The theoretical part of the diploma thesis contains didactic analysis of word problems, that is the definition of a word problem, classification of word problems from various perspectives and methods of solving word problems, according to czech specialists in didactics of mathematics. The second part describes the teaching of mathematics at the secondary Waldorf schools with an emphasis on teaching in main lesson blocks. The core of the work lies in the experimental part which consists of two sections. The first section describes the preparation, implementation and evaluation of educational experiments on the subject of word problems. The educational experiment was conducted in the first class of the Waldorf lyceum in Prague in the academic year 2014/2015. All days of the main lesson block are described. Part of the reflection of the teacher and an observer who participated in the entire main lesson block is the part of thesis. The practical part continues with the pupil's solving strategies analysis. Pupils wrote a didactic test with word problems once before the teaching experiment and once after it. The analysis of each problem is following, in which the interesting phenomena that emerged in the pupils' solutions are explored. The conclusion summarises the main points of the research conducted...

This study sought to (a) investigate the effect of Van Hiele theory-based instruction on Grade 11 students’ geometric proofs learning achievement, (b) explore students’ views on their geometry learning experiences, and (c) develop a framework for better teaching and learning of Grade 11 Euclidean geometry theorems and non-routine geometric proofs. The study is based on Van Hiele’s theory of geometric thinking. The research involved a convenience sample of 186 Grade 11 students from four matched secondary schools in the Capricorn district of Limpopo province, South Africa. The study employed a sequential explanatory mixed-methods design, which combined quantitative and qualitative data collection methods. In the quantitative phase, a non-equivalent groups quasi-experiment was conducted. A Geometry Proof Test was used to assess students’ geometric proof construction abilities before and after the teaching experiment. Data analysis using non-parametric analysis of covariance revealed that students from the experimental group of schools performed significantly better than their counterparts from control group schools. In the qualitative phase, data were collected using focus group discussions and students’ diary records. Results revealed that the experimental group students had positive views on their geometry learning experiences, whereas students from the control group of schools expressed negative views towards the teaching of Euclidean geometry and geometric proofs in their mathematics classes. Based on the quantitative and qualitative data findings, it was concluded that in addition to organizing instruction according to the Van Hiele theory, teachers should listen to students’ voices and adjust their pedagogical practices to meet the expectations of a diverse group of students in the mathematics class. A framework for better teaching and learning of Grade 11 Euclidean geometry theorems and non-routine geometric proofs was thus developed, integrating students’ views and Van Hiele theory-based instruction. The study recommends that teachers should adopt the modified Van Hiele theory-based framework to enhance students’ mastery of non-routine geometric proofs in secondary schools.

This study focuses on challenges and prospects of the teaching of the Doppler Effect to grade 12 learners. The challenges of teaching the Doppler Effect were established and these findings influenced the development of activities. These activities were tested, refined and re-tested in an iterative cycle and finally provided prospects on teaching the Doppler Effect. Educational Design Research (EDR) was used to bridge theory and practice in education. This study was done in the Vhembe district in the Limpopo province. In the first cycle, questionnaires and interviews with 32 teachers and a subject advisor were used to establish the baseline with regards to the challenges of teaching the Doppler Effect. After the analysis of the data which forms the first cycle of EDR, the content and methodological problems faced by teachers when teaching the Doppler Effect were revealed. In the second cycle of the EDR, learning activities were developed that was informed by the analysis and tried out in 2 schools by learners and their teachers. Completed activity sheets were marked and the results were used to determine if there were a correlation between the activity sheets and the written test. Problems were documented and changes to the activities were again made and tried out in 10 schools by 216 learners with the help of 10 teachers. The data collected from the learners` work sheets were analysed. Pearson`s product moment correlation has shown that there is a statistically significant relationship (r = 0.65; p < 0.01) that exists between these design-research activities and solving of problems on the Doppler Effect. An instructional manual was developed comprising of the final activities. This was distributed amongst the district officials and teachers to assist them in the teaching of the Doppler Effect in the Vhembe district. / Physics / M.Sc.(Mathematics, Science and Technology Education)

This thesis deals with the use of the activating teaching approaches and their effectiveness for understanding and mastering the grammatical phenomena of adult students, mainly in the corporate courses for German language. The students of the corporate courses have their specific set of learning aspects, particularly in the field of their learning biography, motivation, and the learning process that distinguishes them from the school-age students. These students, usually at the language level from A1 to B1 (CEFR), require the acquisition of grammatical features to improve their language production. Grammatical phenomena are taught in this method of teaching using classical, complex and activating approaches. The empirical research of this thesis deals specifically with the activating teaching approaches in the corporate courses. It contains the observations of the individual corporate lessons using activating approaches as well as questionnaires filled in by participating students. The thesis concludes und evaluates the contribution of activating teaching approaches to the motivation during the lesson, the effect that they have on the understanding and acquisition of the given grammatical phenomena for the target group of adult students. For the thesis conclusion, there have been formulated five...

This qualitative study has investigated a month-long French-as-a-foreign-language summer program. Its goal was to compare teacher (n=4) and student (n=6) perspectives regarding learning objectives, challenges, and preferred teaching/learning approaches and methods, and to evaluate results against Whyte (2011), who argued that a schism in French university language teaching leads to the dominance of explicit (traditional teacher-fronted) instruction at the expense of more communicative teaching approaches. Data collection took place via classroom observations, pre-course interviews and surveys, a post-course teacher focus group, and weekly student reflective logs. A total of 2,211 references were coded to 276 thematic nodes. Results suggest that the teachers involved primarily embrace a traditional classroom dynamic but apply strategies associated with multiple methods, providing evidence for use of what has become known as the Eclectic Method. Some alignment was found between teachers and students concerning goals, challenges, and teaching approaches, and mixed support was obtained for Whyte’s claim regarding a deficit of communicative language teaching, in that both explicit and implicit teaching were observed. / Graduate

This study establishes a framework for the practice and the acquisition of mathematical knowledge. The natures of mathematics and rituals/ritual-like activities are examined compared and contrasted. Using a four-fold typology of core features, surface features, content features and functions of mathematics it is established that the nature of mathematics, its practice and the acquisition is typologically similar to that of rituals/ ritual-like activities. The practice of mathematics and its acquisition can hence be metaphorically compared to that of rituals/ritual-like activities and be enriched by the latter. A case study was conducted using the ritual metaphor at two levels to introduce and teach a topic within the current year eleven West Australian Geometry and Trigonometry course. In the first level, instructional materials were written using a ritual-like mentor-exemplar, exposition, replicate and extrapolate model (through the use of specially organised examples and exercises) based on the approaches of several mathematics text book authors as they attempted to introduce a topic new to the West Australian mathematics curriculum. / In the second level, the classroom instruction was organised using a ritual-like pattern with direct exemplar mentoring and exposition by the teacher followed by replication and extrapolation from the students. Embedded within this ritual-like process was the personal (and communal) engagement with each student vis-a-vis the establishment of the relationships between the referent concepts, procedures and skills. This resulted in the emergence of solution behaviours appropriate to specific tasks imitating and extrapolating the mentored solution behaviours of the teacher. In determining the extent to which the instruction, mentoring and acquisition was successful, each student's solution 'behaviour was compared "topographically" with the expected solution behaviour for the task at various critical points to determine the degree of congruence. Marks were allocated for congruence (or removed for incongruence), hence a percentage of congruence was established. The ritual-like model for the teaching and acquisition of mathematical knowledge required agreement with all stake-holders as to the purpose of the activity, expert knowledge on the part of the teacher, and within a classroom context requires students to possess similar levels of prerequisite mathematical knowledge. / This agreement and the presence of an expert practitioner, provides the affirmation and security that is inherent in the practice of rituals. The study concluded that there is evidence to suggest that some aspects of mathematical ability are wired into the cognitive structures of human beings providing support to the hypothesis that some aspects of mathematics are discovered rather than created. The physical origin of mathematical abilities and activities was one of the factors used in this study to establish an isomorphism between the nature and practice of mathematics with that of rituals. This isomorphism provides the teaching and learning of mathematics with a more robust framework that is more attuned to the social nature of human beings. The ritual metaphor for the teaching and learning of mathematics can then be used as a framework to determine the relative adequacies of mathematics curricula, mathematics textbooks and teaching approaches.

With the internationalization of English there is a growing demand for high quality English language education around the globe, particularly in non-English speaking countries. Consequently, there is an increasing demand worldwide for competent English teachers and more effective approaches to teaching and teacher professional development. In Egypt, in a context of educational reform where communicative language teaching approaches have been adopted as a way to improve teaching, this study explores how teachers perceive and respond to this call for change in instructional practices. It examines the professional development experiences of a group of English as a foreign language (EFL) and English-medium subject (EMS) teachers working in the private and public basic educational sectors in Cairo, Egypt. The research questions focus on teachers’ perceptions of change and improvement occurring in their teaching practices, their beliefs on the sources of change available to them, and the perspectives of school principals and professional development providers on teachers’ change prospects. In this study, a multi-method approach was applied, with a teacher survey administered to 174 teachers; in-depth, semi-structured interviews with 36 teachers, 15 principals, and 8 professional development (PD) providers; field observation; and examination of relevant documents and artifacts. The analysis of data is informed by sociocultural theory perspectives (Vygotsky, 1978). The findings indicate that (1) teachers perceive great change in their practices, though their conceptions and implementation of communicative approaches are context-bound, (2) teaching is influenced by various professional learning opportunities, and (3) change or lack thereof results from teachers’ adaptability to their local contextual demands through a process of resistance, resilience, or maintaining the status quo. The findings highlight the centrality of teachers in change processes.They suggest that change results from a process of interaction between teachers and other individuals within their community, and that the nature of change as experienced by the participants is shaped by a multitude of contextual factors. The implications of the study include the need to replace the technical conception of professional development with a more ecological orientation, to establish professional learning communities among teachers and within schools, and to establish a coherent framework for change initiatives.

With the internationalization of English there is a growing demand for high quality English language education around the globe, particularly in non-English speaking countries. Consequently, there is an increasing demand worldwide for competent English teachers and more effective approaches to teaching and teacher professional development. In Egypt, in a context of educational reform where communicative language teaching approaches have been adopted as a way to improve teaching, this study explores how teachers perceive and respond to this call for change in instructional practices. It examines the professional development experiences of a group of English as a foreign language (EFL) and English-medium subject (EMS) teachers working in the private and public basic educational sectors in Cairo, Egypt. The research questions focus on teachers’ perceptions of change and improvement occurring in their teaching practices, their beliefs on the sources of change available to them, and the perspectives of school principals and professional development providers on teachers’ change prospects. In this study, a multi-method approach was applied, with a teacher survey administered to 174 teachers; in-depth, semi-structured interviews with 36 teachers, 15 principals, and 8 professional development (PD) providers; field observation; and examination of relevant documents and artifacts. The analysis of data is informed by sociocultural theory perspectives (Vygotsky, 1978). The findings indicate that (1) teachers perceive great change in their practices, though their conceptions and implementation of communicative approaches are context-bound, (2) teaching is influenced by various professional learning opportunities, and (3) change or lack thereof results from teachers’ adaptability to their local contextual demands through a process of resistance, resilience, or maintaining the status quo. The findings highlight the centrality of teachers in change processes.They suggest that change results from a process of interaction between teachers and other individuals within their community, and that the nature of change as experienced by the participants is shaped by a multitude of contextual factors. The implications of the study include the need to replace the technical conception of professional development with a more ecological orientation, to establish professional learning communities among teachers and within schools, and to establish a coherent framework for change initiatives.

This study focuses on challenges and prospects of the teaching of the Doppler Effect to grade 12 learners. The challenges of teaching the Doppler Effect were established and these findings influenced the development of activities. These activities were tested, refined and re-tested in an iterative cycle and finally provided prospects on teaching the Doppler Effect. Educational Design Research (EDR) was used to bridge theory and practice in education. This study was done in the Vhembe district in the Limpopo province. In the first cycle, questionnaires and interviews with 32 teachers and a subject advisor were used to establish the baseline with regards to the challenges of teaching the Doppler Effect. After the analysis of the data which forms the first cycle of EDR, the content and methodological problems faced by teachers when teaching the Doppler Effect were revealed. In the second cycle of the EDR, learning activities were developed that was informed by the analysis and tried out in 2 schools by learners and their teachers. Completed activity sheets were marked and the results were used to determine if there were a correlation between the activity sheets and the written test. Problems were documented and changes to the activities were again made and tried out in 10 schools by 216 learners with the help of 10 teachers. The data collected from the learners` work sheets were analysed. Pearson`s product moment correlation has shown that there is a statistically significant relationship (r = 0.65; p < 0.01) that exists between these design-research activities and solving of problems on the Doppler Effect. An instructional manual was developed comprising of the final activities. This was distributed amongst the district officials and teachers to assist them in the teaching of the Doppler Effect in the Vhembe district. / Physics / M.Sc. (Mathematics, Science and Technology Education)

The fact that people tend to alternate between languages for various communicative purposes seems to increasingly interest researchers all over the world. Thus, the linguistic phenomenon of codeswitching has been given more academic attention in recent years than ever before. This particular topic has also been infused by new research because of an ongoing pedagogic debate about whether languages other than the target language should be used in foreign languages classroom or not. The debate consists of two major opinions. On one side, adherents claim that use of non-target languages limits natural target language-input and therefore damages the learning process. On the other, it is argued that non-target languages may even be beneficial for the learning process since they carry many pedagogic opportunities with them otherwise gone lost. This paper aims to find out how, and to what extent, foreign language teachers at a Swedish for Immigrants-school codeswitch into English in class. Moreover, it is also of interest to investigate how they think about their own codeswitching and how their reasoning may reflect their codeswitching self-awareness. In search for answers to these questions, three teachers have been observed in class. Later, the teachers have been interviewed to reflect upon their own codeswitching. The study revealed clear differences in the teachers’ codeswitching and codeswitching-reasoning, However, similarities were also found, and that all three teachers shared the main objective to develop their students’ communicative competence. Moreover, they also proved to have a rather realistic picture their own codeswitching. Not only were they able to roughly estimate how, and how much, they each codeswitched. Their individual results also went in line with their reasoning to a high extent, suggesting that they all have a high degree of codeswitching self-awareness.