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The results reported here are the product of the research titled: Using history in the teaching of mathematics. The subjects are students in two classes of algebra II course at Florida State University High School-- 36 students-- makes and females whose ages are mostly 18 and a few 17 and 16 years old. Algebra II is a course that is usually taken by high school seniors in 12th grade and a few 11th or 10th grade students which explains why the ages of the students are mostly 18 and a few 17 and 16 years old. In this investigation, both quantitative study and qualitative study were employed. The quantitative study was the main study-- a teaching experiment using quasi-experimental methodology that involves two groups-- group 1 and group 2. Group 1 is the control group, where various algebraic/mathematical concepts, or topics were taught or explained to students with the necessary formulas. Group 2 was the experimental group in which the accounts of the historical origin of algebraic/mathematical concepts and the mathematicians (Lewis Carroll, Archimedes, Pythagoras, and Sophie Germain) who brought forward or created the concepts were used to augment pedagogical lessons and exercises used for this study as the main feature of pedagogy. The qualitative study augmented the main quantitative study; it was a follow-up interview for students to probe further an in-depth rationale for the research theme, using history in the teaching of mathematics. The statistical analysis results indicated that there is a significant difference in the mean of score for the control group students and the mean of scores of the experimental group is greater than the mean on scores of student's performance in the control group; and the interview questions responses indeed corroborate the fact that the use of history in teaching mathematics does improve learning and understanding of algebraic/mathematical concepts. / Typescript. / "Submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy." / Advisors: Elizabeth Jakubowski, Herbert Wills III, Professors Co-Directing Dissertation. / Includes bibliographical references (leaves 202-205).

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D.Litt. et Phil. (Applied Linguistics & Literary Theory) / In this thesis I wish to state the case for, and argue the merits of, the teaching of literature as an independent subject, in standards 6 to 10, in South African high schools. I shall therefore discuss the relevant sections of the Department of Education and Culture Core Syllabi for English Second Language and for English First Language Higher Grade for Standards 8, 9 and 10. These are the syllabi on which all present departments of education base their teaching and prescription of set works and the core syllabi also represent (being for the senior standards and the Higher Grade) the highest requirements set for English Second Language and for English 2First Language in South Africa. I shall also briefly discuss the Province of Cape of Good Hope Core Syllabus for English Literature, Standard Grade, Standards 8, 9, & 10 and the Province of Cape of Good Hope Kernsillabus vir Afrikaanse Letterkunde Standaardgraad, Standerds 8- 10. (While this thesis argues mainly from the point of view of English Second Language, the Kernsillabus vir Afrikaanse Letterkunde is included, because, at the moment, it is one of the only two literature syllabi available in South Africa.) From these syllabi I shall extract the present philosophy underlying the teaching of literature, and proceed to various purposes that can be served by literature as subject and I shall propose aims, learning content, prescribed material, methodology and testing methods for such teaching, because I believe that literature is enriching and: "Enrichment programs should be an organic part of the formal curriculum, not », optional extramural activities" (Mphahlele, 1990: 46).

M.A. / A review of research titles produced since 1985 at RAU indicates that no formal research has been conducted on the evaluation of the counselling psychology curriculum. An overview of the literature in this field indicates that the profession has not consolidated a unique identity, and its evolution continues since its inception in approximately 1890 together with the origination of the general field of psychology. It thus becomes difficult to define a standard counselling psychology curriculum in this changing growth process, and this study examines only a single curriculum while attempting to determine efficiency, effectiveness and relevance within the changing South African context. Thus while the literature and existing theoretical models served to provide some bench marks in the evaluation process in terms of current trends, the related needs of a diverse and changing South African population were also utilised. It was anticipated that this evaluation process would provide the training system with relevant feedback to be used for possible future implementation. Given the limitations of a dissertation the aim was not to conduct an empirical study, but rather to obtain as much useful information as possible by using a questionnaire with rating scales and open ended questions in order to best determine efficiency, effectiveness and relevance of the training curriculum. While the analysis of the results appears to show that students experienced overall satisfaction with training, except for some modules, a trend is also noted where the programme itself has evolved by better meeting the needs of students. However, it is indicated that the programme does not adequately prepare students for the demands of private practice, and that the emphasis is too academic and less applied, which results in producing adequate knowledge but inadequate skills. Serious consideration is found to be needed regarding the relevance of the curriculum in terms of the broader South African community and needs.

Undergraduate science, technology, engineering, and mathematics (STEM) education has been receiving a great deal of attention. Stakeholders in government as well as academic institutions recognize the significance of educational reform in STEM fields to improve student engagement, retention and proficiency. Boston University, through partnership with the Center for the Integration of Research, Teaching and Learning (CIRTL), offers graduate students the opportunity to perform an educational research project in a STEM course in the Teaching-as-Research (TAR) Fellowship. The main goal of a TAR project is to identify educational interventions that improve student outcomes. This study, being a TAR project, examines how scientific literacy of undergraduates enrolled in Introduction to Neuroscience (NE 101) at Boston University changes over the course of a semester in response to a three-skill intervention. Scientific literacy, broadly defined as the ability to leverage evidence and data to interpret scientific research and evaluate the significance of conclusions, has been promoted by academic institutions by some time. Be that as it may, best practices for teaching scientific literacy and standardized methods of measurement have yet to be explicitly outlined. There are, however, validated paradigms that are gaining momentum: The integrated STEM education model and the Test of Scientific Literacy Skills (TOSLS). Integrated STEM education incorporates multiple academic disciplines (within and outside STEM fields) and promotes application of knowledge to solving real-world problems. The TOSLS is an assessment tool in sync with this educational model; its purpose is to gauge students’ proficiency in nine key skills of scientific literacy by posing questions that require students to implement these skills in meaningful scenarios. In this study, I used a subset of the scientific literacy skills outlined in the TOSLS to design curriculum for the discussion component of NE 101. I also used pre- and post-intervention adaptations of the TOSLS for measuring students’ achievement of scientific literacy in addition to weekly quiz questions. However, another focus of this study was to highlight changes in students’ motivation and attitudes toward scientific inquiry pre- to post-intervention. Research conducted by Carberry et al. suggests that employing a variety of quantitative and qualitative measurements provides a more holistic picture of students’ learning. To this end, two focus groups were held and a post-course discussion survey was deployed at the end of the course. The quantitative and qualitative data collected from these instruments indicate vital points for STEM educators to consider when designing and implementing course curriculum, especially those courses oriented toward promoting scientific literacy in their student population. Major considerations include: 1. Design problem-based activities that integrate multiple scientific literacy skills 2. Incorporate scientific literature from non-primary sources and that is representative of students’ interests 3. Develop students’ competency in reading primary scientific literature by gradually increasing the difficulty of material 4. Provide students with an intuitive and explicit framework for deciphering primary scientific literature 5. Use formative assessment to identify students’ strengths and challenges; leverage strengths to improve upon areas of difficulty

The literature review shows that student alternative conceptions or misconceptions are important for teaching and learning. Causes of such student difficulties may include the counter-intuitive nature of some chemistry concepts or to instruction itself. However, over 30 years research into student conceptual difficulties has had little impact on teaching and learning chemistry. In this study, a critical analysis and synthesis of published research into student conceptions in acid-base chemistry was carried out in the naturalist nomothetic paradigm using a constructivist framework. Historical models which were included were an operational macroscopic model and the theoretical Arrhenius and Brønsted models. Firstly, a comprehensive search strategy with defined inclusion/exclusion criteria identified 42 suitable reports which were mostly peer-reviewed. The identified research was not limited to Anglophone countries although Africa and South America were underrepresented and research among secondary students predominated. Then a critique of the research showed it was of variable quality and often poorly reported. An outcome was a set of guidelines for research into student conceptions. The variable quality and reporting of research then also necessitated a four-level framework to reflect the stability of descriptions of student difficulties. A new method for synthesis of descriptions of student conceptual difficulties was developed which entailed mapping qualitative data on the difficulties, which had been extracted from research publications, to propositional knowledge statements derived in this study. This was an iterative process which simultaneously honed descriptions of difficulties and illuminated propositional knowledge implicated in them. The second major outcome was synthesized descriptions of 10 student difficulties with acid-base species, 26 difficulties with acid-base properties and 17 difficulties concerning terminology and symbolism particular to acid-base chemistry. Some conceptions were also found to have been mis-reported as ‘misconceptions’. The difficulties could be broadly due to student conceptions concerning acid-base models, or students not relating empirical observations to theoretical models or their poor understanding of underlying chemical principles. Some difficulties were found to have been over-researched, while further work was needed to clarify the nature some difficulties with conceptions of bases, acid-base reactions, and symbolism used in acid-base chemistry. The third major outcome from the synthesis was 218 propositional knowledge statements which were shown to be suitable for teaching high-school students, avoided hybrid historical models and were acceptable to expert chemists. These propositional statements were integrated as a set of 11 concept maps. The maps showed the hierarchy and interconnectedness of concepts as well as the propositional links which had been implicated in the difficulties. Furthermore the concept maps indicated critical concepts where teaching in each topic should focus as well as cross-linked concepts that can be used to integrate different aspects of the topic. Accordingly they contribute to PCK in the acidbase topic as they represent the fine-grained yet well integrated conceptual knowledge characteristic of a teacher with highly developed PCK. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.

The study was conducted to investigate whether the use of a wider range of teaching methods can improve the quality of environmental learning in five Zambian primary schools. Nine teachers from five schools were involved in the preliminary stage of answering of questionnaires, interviews and focus group discussions about the use of dominant teaching methods and new teaching methods; while only four were involved in the observations of four lessons. The study is a contribution to the on‐going debate on the investigation of whether teaching methods used by teachers can be one of the factors that can influence the quality of education. Definitions of quality and educational quality in particular, are not easy to establish and no agreed upon framework for educational quality exists at present. This study reviews the debates on educational quality, and identifies three major paradigms or discourses on educational quality; and considers the human rights, social justice and capabilities approaches and educational quality frameworks as being relevant to environmental learning and education for sustainable development in the Southern African Development Community context. This, together with a review of research on teaching methods in environmental education, provides the theoretical framework for this study. Using action research and an interpretative methodological framework, a series of research activities were undertaken to generate research data because the study was investigating the teachers’ practice with a view to probe change and to analyse the findings. Nine teachers participated in the preliminary stage of answering questionnaires and focus group interviews reflecting on existing teaching methods. In stage two of this study, teachers went through a planning workshop during which they planned lessons using new preferred teaching methods. The third stage was lesson observations of planned lessons. The final stage was the reflection workshop during which the teachers shared their experiences with the use of new teaching methods. The teaching practices of teachers using the new teaching methods were the subject of further analysis. In order to find out how the use of a wide range of teaching methods can improve quality of environmental learning in primary schools nine teachers were observed teaching lessons with new teaching methods. The Nikel and Lowe (2010) fabric of dimensions of educational quality was adapted and used to find out if teachers included dimensions of quality in the teaching process. Additional socio‐cultural and structural quality dimensions, identified through a review of southern African research, were used to find out if teachers included contextualized regional dimensions of educational quality. This was done to investigate whether the process of teaching and learning was relevant to the learners. Teachers involved in the research reflected that when they used a wider range of teaching methods the result was that the learning opportunities for learners were enhanced and that the methods added value to their teaching, improving the quality of their teaching. The use of a wider range of teaching methods showed the presence of several indicators of dimensions of educational quality, as reflected in the quality analysis tool. Teachers indicated that the use of a wider range of teaching methods led them to include the socio‐cultural dimensions such as the use of local languages and structural dimensions such as informal seating arrangements or group work that they would otherwise neglect if they used the traditional narrow range of teaching methods. A wider range of teaching methods provided learners with an enjoyable learning atmosphere during the lesson. The research also identified that this study can be taken further through broader observations, and that the educational quality dimensions tool is useful for different levels of the education system, and that it has potentially productive uses in teacher education, particularly for observations during teaching practice.

The Namibian government through the Ministry of Education seeks for teachers to meet the demands and rise to the challenges of the post-independence basic education system. Therefore the University of Namibia Education Faculty must ensure through the training of student teachers for both lower, upper primary and secondary school level that these demands are met. Research shows that one of the major challenges in teacher training programs, specifically in the mathematics education programmes, lies with the student teachers’ difficulties in dealing with various topics in mathematics, particularly fractions. The teaching of fractions is a challenging area at primary level and lays the foundation for understanding different topics in upper grades such as algebra, ratio and proportion, statistics and probability, to mention just a few. This study focused on an exploration of teaching fractions by five student teachers during their teaching practice.The main purpose was to gain an understanding of the experiences of the level 5-7 student teachers with regard to their practice of fraction teaching; their experience of the mathematics education course with respect to the teaching of fractions; and their prior experience related to fractions and fraction teaching at Grade 6 level. The findings from this research showed that student teachers viewed mathematics, specifically fractions, as just about doing calculations, doing drill and practice as in this way learners’ understanding of fractions is enhanced. The importance of using rules and procedures was emphasized as paving the way to mastering fractions. The data analysis also revealed that student teachers employed different teaching approaches when they considered learners’ prior knowledge. However, they misinterpreted the learner-centred approach in terms of group work and class discussion in their teaching of fractions. The data also revealed that some student teachers had an understanding of fractions as they managed to redirect their learners from applying some fraction misconceptions. The findings further showed that due to lack of understanding most of the participants experienced fear and anxiety in their fraction teaching; attempted an approach then reverted to old practices used in schools; taught fractions as symbolic representations where no meaning was involved; used incorrect terminologies such as ‘1 over 4’ or ‘1 out of 4’ instead of a ‘quarter’ or ‘one-fourth’. It is further revealed that the some student teachers viewed a fraction as a pair of two different whole numbers and can be broken apart. The findings of this study yielded one main implication for the teaching of mathematics: that the teacher training programs, specifically for mathematics teachers, must take into consideration the weaknesses and strengths of the student teachers shown in this study to properly train and prepare them to become effective mathematics teachers.

This study investigated the experiences of four participating student teachers in using multiple representative approaches in the teaching of Grade 6 proportion word problems. The multiple representative approaches include the Between Comparison Method, the Within Comparison Method, the Diagrammatic Method, the Table Method, the Graph Method, the Cross-product Method, and the Oral Informal Method. An intervention programme was organised, using workshops where student teachers were prepared to teach Grade 6 proportion word problems using multiple representative approaches. The teaching practice lessons of the four participating student teachers in two primary schools were video recorded, and the focus group interview was conducted at the University Campus. With the exception of the Graph Method and the Cross-product Method, it was revealed that the multiple representative approaches were generally effective in the teaching of Grade 6 proportion word problems. The study further revealed that multiplicative relationships can be explored through using the different individual representative approaches. The study argues that the cross-product method is not the only way to teach Grade 6 proportion word problems. There are multiple representative approaches that should be used in conjunction with each other to enhance the teaching of proportion word problems. Furthermore, this study revealed that a number of challenges were encountered when using multiple representative approaches. The challenges include difficulties with the English language, different and unique abilities of the learners, lack of plotting skills and the lack of proficiency in the learners’ multiplication and division skills. This study made recommendations on the integration of multiple representative approaches in the mathematics education curriculum and textbooks. It further recommended that in-service workshops for teachers and student teachers on the integration of multiple representative approaches in the teaching of Grade 6 proportion word problems should be initiated.