Academic literature on the topic 'Mathematics Study and teaching (Secondary) Victoria Case studies'

ABSTRACT: Teacher performance has been the focus of educational policy reforms in recent decades for the professional development of teachers. The purpose of this study was to determine the effect of teaching experience and peer teaching skills on basic training on ECE teacher performance. This research uses ex-post facto quantitative method of comparative analysis and design by level. The population is all ECE teachers who attend basic-level education and training in Tangerang Regency, totaling 3358 people consisting of 116 male teachers and 3,242 female teachers. Data collection techniques using a questionnaire with data analysis include descriptive analysis. Requirements test analysis and inferential analysis. The results show that there are differences in the performance of ECE teachers between teachers with more than five years of teaching experience and less than five years, in the group of ECE teachers with high peer teaching skills and low peer teaching skills. The implication of this research is that it is hoped that various parties will become more active in aligning ECE teacher training so that it can improve the performance of ECE teachers. Keywords: teaching experience, peer teaching ability, tiered basic training, ECE teacher performance References: Adeyemi, T. (2008). Influence of Teachers’ Teaching Experience on Students’ Learning Outcomes in Secondary Schools in Ondo State, Nigeria. African Journal of Educational Studies in Mathematics and Sciences, 5(1), 9–19. https://doi.org/10.4314/ajesms.v5i1.38609 Ahmad, N. J., Ishak, N. A., Samsudin, M. A., Meylani, V., & Said, H. M. (2019). Pre-service science teachers in international teaching practicum: Reflection of the experience. Jurnal Pendidikan IPA Indonesia, 8(3), 308–316. https://doi.org/10.15294/jpii.v8i3.18907 Andrin, G. R., Etcuban, J. O., Watin, A. K. O., Maluya, R., Rocha, E. D. V, & Maulit, A. A. (2017). Professional Preparation and Performance of Preschool Teachers in the Public and Private Schools of Cebu City, Philippines. ACADEME, 10. Andrin, Glenn R, Etcuban, J. O., Watin, A. K. O., Maluya, R., Rocha, E. D. V, & Maulit, A. A. (2017). Professional Preparation and Performance of Preschool Teachers in the Public and Private Schools of Cebu City, Philippines. ACADEME, 10. Armytage, P. (2018). Review of the Victorian Institute of Teaching. Bichi, A. A. (2019). Evaluation of Teacher Performance in Schools: Implication for Sustainable Evaluation of Teacher Performance in Schools: Implication for Sustainable Development Goals. December 2017. Campolo, M., Maritz, C. A., Thielman, G., & Packel, L. (2013). An Evaluation of Peer Teaching Across the Curriculum: Student Perspectives. International Journal of Therapies and Rehabilitation Research, 2(1), 1. https://doi.org/10.5455/ijtrr.00000016 Clearinghouse, W. W. (2018). National Board for Professional Teaching Standards Certification. Colthart, I., Bagnall, G., Evans, A., Allbutt, H., Haig, A., Illing, J., & McKinstry, B. (2008). The effectiveness of self-assessment on the identification of learner needs, learner activity, and impact on clinical practice: BEME Guide no. 10. Medical Teacher, 30(2), 124–145. Darling-Hammond, L. (2011). Teacher quality and student achievement. Teacher Quality and Student Achievement, 8(1), 1–215. https://doi.org/10.14507/epaa.v8n1.2000 Donaldson, M. L. (2009). So long, Lake Wobegon? Using teacher evaluation to raise teacher quality. Center for American Progress, 1–32. Fogaça, N., Rego, M. C. B., Melo, M. C. C., Armond, L. P., & Coelho, F. A. (2018). Job Performance Analysis: Scientific Studies in the Main Journals of Management and Psychology from 2006 to 2015. Performance Improvement Quarterly, 30(4), 231–247. https://doi.org/10.1002/piq.21248 Frye, E. M., Trathen, W., & Koppenhaver, D. A. (2010). Internet workshop and blog publishing: Meeting student (and teacher) learning needs to achieve best practice in the twenty-first-century social studies classroom. The Social Studies, 101(2), 46–53. Hanushek, E. A. (2011). The economic value of higher teacher quality. Economics of Education Review, 30(3), 466–479. Heryati, Y., & Rusdiana, A. (2015). Pendidikan Profesi Keguruan. Bandung: CV Pustaka Setia. John P. Papay Eric S. Taylor John H. Tyler Mary Laski. (2016). Learning Job Skills From Colleagues At Work: Evidence From A Field Experiment Using Teacher Performance Data (p. 49). Katz, L. G., & Raths, J. D. (1985). Dispositions as goals for teacher education. Teaching and Teacher Education, 1(4), 301–307. Kavanoz, S., & Yüksel, G. (2015). An Investigation of Peer-Teaching Technique in Student Teacher Development An Investigation of Peer-Teaching Technique in Student Teacher Development. June 2010. Kurniawan, A. R., Chan, F., Sargandi, M., Yolanda, S., Karomah, R., Setianingtyas, W., & Irani, S. (2019). Kebijakan Sekolah Dalam Penggunaan Gadget di Sekolah Dasar. Jurnal Tunas Pendidikan, 2(1), 72–81. Lim, L. L. (2014). A case study on peer-teaching. Open Journal of Social Sciences, 2(08), 35. Manchishi, P. C., & Mwanza, D. S. (2016). Teacher Preparation at the University of Zambia: Is Peer Teaching Still a Useful Strategy? International Journal of Humanities, Social Sciences and Education, 3(11), 88–100. https://doi.org/10.20431/2349-0381.0311012 Mansur, M. (2007). KTSP: Pembelajaran Berbasis Kompetensi dan Kontekstual, Jakarta: PT. Bumi. Marais, P., & Meier, C. (2004). Hear our voices: Student teachers’ experiences during practical teaching. Africa Education Review, 1(2), 220–233. https://doi.org/10.1080/18146620408566281 McFarland, J., Hussar, B., Wang, X., Zhang, J., Wang, K., Rathbun, A., Barmer, A., Cataldi, E. F., & Mann, F. B. (2018). The Condition of Education 2018. NCES 2018-144. National Center for Education Statistics. Meilanie, R. S. M., & Syamsiatin, E. (2020). Multi Perspectives on Play Based Curriculum Quality Standards in the Center Learning Model. Jurnal Pendidikan Usia Dini, 14(1), 15–31. Michael Luna, S. (2016). (Re)defining “good teaching”: Teacher performance assessments and critical race theory in early childhood teacher education. Contemporary Issues in Early Childhood, 17(4), 442–446. https://doi.org/10.1177/1463949116677932 Morgan, G. B., Hodge, K. J., Trepinski, T. M., & Anderson, L. W. (2014). The Stability of Teacher Performance and Effectiveness: Implications for Policies Concerning Teacher Evaluation Grant. Mulyasa, E. (2013). Uji kompetensi dan Penilaian Kinerja guru. Bandung: PT Remaja Rosdakarya. Nasrun, Dr., & Ambarita, D. F. P. (2017). The Effect of Organizational Culture and Work Motivation on Teachers Performance of Public Senior High School in Tebing Tinggi. Atlantis Press, 118, 320–326. https://doi.org/10.2991/icset-17.2017.53 Nguyen, M. (2013). Peer tutoring as a strategy to promote academic success. Research Brief. Noelke, C., & Horn, D. (2010). OECD Review on Evaluation and Assessment Frameworks for Improving School Outcomes-Hungary Country Background Report. OECD: PARIS. OECD. (2005). Teacher’s matter. Attracting, developing, and retaining effective teachers. Paris. OECD-Education Committee. Pablo Fraser, Gabor Fülöp, M. L. and M. S. D. (2018). I.  What teachers and school leaders say about their jobs. TALIS, 2, 1–7. Parihar, K. S., Campus, D., Principal, J., & Campus, D. (2017). Study Of Effect Of Pre Teaching Training Experience On. 5, 59–62. https://doi.org/10.5281/zenodo.1039595 Parsons, S. A., Vaughn, M., Scales, R. Q., Gallagher, M. A., Parsons, A. W., Davis, S. G., Pierczynski, M., & Allen, M. (2018). Teachers’ instructional adaptations: A research synthesis. Review of Educational Research, 88(2), 205–242. Pillay, R., & Laeequddin, M. (2019). Peer teaching: A pedagogic method for higher education. International Journal of Innovative Technology and Exploring Engineering, 9(1), 2907–2913. https://doi.org/10.35940/ijitee.A9106.119119 Popova, A., Evans, D. K., & Arancibia, V. (2018). Training Teachers on the Job What Works and How to Measure It. Policy Research Working Paper, September 2016. Ramadoni, W., Kusmintardjo, K., & Arifin, I. (2016). Kepemimpinan Kepala Sekolah dalam Upaya Peningkatan Kinerja Guru (Studi Multi Kasus di Paud Islam Sabilillah dan Sdn Tanjungsari 1 Kabupaten Sidoarjo). Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 1(8), 1500–1504. Rees, E. L., Quinn, P. J., Davies, B., & Fotheringham, V. (2016). How does peer teaching compare to faculty teaching? A systematic review and meta-analysis. Medical Teacher, 38(8), 829–837. Sawchuk, S. (2015). Teacher evaluation: An issue overview. Education Week, 35(3), 1–6. Skourdoumbis, A. (2018). Theorising teacher performance dispositions in an age of audit. 1–16. https://doi.org/10.1002/berj.3492 Springer, M. G., Swain, W. A., & Rodriguez, L. A. (2016). Effective teacher retention bonuses: Evidence from Tennessee. Educational Evaluation and Policy Analysis, 38(2), 199–221. Staiger, D. O., & Rockoff, J. E. (2010). Searching for effective teachers with imperfect information. Journal of Economic Perspectives, 24(3), 97–118. Suyatno, H., & Pd, M. (2008). Panduan sertifikasi guru. Jakarta: PT Macanan Jaya Cemerlang. ten Cate, O. (2017). Practice Report / Bericht aus der Praxis: Peer teaching: From method to philosophy. Zeitschrift Fur Evidenz, Fortbildung Und Qualitat Im Gesundheitswesen, 127–128, 85–87. https://doi.org/10.1016/j.zefq.2017.10.005 Thurlings, M., & den Brok, P. (2018). Student teachers’ and in-service teachers’ peer learning: A realist synthesis. Educational Research and Evaluation, 24(1–2), 13–50. https://doi.org/10.1080/13803611.2018.1509719 Toch, T., & Rothman, R. (2008). Rush to Judgment: Teacher Evaluation in Public Education. Education Sector Reports. Education Sector. Ünal, Z., & Unal, A. (2012). The Impact of Years of Teaching Experience on the Classroom Management Approaches of Elementary School Teachers. International Journal of Instruction, 5(2), 41–60. Vasay, E. T. (2010). The effects of peer teaching in the performance of students in mathematics. E-International Scientific Research Journal, 2(2), 161–171. Weisberg, D., Sexton, S., Mulhern, J., Keeling, D., Schunck, J., Palcisco, A., & Morgan, K. (2009). The widget effect: Our national failure to acknowledge and act on differences in teacher effectiveness. New Teacher Project. Winters, M. A., & Cowen, J. M. (2013). Would a value‐added system of retention improve the distribution of teacher quality? A Simulation of Alternative Policies. Journal of Policy Analysis and Management, 32(3), 634–654.

Interactive whiteboard offers a high-potential innovative tool in mathematical educational environments, in which teachers’ modeling processes and students’ exploring activities can easily be executed. Nevertheless, these affordances are not self-evident. There is a gap between the potential claims of the tool and its actual use in the classrooms. This study investigated, through two parallel case studies, the interactive whiteboard potential in view of optimizing the exploitation of the interactive whiteboard, improving conceptual understanding, and fostering interactivity in secondary mathematics classrooms. Two main patterns for a productive interactive whiteboard use emerged: (a) a problem-solving pattern consisting of interactive whiteboard supporting problem-solving activities and (b) an organizer pattern consisting of using interactive whiteboard as a kind of advanced organizer and stimulating students’ reflection and mathematical contributions. The two patterns were used to design and teach lessons that were analyzed through the instrumental orchestration framework elaborated by Drijvers, Tacoma, Besamusca, Doorman, and Boon. Analysis showed how the interactive whiteboard acted as a useful instrument for students’ discussion and collective construction of mathematical knowledge.

Professional organizations have provided recommendations for mathematics teaching and learning; however, few studies have investigated the practical integration of those recommendations into mathematics teacher education programs. In this study, we examine how the reported “big ideas” of courses in secondary mathematics teacher education programs emphasized the content and teaching practices necessary for future mathematics teachers, as recommended by policy documents. As part of a larger study, we conducted a series of interviews in secondary mathematics teacher education programs at four universities (names are descriptive pseudonyms): Great Lakes University (GLU), Midwestern Research University (MRU), Midwestern Urban University (MUU), and Southeastern Research University (SRU). We selected the institutions and programs based on their Carnegie Classification, the types of communities in which they were situated, the average number of graduates from a program, the departmental homes of their secondary mathematics education programs, and the demographics of their student populations. The analysis of data collected from 12 courses across four universities revealed specific ways in which big ideas in secondary mathematics teacher education programs emphasized areas related to mathematics learning, teaching, and issues of equity and access.

This study presents findings from multiple case studies undertaken in three secondary schools in South Africa’s Limpopo Province. The goal was to collect input from students on mathematics teaching practices in their classrooms. The study included a self-selected sample of eleven grade 12 students. Unstructured individual interviews and students’ written reports were used to collect data, which was then analyzed based on emerging themes. Students expressed genuine concerns about teachers’ lesson preparation, subject and pedagogical knowledge, classroom management, attention given to slow learners, quality of classwork and homework tasks given to students, exam preparation, class attendance, and utilization of contact time, teachers’ attitudes, and their emotional intelligence, among others. Based on the study’s findings, the author suggests that student evaluation of teaching be used in secondary schools to help teachers reflect on their teaching practices in order to create learning environments that most students would enjoy.

Purpose – Given that students were out of school in response to the COVID-19 pandemic public health measures, traditional teaching practices have been forced to switch to online mediated learning environments. This study represents the first research effort to capture the experience of Malaysian mathematics teachers about their teaching during the pandemic. This includes investigating digital education tools mathematics teachers used, issues they encountered, and the knowledge and skills they need to improve during the enforced online teaching situation. Methodology – This study employed a survey design and qualitative data were collected using an online questionnaire. A total of 202 primary and secondary mathematics teachers from Malaysia participated in the study. The data were analysed through thematic analysis and descriptive statistics. Findings – First, it was found that the mathematics teachers employed a variety of digital education tools during the pandemic and the most commonly used tool was WhatsApp. Second, the top two issues faced by the teacher respondents were due to internet problems and students’ engagement during the online learning. A particular striking finding revealed that three-fifths of the teacher respondents who were concerned about the issue of students’ engagement were secondary mathematics teachers. Third, findings of the study further clarified that most of the teacher respondents wanted to improve their technological skills. Significance – This study supports mathematics teachers in making informed decisions about their teaching during school closures. The findings of this study also serve to alert the education sector about the issues related to the implementation of online education in times of the pandemic. In general, this study necessitates in developing preparedness for future pandemics.

Abstract Analysis of the experimental results presented in the following chapter reveals experiences with introduction of active learning methods in basic mathematics courses at the Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava. Experiment was implemented in the academic year 2018/19, in basic courses Mathematics I and Mathematics II scheduled in the first year of bachelor study programs and in subject Basics of Statistical Analysis for bachelor students in the second year of their studies. The aim of the experiment was to find achieved level of knowledge acquisition and to compare abilities of students to solve mathematical problems individually or by collective work and collaboration in small groups. Anonymous questionnaire answered by students after completion of the experiment provided rich feedback and overview of their opinions, from which their attitudes towards different teaching methods applied in 3 compulsory subjects from their study programs could be deduced and summarised. Based on received data, research analysed also results that students achieved comparing their achievement from the secondary schools and in both maths courses at the university.

Limited studies investigate the high school teachers’ challenges and ­strategies while teaching science and mathematics in English as the target language through the ­content and ­language integrated learning (CLIL) approach. Hence, this study aimed to ­investigate the ­challenges that science and math teachers encounter and the strategies they employ while fostering students’ development of proficiency in English as the target language in ­physics, ­chemistry, biology, and mathematics courses in the International General Certificate of ­Secondary ­Education (IGCSE) and International Baccalaureate Diploma Program (IBDP). The study utilized ­various qualitative tools such as semi-structured interviews, open-ended ­questionnaires, and lesson ­observations to analyze science and math teachers’ strategies and challenges at a case school in eastern Turkey. The study revealed that as part of the CLIL approach, the ­participant teachers indicated various challenges such as a lack of vocabulary repertoire, translation ­problems, and weak foundational knowledge. They used common strategies such as group work ­interactions, interdisciplinary activities, individualized feedback, the promotion of higher-order thinking skills, inquiry-based learning, and reinforcement of language used to deal with these ­challenges. The study presents further implications for good practices and recommendations to resolve ­challenges.

The purpose of this article is to specify whether there is any influence of school practices towards mathematics self-efficacy and mathematics outcomes. The studies about the effect of school practice on student achievement have a long history both domestically and abroad. However, the investigation of how the social context of school and practices affect student performance is not clear, especially in mathematics. To investigate this, I will chose al-touri secondary school where I teach as a case-study for my research. The instrument use for the article will be based on a questionnaire, which contains 2 sections. Section 1 will contain “School Level Environment Questionnaire” (SLEQ). Section 2 will contain “Mathematic Self-efficacy Questionnaire” (MSEQ). The mathematic scores of students will be taken for the first and second semester to compare between them and to see if there is a significant relationship between school practices and mathematics self-efficacy and mathematics outcomes. The findings indicate that there is a significant difference in students’ perception about their school practice and mathematic self-efficacy based on their achievement and according to ANOVA test, there is a relationship between school practices and mathematic self-efficacy. The result from this study can be generalized to the population of all schools in the Arab Sectors in Israel. Moreover, we can use the questionnaires obtained in the study to identify the strengths and weaknesses of schools in their teaching and learning process and to focus on improving their latter, at the same time maintaining the strength of their teaching strategies.

The purpose of this article is to specify whether there is any influence of school practices towards mathematics self-efficacy and mathematics outcomes. The studies about the effect of school practice on student achievement have a long history both domestically and abroad. However, the investigation of how the social context of school and practices affect student performance is not clear, especially in mathematics. To investigate this, I will chose al-touri secondary school where I teach as a case-study for my research. The instrument use for the article will be based on a questionnaire, which contains 2 sections. Section 1 will contain “School Level Environment Questionnaire” (SLEQ). Section 2 will contain “Mathematic Self-efficacy Questionnaire” (MSEQ). The mathematic scores of students will be taken for the first and second semester to compare between them and to see if there is a significant relationship between school practices and mathematics self-efficacy and mathematics outcomes. The findings indicate that there is a significant difference in students’ perception about their school practice and mathematic self-efficacy based on their achievement and according to ANOVA test, there is a relationship between school practices and mathematic self-efficacy. The result from this study can be generalized to the population of all schools in the Arab Sectors in Israel. Moreover, we can use the questionnaires obtained in the study to identify the strengths and weaknesses of schools in their teaching and learning process and to focus on improving their latter, at the same time maintaining the strength of their teaching strategies.

This study focuses on the statistical analysis of the performance of students of different ages in solving electricity problems, after learning Physical Matter Sciences (PMS), Chemical Matter Sciences (CMS), Mathematical Sciences and Applications (MSA) and Mathematical and Computer Sciences (MCS) programs in the first year at Ibn Tofail University in Morocco. The student’s scores were obtained in mathematics (analysis and algebra), French, and electricity exams in terms of the 2017/2018 year. The data collected from the written student responses in the electricity exams were analyzed by SPSS software (version 25) using the multiple correspondence analysis method to study the influence of diverse variables: gender (M/F), age, and performance in analysis, algebra and French. The Cronbach's alpha coefficient (0.81) reflects the consistency and reliability of the used method, where 50% of the variability is explained by Dimension 1, and 36% is explained by Dimension 2. The discussion is made on the basis of previous studies conducted in secondary and university cycles of various contexts. It was found that students who perform better in solving electricity problems do not necessarily have a high level in the French teaching language. The teaching language correlates weakly with students' performance in solving electricity problems and their learning electrical concepts and phenomena. A positive correlation between performance in mathematics, particularly algebra, and performance in electricity is confirmed as stated elsewhere. So, the learning electricity at the university level cannot be done without deep mathematical knowledge. The analysis showed that the performance in electricity was not affected by the gender and age of the students.

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.

This study is inspired by and utilises the van Hiele theory of geometric thought levels, currently acclaimed as one of the best frameworks for studying teaching and learning processes in geometry. The study aims both to explore and explicate the van Hiele levels of geometric thinking of a selected group of grade 10, 11 and 12 learners in Nigerian and South African schools. The study further aims to provide a rich and indepth description of the geometry instructional practices that possibly contributed to the levels of geometric conceptualisation exhibited by this cohort of high school learners. This collective case study, presented in two volumes, is oriented within an interpretive research paradigm and characterised by both qualitative and quantitative methods. The sample for the study comprised a total of 144 mathematics learners and 6 mathematics teachers from Nigeria and South Africa. They were selected using both purposive and stratified sampling techniques. In using the van Hiele model to interrogate both learners’ levels of geometric conceptualisation and teaching methods in geometry classrooms, the study employs a qualitative and qunatitative approach to the data-collection process, involving the use of questionnaires (in the form of various pen-and-paper tests, hands-on activity-based tests), interviews and classroom videos. Although the data analysis was done largely through descriptive statistics, the whole process inevitably incorporated elements of inferential statistics (e.g. ANOVA and Tukey HSD post-hoc test) in the quest for indepth analysis and deeper interpretation of the data. Learners were assigned to various van Hiele levels, mainly according to Usiskin’s (1982) forced van Hiele level determination scheme. The whole process of analysing the classroom videos involved a consultative panel of 4 observers and 3 critical readers, using the checklist of van Hiele phase descriptors to guide the analysis process. Concerning learners’ levels of geometric conceptualisation, the results from this study reveal that the most of the learners were not yet ready for the formal deductive study of school geometry, as only 2% and 3% of them were respectively at van Hiele levels 3 and 4, while 47%, 22% and 24% were at levels 0, 1 and 2, respectively. More learners from the Nigerian subsample (53%) were at van Hiele level 0 than learners from the South African subsample (41%) at this level. No learner from the Nigerian subsample was at van Hiele level 4, while 6% of the South African learners were at level 4. In general, learners from the Nigerian subsample had a poorer knowledge of school geometry than their peers from the South African subsample, as learners from the latter subsample obtained significantly higher mean scores in the van Hiele Geometry Test (VHGT) and each of the other tests used in this study. Results relating to gender differences in performance generally favour the male learners in this study. For each of the participating schools, learners’ van Hiele levels (as determined by their scores on the VHGT) strongly correlate with their performance in geometry content tests and mathematics generally. For each of the Nigerian and South African subsamples, for n ≤ 2, learners at van Hiele level n obtained higher means on nearly all the tests administered in this study than their peers at level n–1. This finding provides support for the hierarchical property of the van Hiele levels.

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.

I embarked upon this study to investigate mathematics teachers' practices that have led to the persistence of traditional teaching methods in grade 9 mathematics classrooms in Rundu. The study was conducted from a learner-centred (L-C) perspective or reform approach in the Namibian context. It is a qualitative study oriented in the interpretive paradigm- a paradigm that seeks to understand the meanings attached to human actions. The participants involved in this study were purposively selected and they are composed of two mathematics teachers and their grade 9 learners. This study was conducted at two schools in Rundu. One is an urban school while the other one is a rural school on the outskirts of Rundu. The research tools employed in this study are questionnaires, interviews and observations. The questionnaires were used to identify and select my participants while the observations were used to investigate the participants teaching strategies. The purpose of the interviews was mainly to investigate teachers' understanding, interpretation and implementation of learner-centre education (LCE). Amongst other findings, this study reveals that inadequate teacher-training, controversial educational policies and challenges such as overcrowdedness in mathematics classrooms, lack of teaching and learning materials, lack of cooperation among mathematics teachers and learners' negative attitude towards mathematics are some of the contributing factors to the persistence of traditional teaching methods in mathematics classrooms. Moreover, the study reveals that the persistence of traditional teaching methods in mathematics classes can no longer be attributed to the lack of understanding of LCE. The teachers in this study seem to be well acquainted with the theoretical aspect of the LCE framework while the implementation aspect seems to be a concern.

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.

The Australian Catholic University (ACU National at www.acu.edu.au) is a public university funded by the Australian Government. There are six campuses across the country, located in Brisbane, Queensland; North Sydney, New South Wales; Strathfield, New South Wales; Canberra, Australian Capital Territory (ACT); Ballarat, Victoria; and Melbourne, Victoria. The university serves a total of approximately 27,000 students, including both full- and part-time students, and those enrolled in undergraduate and postgraduate studies. Through fostering and advancing knowledge in education, health, commerce, the humanities, science and technology, and the creative arts, ACU National seeks to make specific and targeted contributions to its local, national, and international communities. The university explicitly engages the social, ethical, and religious dimensions of the questions it faces in teaching, research, and service. In its endeavors, it is guided by a fundamental concern for social justice, equity, and inclusivity. The university is open to all, irrespective of religious belief or background. ACU National opened its doors in 1991 following the amalgamation of four Catholic tertiary institutions in eastern Australia. The institutions that merged to form the university had their origins in the mid-17th century when religious orders and institutes became involved in the preparation of teachers for Catholic schools and, later, nurses for Catholic hospitals. As a result of a series of amalgamations, relocations, transfers of responsibilities, and diocesan initiatives, more than twenty historical entities have contributed to the creation of ACU National. Today, ACU National operates within a rapidly changing educational and industrial context. Student numbers are increasing, areas of teaching and learning have changed and expanded, e-learning plays an important role, and there is greater emphasis on research. In its 2005–2009 Strategic Plan, the university commits to the adoption of quality teaching, an internationalized curriculum, as well as the cultivation of generic skills in students, to meet the challenges of the dynamic university and information environment (ACU National, 2008). The Graduate Diploma of Education (Secondary) Program at ACU Canberra Situated in Australia’s capital city, the Canberra campus is one of the smallest campuses of ACU National, where there are approximately 800 undergraduate and 200 postgraduate students studying to be primary or secondary school teachers through the School of Education (ACT). Other programs offered at this campus include nursing, theology, social work, arts, and religious education. A new model of pre-service secondary teacher education commenced with the introduction of the Graduate Diploma of Education (Secondary) program at this campus in 2005. It marked an innovative collaboration between the university and a cohort of experienced secondary school teachers in the ACT and its surrounding region. This partnership was forged to allow student teachers undertaking the program to be inducted into the teaching profession with the cooperation of leading practitioners from schools in and around the ACT. In the preparation of novices for the teaching profession, an enduring challenge is to create learning experiences capable of transforming practice, and to instill in the novices an array of professional skills, attributes, and competencies (Putnam & Borko, 2000). Another dimension of the beginning teacher experience is the need to bridge theory and practice, and to apply pedagogical content knowledge in real-life classroom practice. During the one-year Graduate Diploma program, the student teachers undertake two four-week block practicum placements, during which they have the opportunity to observe exemplary lessons, as well as to commence teaching. The goals of the practicum include improving participants’ access to innovative pedagogy and educational theory, helping them situate their own prior knowledge regarding pedagogy, and assisting them in reflecting on and evaluating their own practice. Each student teacher is paired with a more experienced teacher based at the school where he/she is placed, who serves as a supervisor and mentor. In 2007, a new dimension to the teaching practicum was added to facilitate online peer mentoring among the pre-service teachers at the Canberra campus of ACU National, and provide them with opportunities to reflect on teaching prior to entering full-time employment at a school. The creation of an online community to facilitate this mentorship and professional development process forms the context for the present case study. While on their practicum, students used social software in the form of collaborative web logging (blogging) and threaded voice discussion tools that were integrated into the university’s course management system (CMS), to share and reflect on their experiences, identify critical incidents, and invite comment on their responses and reactions from peers.