and variety of questions asked. Although all teachers showed the largest number of questions in the Socratic questioning category, differences were prominent in the semantic tapestry and framing categories. Results regarding teacher responses to pivotal teaching moments showed that four teachers favored a procedural emphasis in their responses to students, and two teachers used responses to direct students to make clear connections within or outside of mathematics. Perceived influences identified include: (1) reflection on experience and mathematical knowledge for teaching, (2) time, and (3) relationship with students, teachers, and parents, and knowledge of student background.
Practicing teachers can expand the types of questions they use in the classroom, making particular efforts to include those areas that this study showed to be most lacking: semantic tapestry questions that help students build a coherent mental framework related to a mathematical concept, and framing questions that help frame a problem and structure the discussion that follows. The comparison between beginning and experienced teachers also shed light on important practices for teacher education. The beginning teacher participants from this study had no trouble noticing pivotal teaching moments in their lessons but were less developed in their responses to them. Recommendations for mathematics teacher education programs are to provide opportunities to develop content, pedagogical knowledge including specific instruction on questioning strategies, and also to provide parallel field experiences where pre-service teachers can apply the knowledge and skill they are learning.
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Li, Che-cheung Philip, and 李志昌. "The explication of a model of mathematics learning: in the context of the IEA mathematics study (1980 HongKong)." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B38627668.
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Karumazondo, Washington. "A case study of the experiences of newly qualified teachers during their first year of teaching in secondary schools in Zimbabwe." Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.560515.
Full textAbstract:
This thesis focuses on research that was conducted in secondary schools in Zimbabwe in 2003. This study was inspired by the researcher's growing interest in continuing professional development, which started from the experience of working with newly qualified teachers (NQTs) as a headteacher in Zimbabwe in the 90s. This interest was further enhanced by the study of the induction of newly qualified teachers in Oxfordshire in 2000, and the absence of published research into the learning of novice NQTs in Zimbabwe. The study focused on exploring the experiences of NQTs during their first year of teaching in secondary schools in Zimbabwe. The purpose of this study was to generate an in-depth understanding of the experiences of NQTs, their professional development needs and the forms of support they received. Such an understanding, in a context where no research of this nature had been conducted, required a strategy that could enable the researcher to get as close to the researched as possible in a manner that could allow for great flexibility in adapting research to contextual realities. An exploratory/descriptive qualitative case study was considered the most suitable strategy against the background of no previous research on this focus. Data was generated through interviews and observation from two samples with schools in Harare and Mashonaland East regions, which the researcher considered safe to research in, given the political climate in Zimbabwe at the time. The learning of the NQTs during the first year of teaching is one of the key issues underpinning this study. This thesis explores what and how NQTs learn during their first year of teaching in secondary schools in Zimbabwe. Models of teacher learning are reviewed and used in analysing the experiences of the NQTs. There is an on- going debate on support for novice teachers in schools in literature in the Western world. On the one hand there are proponents of formal induction while on the other hand any planned support is viewed as interference with the new teacher's learning. Literature on learning in the workplace provides scope on the significance of the school climate on the learning of teachers. Findings reveal that NQTs had negative experiences at the beginning of the year with major problems in their deployment, delays in processing of salaries during the first term and a critical shortage of resources. The participants indicated professional development needs of NQTs including classroom management and control, teaching methods, adjusting subject content to the level of students, the need to be observed and to observe other teachers and support in implementing new ideas. The study also revealed that there were varying formal and informal provisions for support in schools, as there is no formal national policy guiding the induction of NQTs in schools. The findings of this study provide a basis for key recommendations for educational practice and research.
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Cheng, Wing-kin, and 鄭永健. "Junior secondary students' schemata on a line reflection construction task." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2015. http://hdl.handle.net/10722/209523.
Full textAbstract:
This study explores junior secondary students’ schemata on a line reflection construction task, the research of which was conducted in a secondary school in Hong Kong.
The theories drawn on in this study come from the literature on theories of schemata and the corresponding knowledge embedded within, namely conceptual knowledge, manipulation and procedural knowledge. The research built on existing theories on schemata and attempted to categorize the different kinds of schemata as well as investigating the relationship between them among four junior secondary students in the construction of a line reflection task. The study also tried to find out how and why students manipulated in a line reflection construction task and the extent to which manipulation could lead learners to successfully tackle the task.
This study researched on four junior secondary students, drawing mainly on qualitative data used in the analysis, including task-based interview with the employment of think aloud method in a designed line reflection construction task, as well as study of students’ drawings. The data analysis mainly focused on three areas. First, the analysis of each of the four cases was conducted by looking into the different kinds of schemata possessed by the student informants. Second, analysis of the different knowledge (conceptual knowledge, manipulation and procedural knowledge) embedded in the schema possessed by the student informants was done. Third, synthesis was drawn upon the analysis made in an attempt to answer the research questions posed in this study.
Findings from the study confirmed the core role conceptual knowledge plays in the establishment of a learner’s schemata. Findings also revealed that different learners may possess different schemata towards the same concept such as the concept of same distance. When investigating the manipulative actions employed by student informants, it was found that there is a reciprocal relationship between a learner’s conceptual knowledge and his manipulation. This is also apparent in cases where there was a misconception in the learner’s schemata.
The research also found that students exercised manipulation very differently and these manipulative actions were largely informed by their corresponding conceptual knowledge. With regard to why they manipulated, the research revealed reasons including manipulation for exploration, manipulation for representation and manipulation for verification. Based on the observation and analysis done in the four cases, it was found that manipulation helped students in the completion of the task to different extents. Learners with weaker conceptual knowledge in line reflection benefited more from the manipulation done in the construction task.
These findings have implications for the teaching and learning of line reflection. Teachers are suggested to consider introducing using manipulative tools when approaching the teaching of line reflection, especially when they are dealing with students without rich conceptual knowledge in the area. The effectiveness of having hands-on experience implies that simply teaching definition and inviting learners to rote-learn does not necessarily lead to effective acquisition of knowledge in the Mathematics topic of line reflection.published_or_final_version
Education
Doctoral
Doctor of Education
41
Balyta, Peter. "Using multiple representation systems to deepen understanding of functional relationships in mathematics." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103190.
Full textAbstract:
This thesis describes an experiment using technology to develop conceptual understanding of functions through graphical representations. It examines the effects of including dynamic representations in a conceptual approach to the teaching of functions. The study was implemented over a 5-day period in a Grade 9 class in a small, generally working class, rural school in Eastern Massachusetts. Participating students were observed during class discussions and video analysis, and their written responses and created functions were analyzed. The procedure used in the experiment was based on the Theory of Didactic Situations and used the Didactic Engineering methodology. The structure and sequencing of the thesis is also based on these concepts. Conclusions are drawn regarding the effects of using multiple representations systems to deepen understanding of functional relationships and suggested improvements to the introduction of the function concept in high school instructional programs are given.
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Raghavan, Prasannakumary. "Social constructivist mathematics education in a Ciskeian secondary school classroom." Thesis, Rhodes University, 1994. http://hdl.handle.net/10962/d1003652.
Full textAbstract:
The researcher's experience as a high school mathematics teacher in several African countries convinced her that a good number of mathematics learners exhibit serious difficulties in conceptualising mathematics properly. Her experience in teaching the subject in the Ciskei since 1990 reinforced this conviction. The researcher's natural curiosity to probe into the causes of the poor state of mathematics education in the region served as the springboard into her investigation. Her thoughts developed in line with the emerging educational theories of social constructivism. This provided a conceptual framework for the solution of the problem, the feasibility of which was put to test practically in a Ciskeian classroom. She explicates that the difficulties experienced by the pupils in conceptualising mathematics are philosophically deep rooted and latent in the present system of mathematics education itself, which, in Ciskei, impedes the learners' conceptualisation owing to numerous problems related to their linguistic and cultural situatedness. In the analysis of the present system of mathematics education in the Ciskei she reviews a few recently published mathematics text books in the context of the topics chosen for her research study. The results of her classroom investigation establish that a possible solution to the problem lies in the social constructivist teaching approaches.
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Lam, Tsz-wai Eva, and 林紫慧. "Studying teachers' use of metaphors in the context of directednumbers." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2012. http://hub.hku.hk/bib/B49828538.
Full textAbstract:
People use metaphors to describe or understand one thing in terms of another. The central idea of this thesis is that metaphors can be used to teach mathematics, particularly abstract topics such as directed numbers. Using directed numbers as a context, this study develops a framework and a coding scheme that can be used as a tool for analysing the use of metaphors in the teaching of mathematics.
The part of the theoretical framework of the coding scheme is based on the work of Lakoff and Johnson (1980) and Lakoff and Nunez (2000). In those studies, the authors classify metaphors used for teaching mathematics into one of three categories: ontological, orientational and structural metaphors. By considering the source domain of metaphors, they can be classified into either grounding or linking metaphors. Similarly, the target domain of the metaphors can be categorized by the intended learning outcomes and by the functions of the metaphors.
One of the primary contributions of this thesis is the development of a coding scheme that is specifically designed to analyze the use of metaphors in mathematics lessons. The scheme was then used and validated through the analysis of mathematics lessons taught by two teachers with contrasting academic backgrounds and teaching experiences. Three lessons taught by each teacher on the topic of directed numbers at Secondary One level were recorded and analysed. The metaphors used by each teacher were identified, coded and analyzed in order to determine how metaphors can be extended and transformed into other metaphors.. Finally, this thesis compared how the two teachers differed in their use of metaphors, particularly in terms of the selection, sequencing and organization of the metaphors used. This can be indicative the level of conceptual learning that is made available for students in their classes.
The research questions:
1. What kinds of metaphors did the teachers use to introduce and explain the concepts and computational processes of directed numbers?
2. What functions did these metaphors serve?
3. What is the developmental path of these metaphors within and across the lessons?
4. What were the differences in the selecting, sequencing, and organization of the metaphor used by the two teachers?
Findings
This thesis designed and tested an original coding scheme. The findings revealed that the two teachers had used many kinds of metaphors in their lessons. They were used for classifying different kinds of numbers, constructing concepts, and explaining the properties and computational processes of directed numbers. Most of the metaphors found in this study were used to provide a cognitive function that facilitates the introduction of new mathematical concepts and helps the students make sense of the operational processes; only a few metaphors served a memorable function.
When comparing the use of metaphors by the two teachers, we can analyze their teaching philosophies. Teacher 1’s use of metaphors demonstrated a linear development path from a simple to a more advance perspective, whereas Teacher 2’s use of metaphors revealed more comprehensive, sophisticated and multi-layered perspective.
Significance of the study
This study provides insights into the meaning and implication of using metaphors in teaching mathematical concepts. At research level, this study extends the existing work of Lakoff and develops an analytical tool specifically designed to understand the pedagogical values of using metaphors to teach abstract mathematical concepts such as directed numbers. At pedagogical level, the metaphor coding scheme can act as an initial foray into how metaphors can be used in and for teaching. Moreover, the Metaphor-Concept Development Chart developed in this study is a practical tool that can help teachers to analyze and improve their own use metaphors, thereby furthering their professional development and teaching effectivenss.published_or_final_version
Education
Doctoral
Doctor of Education
44
Marongwe, Anesu Desmond. "An enquiry into the formative and summative assessment procedures, and perceptions thereof, of grade 10 mathematics teachers : a Namibian case study." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1001513.
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The purpose of this study was to gain insight into observed discrepancies between continuous assessment and final examination average marks in Grade 10 Mathematics in the Oshikoto region of Namibia. The study is framed as a case study and is grounded within the interpretive paradigm. A mixed methods approach was applied, eliciting both quantitative as well as qualitative data. The study took place in two phases. In Phase 1, continuous assessment and Grade 10 final examination average marks for 62 Junior Secondary Schools for the period 2008-2010 were gathered and analyzed. Schools were characterized in terms of the relationship between their continuous assessment and final examination average marks for each of the three years. Phase 2, which was informed by Phase 1, took the form of structured interviews with a sample of three Mathematics teachers and three principals along with a focus-group interview of twelve teachers in order to investigate more deeply the perceptions of teachers and principals toward assessment policy and practice. The study shows that Grade 10 assessment practice in Namibian schools is far from ideal. Many teachers are not fully conversant with the various continuous assessment components as outlined by policy, and teachers are not confident about setting appropriate continuous assessment tasks. There is a strong perception that continuous assessment marks can easily be inflated and those teachers who gave high continuous assessment marks to their learners were generally perceived as being either incompetent or dishonest. While continuous assessment was seen as an important component of teaching and learning, it is evident that teachers and principals would welcome greater clarity, along with standardization and moderation, with respect to continuous assessment practice.
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Vaughn, Christy H. "Middle School Mathematics Students' Perspectives on the Study of Mathematics." ScholarWorks, 2011. https://scholarworks.waldenu.edu/dissertations/980.
Full textAbstract:
This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework of the study was grounded in philosophies of motivation, including achievement goal theory, self-worth theory, self-efficacy theory, expectancy-value theory, and attribution theory. The study used a phenomenological research design to answer the key research question, which focused upon the experiences of students and the meaning that was given to these experiences. Data were collected and analyzed from individual interviews with 9 students and a focus group session. The findings of the study revealed that participants' past experiences influenced their current attitudes about the study of mathematics. Perceptions of mathematical ability, history of success or failure with grades, and the influence of the teacher and peers in the learning environment most influenced students' attitudes about mathematics. Moreover, current feelings impact the degree to which a student puts forth effort in the study of mathematics, and the relationship with the mathematics teacher had the greatest impact on student attitudes. To improve the perceptions that students have about the study of mathematics, expanded professional development opportunities may bring increased awareness of students' perceptions of the study of mathematics, and develop remedial mathematics programs that remove the negative stigma associated with them. The research study could lead to social change as its purpose is to improve student achievement in mathematics through changes in the remedial mathematics program.
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Joseph, Jenead Diana Nicole. "Mathematics teachers’ experiences of the influence of the changing curriculum on their professional practice in grades 10 - 12 in the Cape Winelands district." Thesis, Cape Peninsula University of Technology, 2016. http://hdl.handle.net/20.500.11838/2495.
Full textAbstract:
Thesis (MEd (Education))--Cape Peninsula University of Technology, 2016.Education in South Africa is a concern to many stakeholders, including government, teachers, teacher unions and non-governmental organisations, owing to the poor academic performances of learners. Mathematics teachers, the focus of this study, are confronted with a constantly changing curriculum. Teachers are often targeted by the education authorities and general public as the primary cause of the poor outcomes of education in South Africa. This study considers the experiences of Grades 10–12 mathematics teachers in the Cape Winelands regarding curriculum change and its influence on their professional practice. The basic assumptions of social constructivism served as overarching theory. The researcher judged that a conceptual framework would make for a clearer and more systematic way of dealing with the constructs that underpin this study. The conceptual analysis framework, which was developed by combining the work of Rogan and Grayson, as well as that of Remillard, which is a perfect fit to this study, guided the interpretation and analysis of the data. A deductive approach in data analysis was applied in accordance with the conceptual framework used in this study. Being explorative in nature, this study is a qualitative design and therefore an interpretive methodological approach was followed. A purposive and convenience sampling method was used whereby teachers from six schools were pre-selected: two from ex-Model C schools, two from previously disadvantaged black schools and two from previously disadvantaged coloured schools. Semi-structured interviews were conducted. The findings of this study pointed to teachers’ acceptance of education reform and changes in the curriculum, provided they were not too radical. Teachers requested involvement on a broad spectrum throughout the planning and implementation process, and proper training and support prior to implementation. Factors that militated against implementation were, among others, poor facilities, resources and instructional aides; poorly trained change facilitators; poor leadership and management at schools; and the many constraints that the learners brought to the school and the classroom.
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Junius, Daniel Franscius, and Danie Junius. "How do teachers characterise their teaching for conceptual understanding and procedural fluency?: a case study of two teachers." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1001426.
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Over many years the practice or art of teaching Mathematics posed itself as, not only being different from the practice of teaching any other subject, but to have many challenges and opportunities that ask for exploration and understanding. Just after independence in 1990, Namibia has embarked upon a reform process for the entire education system. Many changes were brought about to create a uniform, equal system for all. However, many challenges still remain to be addressed. Mathematics education remains one of the key areas where Namibian teachers can contribute towards the improvement of the subject. Unsatisfactory results, under-qualified teachers, and a negative disposition towards Mathematics are some of the challenges. These challenges are not unique to Namibia. Across the globe psychologists, philosophers and educators continue to engage in debates and research projects in search of answers and solutions for the improvement of Mathematics education. Despite encountering numerous obstacles, many teachers are dedicated and achieve outstanding results with their learners. This thesis reports on a research project that focused on the Mathematics teaching practice of two teachers whose experiences can make a positive contribution to the improvement of Mathematics teaching in Namibia. Furthermore, this case study investigated and attempted to understand the Mathematics teaching practices of two proficient teachers who each claimed to have a specific and unique approach to teaching Mathematics. The one claimed to be mainly procedural in her Mathematics teaching, while the other one claimed to teach mainly in a conceptual manner. Both achieve very good results with their classes and attribute their own teaching orientations to a process of several experiences they went through as students and in their careers. The study revealed that both claims are substantiated and that each teacher was consistent in her claimed approach. Many challenges and constraints were encountered by both teachers, but in their unique and specific ways each teacher’s chosen teaching approach supported them to overcome these. It was evident from the findings that each teacher’s practice came about as an evolutionary process over an extended period of time. As many challenges and limitations are universal, it is believed that in sharing experiences, teachers can benefit from each other by improving their practice. It was clearly stated by both participants that the re-thinking of and reflecting on their own practices provided them with new insights and motivation. Peer support and sharing of practices contribute positively towards the improvement of the teachers’ classroom practices.
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Ngoepe, Mapula Gertrude. "Secondary mathematics teachers' classroom practices : a case study of three township schools in Gauteng Province, South Africa /." Curtin University of Technology, Science and Mathematics Education Centre, 2003. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=14369.
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While there have been enormous changes in the South African system of education since 1994, the legacy of apartheid and the different education of Black teachers is still evident in township schools. This study examined the practices of mathematics teaching in three township secondary schools by conducting a detailed investigation of eight teachers in three schools. Classroom observations and video recordings of teachers of Grades 10 to 12 served as the main data collection method. A sample of 12 lessons was analysed using the Secondary Teaching Analysis Matrix-Mathematics (STAM-Mathematics) (Gallagher & Parker, 1995) instrument. The researcher used STAM to categorise teachers' classroom practices along a three pronged continuum, namely didactic, transitional and conceptual teaching for the purpose of answering research questions about the content, the teaching, the assessment practices, the interactions between the teacher and the student, and the resource availability. Analysis of the data collected using the 22 STAM descriptors showed that the practices of teaching mathematics in township secondary schools was primarily didactic, with only minimal characteristics of transitional teaching and fewer attributes of conceptual teaching. Identifying the gaps between the teachers' practice and the descriptors for transitional and conceptual teaching with respect to the content, the teaching, the approaches to assessment, interactions between teacher and students, and resources availability has provided insight and a baseline for teacher inservice. Consequently, this study has provided research-based evidence for appropriate intervention to improve mathematics teaching and learning as prioritised by the Department of Education since the creation of the democratic government in 1994.It is recommended that mathematics teachers in township schools use the STAM instrument in pairs or groups to observe and analyse each other's lessons with particular focus on the 22 descriptors and to use this framework as a guideline for daily lesson preparations and to help guide the teachers from teacher-centred instruction to conceptual instruction. Further, the STAM could be incorporated into teacher education and professional development programs and thereby lead to more conceptual forms of teaching that could contribute towards a greater understanding of mathematics and ultimately raise the pass rate of learners in external examinations at Grade 12.
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Mulcahy, Diana Leonie. "A case study investigation of the use of a textbook in a secondary mathematics classroom : issues of regulation and control." Master's thesis, University of Cape Town, 1995. http://hdl.handle.net/11427/17500.
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Bibliography: pages 82-84.This dissertation is concerned with aspects of the role of the textbook in school mathematics. An attempt is made to uncover control strategies used by the teacher in textbook use in the classroom, and those implicit in a mathematics textbook. It is argued that these forms of regulation place constraints on the transformative role sometimes attributed to textbooks. The following research question is addressed: how does the teacher recruit the textbook in the classroom, how is he/she 'recruited' by it and how are both recruited by school mathematics? A case study methodology is described, involving a video-recording of a fifty minute mathematics lesson and a follow-up interview with the teacher. Transcriptions are used and a fine-grained analysis of data is attempted. A literature survey examines other research in the areas of content selection, content control and content expression. Content selection refers to choices and omissions, content control refers to sequencing, pacing and authority in the pedagogic relationship, and content expression includes verbal and textual modes of expressing content. Theoretical ideas are drawn from Bernstein (1976, 1991, 1993) and Dowling (1993). Although these works are methodologically different, they both describe aspects of regulation and control. Of particular interest are Bernstein's notions of classification and framing, and Dowling's ideas on discourse and procedure. The hypothesis is put forward here that there is a dialectical relationship involving the positioning of teacher and textbook. The teacher recruits the textbook to regulate pupils and knowledge, but s/he is at the same time constrained by strategies implicit in the textbook. In other words the teacher both positions and is positioned by the textbook. Both in tum are positioned by school mathematics. The data analysis examines the 'how', 'what' and 'who' of control. It considers the regulation of speech, silence, working and listening, as well as the sequencing, pacing, selecting, presenting and authorising of content. It argues that the teacher both recruits and is 'recruited' by the textbook, and that although the framing is strong and the teacher has a high degree of control in the pedagogic relationship, the classification is also strong and the teacher lacks control over what she can teach and the relationship between contents. The research concludes by suggesting that the transformative role sometimes attributed to the textbook is problematic. The strategies of regulation and control operating in the classroom, implicit in the textbook and in school mathematics, limit the possibilities of how textbooks can be used by the teacher and constrain transformation to a significant degree.
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Poon, Ying-ming, and 潘瑩明. "Dialogic learning: experiences in a mathematics club." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B47055467.
Full textAbstract:
The reformed Hong Kong mathematics curriculum for the 21st century consists of three components, namely generic skills, values and attitudes and, lastly, traditional cognitive development. The first two are newly emphasized and expanded. Theoretically, these components correspond closely with communication, socioculture and constructivism respectively, which are the central concepts of dialogic learning (DL). In DL, students are autonomously engaged in egalitarian dialogue, in which they share, reflect and form a learning community. Through DL, a student is expected to develop into an all-rounded and life-long learner. Contrary to the reform, dialogue is still deficient in mathematics classrooms. The role of this study is to present examples of students’ experiences in DL, found in the mathematics club of a secondary girls’ school.
This study aims to explore and investigate: (1) the existence of DL in the club, (2) what the members learnt and (3) how they did it. This is an ethnographic research, which emphasizes first hand understanding, grounded theories and thorough intricacies. Therefore, I observed the students’ activities as a participant, interviewed them, and then described, analyzed and interpreted my findings accordingly.
Based on my synthesis of relevant literature and the insight I gained from decades of teaching and otherwise interacting with students, I constructed a pentahedral framework to help investigate DL in a more comprehensive and intensive way. It involves the development of various generic skills and the cultivation of values and attitudes, which are usually unrecognized in examination syllabuses and the old curriculum. It consists of five facets, concerning cognitive knowledge, sharing and negotiation, learning skills, metacognition and values and attitudes.
And here are the findings. All significant elements of DL from literature have been identified to exist in the club. As for what the students learnt, they recalled fruitful experiences in all five facets of the DL pentahedron. These findings were then combined with the learning histories of three subjects to yield four representative learning patterns, namely those of a ‘cognitive developer’, a ‘communicative daily life explorer’, a ‘eureka torchbearer’ and a ‘frustrated sharer-explorer’.
These 4 learning patterns were further combined with (i) the purposes for mathematics study from pure examination results to ‘liberation’ and (ii) the understanding of mathematics learning from pure cognitive knowledge to inclusion of generic skills and values and attitude, to form a conceptual model of learning styles. The styles of the ‘eureka torchbearer’ and the ‘communicative daily life explorer’ were found to be exemplars of the ideals of people who favour the most liberal implementation of the curriculum reform. The ‘frustrated sharer-explorer’ was stuck with the style favoured by conservatives who are against hasty reforms. The ‘cognitive developer’ was somewhere in between.
These findings may contribute to the framework of policy debate on mathematics education. In the school and classroom level, they may help teachers overcome learning disaffection and other difficulties, in both theory and practice. Organizers of extracurricular activities may also be inspired by the students’ rich experiences of dialogic learning.published_or_final_version
Education
Doctoral
Doctor of Education