Academic literature on the topic 'Mathematics (Elementary) – Study and teaching – Namibia'

Many studies have shown a link between being competent in early mathematics and achievement in school. Early math skills have the potential to be the best predictors of later performance in reading and mathematics. Movement and songs are activities that children like, making it easier for teachers to apply mathematical concepts through this method. This study aims to develop audio-visual learning media in the form of songs with a mixture of western and traditional musical idioms, accompanied by movements that represent some of the teaching of early mathematics concepts. The stages of developing the ADDIE model are the basis for launching new learning media products related to math and art, and also planting the nation's cultural arts from an early age. These instructional media products were analyzed by experts and tested for their effectiveness through experiments on five children aged 3-4 years. The qualitative data were analyzed using transcripts of field notes and observations and interpreted in a descriptive narrative. The quantitative data were analyzed using gain score statistics. The results showed that there was a significant increase in value for early mathematical understanding of the concepts of geometry, numbers and measurement through this learning medium. The results of the effectiveness test become the final basis of reference for revision and complement the shortcomings of this learning medium. Further research can be carried out to develop other mathematical concepts through motion and song learning media, and to create experiments with a wider sample. Keywords: Early Mathematical Skills, Movement and Song Idiom Traditional, Audio-visual Learning Media References An, S. A., & Tillman, D. A. (2015). Music activities as a meaningful context for teaching elementary students mathematics: a quasi-experiment time series design with random assigned control group. European Journal of Science and Mathematics Education, 3(1), 45–60. https://doi.org/10.1038/srep15999 An, S., Capraro, M. M., & Tillman, D. A. (2013). Elementary Teachers Integrate Music Activities into Regular Mathematics Lessons: Effects on Students’ Mathematical Abilities. Journal for Learning through the Arts: A Research Journal on Arts Integration in Schools and Communities, 9(1). https://doi.org/10.21977/d99112867 Austin, A. M. B., Blevins-Knabe, B., Ota, C., Rowe, T., & Lindauer, S. L. K. (2011). Mediators of preschoolers’ early mathematics concepts. Early Child Development and Care, 181(9), 1181–1198. https://doi.org/10.1080/03004430.2010.520711 Barrett, J. E., Cullen, C., Sarama, J., Miller, A. L., & Rumsey, C. (2011). Children ’ s unit concepts in measurement : a teaching experiment spanning grades 2 through 5. 637–650. https://doi.org/10.1007/s11858-011-0368-8 Basco, R. O. (2020). Effectiveness of Song, Drill and Game Strategy in Improving Mathematical Performance. International Educational Research, 3(2), p1. https://doi.org/10.30560/ier.v3n2p1 Bausela Herreras, E. (2017). Risk low math performance PISA 2012: Impact of assistance to Early Childhood Education and other possible cognitive variables. Acta de Investigación Psicológica, 7(1), 2606–2617. https://doi.org/10.1016/j.aipprr.2017.02.001 Buchoff, R. (2015). Childhood Education. January. https://doi.org/10.1080/00094056.1995.10521830 Clements, D. H. (2014). Geometric and Spatial Thinking in Young Children. In Science of Advanced Materials (Vol. 6, Issue 4). National Science Foundation. https://doi.org/10.1166/sam.2014.1766 Clements, D. H., Baroody, A. J., Joswick, C., & Wolfe, C. B. (2019). Evaluating the Efficacy of a Learning Trajectory for Early Shape Composition. XX(X), 1–22. https://doi.org/10.3102/0002831219842788 Clements, D. H., Swaminathan, S., Anne, M., & Hannibal, Z. (2016). Young Children ’ s Concepts of Shape. 30(2), 192–212. Cross, C. T., Woods, T., & Schweingruber, H. (2009). Mathematics Learning in Early Chidhood Paths Toward Excellence and Equity. The National Academies Press. Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510 Geary, D. C. (2012). Learning Disabilities and Persistent Low Achievement in Mathematics. J Dev Behav Pediatr., 32(3), 250–263. https://doi.org/10.1097/DBP.0b013e318209edef.Consequences Gejard, G., & Melander, H. (2018). Mathematizing in preschool : children ’ s participation in geometrical discourse. 1807. https://doi.org/10.1080/1350293X.2018.1487143 Harususilo, Y. E. (2020). Skor PISA Terbaru Indonesia, Ini 5 PR Besar Pendidikan pada Era Nadiem Makarim. https://pusmenjar.kemdikbud.go.id/ Hsiao, T. (1999). Romanticism with Deep Affection: Selected Articles About the Music of Hsiao Tyzen (Hengzhe Lin (ed.)). Wang Chun Feng Wen Hua Fa Xing. Kasuya-Ueba, Y., Zhao, S., & Toichi, M. (2020). The Effect of Music Intervention on Attention in Children: Experimental Evidence. Frontiers in Neuroscience, 14(July), 1–15. https://doi.org/10.3389/fnins.2020.00757 Kołodziejski, M., Králová, P. D. E., & Hudáková, P. D. J. (2014). Music and Movement Activities and Their Impact on Musicality and Healthy Development of a Child. Journal of Educational Revies, 7(4). Kristanto, W. (2020). Javanese Traditional Songs for Early Childhood Character Education. 14(1), 169–184. Litkowski, E. C., Duncan, R. J., Logan, J. A. R., & Purpura, D. J. (2020). When do preschoolers learn specific mathematics skills? Mapping the development of early numeracy knowledge. Journal of Experimental Child Psychology, 195, 104846. https://doi.org/10.1016/j.jecp.2020.104846 Logvinova, O. K. (2016). Socio-pedagogical approach to multicultural education at preschool. Procedia - Social and Behavioral Sciences, 233(May), 206–210. https://doi.org/10.1016/j.sbspro.2016.10.203 Lopintsova, O., Paloniemi, K., & Wahlroos, K. (2012). Multicultural Education through Expressive Methods in Early Childhood Education. Ludwig, M. ., Marklein, M. ., & Song, M. (2016). Arts Integration: A Promising Approach to Improving Early Learning. American Institutes for Research. Macdonald, A., & Lowrie, T. (2011). Developing measurement concepts within context : Children ’ s representations of length. 27–42. https://doi.org/10.1007/s13394-011-0002-7 Mans, M. (2002). Playing The Music- Comparing Perfomance of Children’s Song and dance in Traditional and Contemporary Namibian Education. In The Arts in Children’s Live (pp. 71–86). Kluwer Academic Publishers. Maričić, S. M., & Stamatović, J. D. (2017). The Effect of Preschool Mathematics Education in Development of Geometry Concepts in Children. 8223(9), 6175–6187. https://doi.org/10.12973/eurasia.2017.01057a Missall, K., Hojnoski, R. L., Caskie, G. I. L., & Repasky, P. (2015). Home Numeracy Environments of Preschoolers: Examining Relations Among Mathematical Activities, Parent Mathematical Beliefs, and Early Mathematical Skills. Early Education and Development, 26(3), 356–376. https://doi.org/10.1080/10409289.2015.968243 Moreno, S., Bialystok, E., Barac, R., Schellenberg, E. G., Cepeda, N. J., & Chau, T. (2011). Short-term music training enhances verbal intelligence and executive function. Psychological Science, 22(11), 1425–1433. https://doi.org/10.1177/0956797611416999 Nketia, J. H. K. (1982). Developing Contemporary Idioms out of Traditional Music. Studia Musicologica Academiae Scientiarum Hungaricae, 24, 81. https://doi.org/10.2307/902027 Nyota, S., & Mapara, J. (2008). Shona Traditional Children ’ s Games and Play : Songs as Indigenous Ways of Knowing. English, 2(4), 189–203. Östergren, R., & Träff, U. (2013). Early number knowledge and cognitive ability affect early arithmetic ability. Journal of Experimental Child Psychology, 115(3), 405–421. https://doi.org/10.1016/j.jecp.2013.03.007 Pantoja, N., Schaeffer, M. W., Rozek, C. S., Beilock, S. L., & Levine, S. C. (2020). Children’s Math Anxiety Predicts Their Math Achievement Over and Above a Key Foundational Math Skill. Journal of Cognition and Development, 00(00), 1–20. https://doi.org/10.1080/15248372.2020.1832098 Papadakis, Stamatios, Kalogiannakis, M., & Zaranis, N. (2017). Improving Mathematics Teaching in Kindergarten with Realistic Mathematical Education. Early Childhood Education Journal, 45(3), 369–378. https://doi.org/10.1007/s10643-015-0768-4 Papadakis, Stamatios, Kalogiannakis, M., & Zaranis, N. (2018). The effectiveness of computer and tablet assisted intervention in early childhood students’ understanding of numbers. An empirical study conducted in Greece. Education and Information Technologies, 23(5), 1849–1871. https://doi.org/10.1007/s10639-018-9693-7 Papadakis, Stamatis, Kalogiannakis, M., & Zaranis, N. (2016). Comparing Tablets and PCs in teaching Mathematics: An attempt to improve Mathematics Competence in Early Childhood Education. Preschool and Primary Education, 4(2), 241. https://doi.org/10.12681/ppej.8779 Paul, T. (2019). Mathematics and music : loves and fights To cite this version. PISA worldwide ranking; Indonesia’s PISA results show need to use education resources more efficiently, (2016). Phyfferoen, D. (2019). The Dagbon Hiplife Zone in Northern Ghana Contemporary Idioms of Music Making in Tamale. 1(2), 81–104. Purpura, D. J., Napoli, A. R., & King, Y. (2019). Development of Mathematical Language in Preschool and Its Role in Learning Numeracy Skills. In Cognitive Foundations for Improving Mathematical Learning (1st ed., Vol. 5). Elsevier Inc. https://doi.org/10.1016/b978-0-12-815952-1.00007-4 Ribeiro, F. S., & Santos, F. H. (2020). Persistent Effects of Musical Training on Mathematical Skills of Children With Developmental Dyscalculia. Frontiers in Psychology, 10(January), 1–15. https://doi.org/10.3389/fpsyg.2019.02888 Roa, R., & IA, C. (2020). Learning Music and Math, Together as One: Towards a Collaborative Approach for Practicing Math Skills with Music. In I. T. (eds) Nolte A., Alvarez C., Hishiyama R., Chounta IA., Rodríguez-Triana M. (Ed.), Collaboration Technologies and Social Computing. Col (Vol. 26, Issue 5, pp. 659–669). https://doi.org/https://doi.org/10.1007/978-3-030-58157-2_10 Sarama, J., & Clements, D. H. (2006a). Mathematics, Young Students, and Computers: Software, Teaching Strategies and Professional Development. The Mathematics Educato, 9(2), 112–134. Sarama, J., & Clements, D. H. (2006b). Mathematics in early childhood. International Journal of Early Childhood, 38(1). https://doi.org/10.1007/bf03165980 Sarkar, J., & Biswas, U. (2015). The role of music and the brain development of children. 4(8), 107–111. Sheridan, K. M., Banzer, D., Pradzinski, A., & Wen, X. (2020). Early Math Professional Development: Meeting the Challenge Through Online Learning. Early Childhood Education Journal, 48(2), 223–231. https://doi.org/10.1007/s10643-019-00992-y Silver, A. M., Elliott, L., & Libertus, M. E. (2021). When beliefs matter most: Examining children’s math achievement in the context of parental math anxiety. Journal of Experimental Child Psychology, 201, 104992. https://doi.org/10.1016/j.jecp.2020.104992 Sterner, G., Wolff, U., & Helenius, O. (2020). Reasoning about Representations: Effects of an Early Math Intervention. Scandinavian Journal of Educational Research, 64(5), 782–800. https://doi.org/10.1080/00313831.2019.1600579 Temple, B. A., Bentley, K., Pugalee, D. K., Blundell, N., & Pereyra, C. M. (2020). Using dance & movement to enhance spatial awareness learning. Athens Journal of Education, 7(2), 153–167. https://doi.org/10.30958/aje.7-2-2 Thippana, J., Elliott, L., Gehman, S., Libertus, K., & Libertus, M. E. (2020). Parents’ use of number talk with young children: Comparing methods, family factors, activity contexts, and relations to math skills. Early Childhood Research Quarterly, 53, 249–259. https://doi.org/10.1016/j.ecresq.2020.05.002 Tsai, Y. (2017). Taiwanese Traditional Musical Idioms Meet Western Music Composition: An Analytical and Pedagogical Approach to Solo Piano Works by Tyzen Hsiao. http://aquila.usm.edu/dissertations/1398 Upadhyaya, D. (2017). Benefits of Music and Movement in young children. Furtados School of Music. https://www.linkedin.com/pulse/benefits-music-movement-young-children-dharini-upadhyaya Vennberg, H., Norqvist, M., Bergqvist, E., Österholm, M., Granberg, C., & Sumpter, L. (2018). Counting on: Long Term Effects of an Early Intervention Programme. 4, 355–362. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-148101 Verdine, B. N., Lucca, K. R., Golinkoff, R. M., Hirsh-, K., & Newcombe, N. S. (2015). The Shape of Things : The Origin of Young Children ’ s Knowledge of the Names and Properties of Geometric Forms. 8372(October). https://doi.org/10.1080/15248372.2015.1016610 Wakabayashi, T., Andrade-Adaniya, F., Schweinhart, L. J., Xiang, Z., Marshall, B. A., & Markley, C. A. (2020). The impact of a supplementary preschool mathematics curriculum on children’s early mathematics learning. Early Childhood Research Quarterly, 53, 329–342. https://doi.org/10.1016/j.ecresq.2020.04.002 Wardani, I. K., Djohan, & Sittiprapaporn, P. (2018). The difference of brain activities of musical listeners. 1st International ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering, ECTI-NCON 2018, 181–184. https://doi.org/10.1109/ECTI-NCON.2018.8378307 Winter, E., & Seeger, P. (2015). The Important Role of Music in Early Childhood Learning. Independent School. Zaranis, N., Kalogiannakis, M., & Papadakis, S. (2013). Using Mobile Devices for Teaching Realistic Mathematics in Kindergarten Education. Creative Education, 04(07), 1–10. https://doi.org/10.4236/ce.2013.47a1001

The purpose of the California Study of Elementary Mathematics is to examine the effects of state education reform in elementary mathematics curriculum on teaching and learning in elementary mathematics classrooms. In this article, we describe the methodology used in the study. We begin by providing an overview of the state policy that is aimed at realizing anew vision of mathematics teaching and learning. Then we describe participants and data collection procedures at each of four levels—state, school district, school, and classroom (teachers and students). We conclude with a description of methods used to collect the classroom-level data from which we constructed the cases in this issue.

The purpose of this study is to investigate the effect of manipulative (concrete learning materials) in teaching elementary mathematics. The study employed a pretest posttest quasi experimental design. The study was conducted in two grade 3 sections of San Agustin Elementary School in the school year 2016-2017. The experimental group was taught mathematics using the manipulative while the control group was taught mathematics using the conventional method. Data were collected and analyzed from both the experimental and control groups using T-test, Paired T-test, and standard deviation. As a result of the research, the pretest and posttest scores of experiment and control groups were found to differ significantly in favor of posttest in both groups. There was a significant mean gain difference in the pupils’ pretest and posttest scores in mathematics exposed to manipulative and conventional method. Generally, the use of manipulative in teaching mathematics is more effective than the use of conventional method.

Elementary school teachers in Indonesia are required to master many subjects to be taught to their students. It is undeniable that the teachers’ mastery of knowledge (material) in some subjects inadequate. Therefore, it is worth to argue that there was a misconception in mathematics teaching in elementary schools. This research was designed using a qualitative approach. The participants of this study were 30 elementary school teachers in Semarang city area, Central Java province, Indonesia. The research data were obtained through questionnaires, and interviews. The purpose of the study was to discuss the types and causes of the misconception of mathematics teaching in elementary schools. Alternative solutions were also presented to problem-solving so that misconceptions do not occur anymore in mathematics teaching. The findings show that, teachers evenly experience types of misconceptions: (1) pre-conception, (2) under-generalization, (3) over-generalization, (4) modelling error, (5) prototyping error; and (6) process-object error in teaching mathematics in elementary schools. Some misconceptions have taken root and are difficult to remove, called "ontological misconceptions" because of teachers' years of belief that the knowledge they received was true when in fact it was not quite right.

Mathematics educators agree elementary teachers should possess confidence and competence in teaching mathematics. Many prospective elementary teachers (particularly women) pursue careers in elementary teaching despite personal repeated experiences of mathematics anxiety. Previous studies of mathematics anxiety have tended to focus on physical sensations that occur during test-taking situations. This study analyzes how three women prospective elementary teachers described, explained, and related their experiences of mathematics anxiety while learning mathematics as K-12 students and while learning to teach mathematics. My research reveals that mathematics anxiety may reach beyond assessment situations and impact women prospective elementary teachers’ larger mathematical histories. I show how women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of social belonging, loss of personal identity, or loss of practical competency) and how specific coping strategies may be invented to cope with the fear. I present evidence of how coping strategies may impede mathematics learning.

Induction has been given much attention in recent years. Research indicates that a comprehensive program with multiple supports for new teachers including reasonable teaching loads and complete curriculum resources are most effective. However, this is not the reality for many beginning teachers. In a study of a two-year, university-based, mathematics-specific induction program for elementary teachers, we found many first-year teachers were given teacher leadership responsibilities at their schools. These leadership experiences were confounded by school contexts in which curriculum resources were incomplete or competed with the BTs visions of “good” mathematics teaching. Qualitative data included interviews, surveys, written reflections, and researcher field notes from the first year of study. This article reports three first-year teachers’ experiences of significant leadership responsibilities. Findings call for ways to prepare BTs in undergraduate and induction programs for the non-instructional duties in teaching and to develop the agency needed to negotiate school-based contextual constraints.

The main problem in this study is the lack of student communication skills and the lack of RME-based teaching materials that use used goods as a learning medium. The long-term objective of the research to be carried out is to support quality improvement and development of basic and regional education policies at the local and national levels through improving the quality of Indonesia's young generation of hope. The purpose of this study was to obtain an overview of the results of the implementation of teaching materials "mathematics learning in elementary schools". The focus of this research problem is: 1) learning steps using teaching materials and 2). Barriers are felt when learning using these teaching materials. And 3). The implementation of teaching materials uses a realistic mathematics education approach in the communication skills of PGSD students with the help of teaching aids made from used materials. The method used is descriptive qualitative, this study describes the application of elementary mathematics learning teaching materials in mathematics communication of students at the PGSD Siliwangi Teacher Training College and the obstacles in implementing teaching materials. The results of this study were the steps for implementing elementary mathematics teaching materials in mathematics communication for PGSD students..

The purpose of this study was to assess the extent to which predictors of teachers’ competencies in teaching mathematics predict the outcomes of mathematics performance among learners at upper primary phase. The determinants were namely gender, teaching experience, region, qualification, and fields of study exert effect on teachers’ competencies in lesson planning and preparation, assessment and evaluation of learners, lesson delivery, the use of teaching strategies, the quality of homework, and the availability of teaching materials. The generic understanding of the impacts of predictors of teaching competencies on learners’ performance significantly informs the development of training programmes components, and teaching and learning processes across the schooling system. Shulman’s theory of teacher content and pedagogical knowledge underpinned the study. The study comprised of holistic samples of 117 mathematics teachers at upper primary phase teachers from 39 schools. The selection of three schools from each region followed three criteria, namely outstanding, moderate, and lower performances in Grade 10 examination. Data is collected from classroom observation and analysis of relevant documents. The findings show that predictor variables such as gender, teacher qualification, teaching experience, field of study, and region exerted effects on the way teachers plan and prepare the lesson, deliver the lesson, assess and evaluate learners, use the teaching materials, and the quality of work. Teachers who specialized in mathematics were more competent in mathematics teaching. The results presuppose that predictors of teachers’ competencies in teaching mathematics are essential for improving teaching and learning of mathematics in schools. The outcome of this study is beneficial to education officials who are directly responsible for coordinating the teaching of mathematics in schools and the allocation of teaching subjects, particularly mathematics. The findings showed that a number of teachers were not trained mathematics. This was an indication of the existing shortage of mathematics teachers in schools nationally. Untrained mathematics teachers negatively influenced learners’ performance. These outcomes implied that education planners at the national, regional and district levels should set up strategies on how to increase the production of mathematics teachers nationally in order to meet the demand of such teachers in schools.

Mathematics as a subject is considered difficult as well as interesting and enjoyable. children like its challenge, its clarity, and the fact that you know when you are right. The solution to a problem makes a feeling of excitement and satisfaction. The objectives of the study were (i) to explore the fun and amusement in teaching mathematics at the elementary level (ii) to review the existing and required facilities at the elementary level (iii) to find out how students take fun in learning mathematics at the elementary level. Four elementary schools were taken as a sample of the study. The questionnaires were used with the teachers and students separately n the themes related to the fun, amusement, and effectiveness in teaching Mathematics. On the basis of analysis, it was found that the majority of the teachers were teaching the out-dated curriculum which does not satisfy the socio-economic needs of students. Although teachers s and students had fun in their teaching and learning process. It is found that the elementary teachers and students were not up to the mark because they were less equipped as compared to the physical and other basic facilities which should be available in the schools. It is proposed that all schools, including the English medium schools, must follow the education policy in the teaching of mathematics and curriculum. Furthermore, the trained and qualified teachers should be appointed on merit both in the government and private schools.

The Namibian curriculum favours knowledge with understanding and application of knowledge and skills, because facts that are learned with understanding are easier to remember. This made learners to be able to represent mathematical situations in different ways and for different purposes. It also motivates teachers to contextualise the content to make mathematics teaching and learning more interesting and enjoyable to teachers and learners. However, some mathematics teachers are challenged by being required to teach multigrade classes, due to a massive response to improved access to education.Multigrade teaching is seen as a difficult practice especially when teachers are not well prepared to teach combined grades. This case study focused on the teaching of mathematics at Upper Primary Phase. An Interpretive paradigm was used to understand the teachers’ experiences and their teaching ethods. Hence the study aimed to investigate how teachers deliver their mathematics lessons in multigrade classrooms, considering the good practices and challenges that may occur. The findings revealed that teachers mostly use their monograde pedagogical knowledge,resulting in using quasi-monograde with a common timetable approach when teaching mathematics in multigrade settings. Although learners have access to the common mathematics syllabus, the quality of teaching the subject in multigrade classrooms seems to be affected due to the lack of teacher training in multigrade teaching. Also, equity and democracy need to be considered more than it currently is in terms of resource distribution to multigrade schools. Good practice of multigrade teaching existed in building on lower grade competencies, introducing lessons with common activities, as well as the concentration on lower grades which make learners independent. However, insufficient time, lack of knowledge in multigrade and curriculum knowledge in particular seem to challenge teachers and learners. Therefore, multigrade teachers need to be part of curriculum development for them to master the syllabus. These teachers will assist in developing multigrade resources for integration, contextualisation and more enrichment activities for high achievers.

Paper 1. The purpose of this analysis is to critically evaluate the Lower Primary Mathematics programme within the context of the Namibian educational reform, against the backdrop of learner-centred education from within the Constructivist epistemology. Through the analysis of a small-scale survey, I will try to determine the extent to which learners, teachers and other educationalists, involved in the Lower Primary school phase, understand the new approach to Mathematics and their pedagogical and theoretical insight into the new programme. I will also analyse the syllabus documents in view of the educational policies and further discuss the social, historical and economic background to the reform. I will then analyse the progress or development of the reform process through discussing the learning environment as well as the learners who are the central participants in education. Paper 2.This critical discussion aims to explore the prospects and underlying principles of the epistemologies of two opposing paradigms of education: Behaviourism and Constructivism. I have critically examined and compared the theoretical aspects that shape and inform the model of instruction and the systemic implications of the learning process. The purpose was to compare both learning theories and to draw a conclusion of which the better epistemology is for the teaching and learning process. Paper 3. This is an investigation into the theories that underpin and inform mathematics teaching in the Lower Primary phase of the primary school in Namibia. The Namibian society requires the development of knowledge and understanding, skills and competencies, attitudes and values, which everyone must have to be able to function adequately in society on a social, economic and political level (MBESC 1996). We need to seek ways of enhancing mathematics teaching in Namibia if we want to live up to the expectations of our society. Paper 4. Mathematicians and researchers across the globe have theorised and speculated about education reform movements, which aim for more than just structural knowledge where it concerns Mathematics. This action research study is based on the findings of a pilot study about 'Problem-based Learning', using this as a basis to investigate the relationship between the intentions of the Lower Primary Mathematics curriculum and its implementation at classroom level. This paper reports on a case study of two grade one teachers' perceptions of problem solving as a key component of Mathematics learning and how the implementation of the problem-based approach could be supported through intervention. Data was gathered from a series of cycles of planning, acting, observing and reflecting. Analysis of the data indicates that teachers' professional development lies within a willingness to change and in reflexive practice. Given focused support to teachers could result in the application of contemporary approaches to Mathematics teaching, with an overall improvement of constructivist-oriented learner-centred education.

The purpose of this study was to investigate and document parental involvement in a San community in Namibia over a period of two months. The emphasis was to investigate whether San parents in the Omusati region were involved in the learning of mathematics of their children. The learner participants were selected according to those who were open to sharing their ideas. An interpretive approach was used to collect and analyse data. The collected data was gathered from 9 participants (4 learners in grade 5 together with their parents, plus their mathematics teacher). Semi-structured interviews, parental contributions and home visit observations were the three tools that I used to collect data. The selected school is located in a rural area in the Omusati region of northern Namibia. The interviews were conducted in Oshiwambo (the participants‟ mother tongue) and translated into English and then analyzed. I discovered that the selected San parents were involved in some but limited school activities. The findings of this study emphasizes that illiteracy may be one of the contributing factors of low or non-involvement of parents among the San community. Other factors which I found caused parents not to assist their children with homework was parents spending much of their time at the local cuca shops during the day until late in the evenings. The study also highlights possible strategies that can be carried out by teachers to encourage parental involvement in school activities.

It can be argued that the Namibian curriculum is largely influenced by a Western epistemology. However, many studies suggest that learners make powerful meanings of mathematical concepts they are learning if they visualise these and experience them in relation to what they already know from their own cultural backgrounds. According to the Namibian National Curriculum for Basic Education (NNCBE, 2010), it is not only important for learners to acquire mathematical knowledge and skills, but also to develop and grow their identities, cultures and values as individuals. The aim of this study was to explore and investigate how selected mathematics teachers employ visualisation as a teaching approach to re-contextualise indigenous knowledge (IK). The study set out to explore how conceptual understanding is enhanced by participation in an intervention programme. The use of visualisation is considered an important mediating and pedagogical tool in the mathematics classroom to enhance the mathematics learning of learners. The research is informed by a socio-cultural theory of learning and is located within an interpretive paradigm. The study was conducted at four schools in the Oshana region of Namibia and involved four mathematics teachers who were purposefully selected due to their willingness to use visualisation-IK approaches in their teaching, based on their responses to the survey. The methodologies used are qualitative and quantitative case study. To gather data, document analysis, a survey, lesson observations and focus group interviews were used. The study found that most teachers in the Oshana region have an understanding of the effective use of visualisation-IK approaches. However, the study revealed that visualisation- IK approaches are mostly used in grades 4 to 7 mathematics classrooms. It also discovered that most of the visualisation approaches that teachers employed aligned well with the curriculum and promoted conceptual understanding in the teaching of mathematics. The results of the study showed that teachers have experience of the enabling and constraining factors in using a visualisation-IK approach to teaching mathematics.

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.

The poor performance in mathematics of learners in schools in Namibia, especially in the grades where learners sit for the national examinations, has been a concern of everybody. Since independence, the Ministry of Education in collaboration with several donor agencies has been aware of the poor performance in mathematics in the country. Several international and local studies have been made in an effort to identify the problems that are hindering learners’ performance in mathematics in Namibia. The findings of some studies that were conducted in the country such as the Southern Africa Consortium Monitoring Education Quality (2004), the Presidential Commission on Education, Culture and Training (1999), and the Mathematics and Science Teachers Extension Program (2002) revealed that the inadequate proficiency of primary teachers in mathematics content could be responsible for learners’ poor performance in mathematics. This study, therefore, is aimed at investigating the mathematical proficiency of lower primary (LP) teachers in Namibia. The study used three instruments to collect data namely, a profile questionnaire – to collect teachers’ demographic data, a proficiency test – to test their proficiency level of mathematics using the content of Grade 4 and 5 learners’ mathematics syllabi and a semi-structured interview schedule – to get views about their own mathematics content knowledge, attitudes towards mathematics as well as problems that hinder effective teaching and learning of mathematics at LP phase. The study was conducted with 30 lower primary teachers from five primary and combined schools in the Ohangwena circuit of the Ohangwena region. The study found out that: (1) the mathematical proficiency of LP teachers is below the Grade 7 Mathematics content. Most teachers are not able to solve the content of mathematics at upper primary (UP) phase. (2) LP education is receiving very little support from the Ministry compared to other phases. (3) There are no workshops or training courses organised for LP teachers. They do not receive enough textbooks and materials, their classrooms are overcrowded and teachers cannot pay attention to individual learners. (4) There is a dire need for LP Head of Departments (HODs) who are specialised at LP; most HODs for LP at schools are not specialised in this area. When it comes to views about future content of mathematics that should be given to LP teachers in Namibia, respondents recommended that future LP teachers should have knowledge of mathematics up to at least Grade 10 but preferably up to Grade 12. They do not want to be restricted to LP mathematics, but would like to have a broader knowledge of mathematics content. This would make them more confident in solving their children’s problems in mathematics. Overall, participants recognised the value of mathematics and the role that it plays in society.

Thesis (MEd)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: This study explored the number sense of 47 final year primary school pre-service teachers in Namibia and was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests. The literature review revealed that learner performance is linked to teacher subject knowledge (Ball, 1990, Ma, 1999) and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics (Ball, 1990; Graven 2004). Number sense studies of pre-service teachers (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) have indicated that the development of number sense should be a focus of primary pre-service teacher education. The data in this mixed method research design were obtained from a Number Sense Questionnaire, a Written Computations Questionnaire and a Mental Calculations Questionnaire. These questionnaires were adapted from instruments developed by Professor Der-Ching Yang for 6th and 8th grade learners in Taiwan. Teacher confidence was measured by the McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Six randomly selected pre-service teachers were interviewed to determine their use of number-sensible strategies. The correlation analysis shows a strong relationship between number sense and mental calculations; between number sense and confidence in both the ability to do and the ability to teach mathematics and between mental and written calculations. The overall results of this study reveal that the final year primary pre-service teachers demonstrate limited number sense and possess very few of the indicators of number sense that were described by Kalchman, Moss and Case (2001). The findings expose a lack of conceptual understanding of the domain numbers and operations, particularly in the domain of rational numbers and the operations of multiplication and division. The pre-service teachers have little or no access to a variety of flexible number-sensible strategies to solve problems and calculate mentally. They lack the fluency in basic facts and procedures to perform written calculations efficiently and correctly. Unexpectedly, the analysis of the confidence survey shows that they are confident in both their ability to do mathematics and their ability to teach mathematics. It is recommended that mental calculations and computational estimation should become a focus of primary school mathematics education. Institutions responsible for teacher training should develop the number sense of pre-service teachers and research effective and long-term professional development programmes. The confidence and willingness of the teachers to learn can be used as an important resource.
AFRIKAANSE OPSOMMING: Hierdie studie ondersoek die getalbegrip van 47 finale jaar primêre skool voordiens-onderwysers in Namibië en is gemotiveer deur die swak prestasie van die Namibiese primêre skool leerlinge in beide nasionale en internasionale gestandaardiseerde assesseringstoetse. Die literatuurstudie het aan die lig gebring dat leerlinge se prestasie gekoppel is aan onderwyservakkennis (Ball, 1990, Ma, 1999) en dat onderwysers se vertroue in hulle vermoë om wiskunde te doen en te onderrig, die manier waarop hulle onderrig en hul bereidwilligheid om wiskunde te leer beïnvloed (Ball, 1990, Graven 2004 ). Studies van voordiens primêre onderwysers se getalbegrip (Kaminski, 1997; Tsao, 2004; Veloo, 2010; Yang, Reys & Reys, 2009) toon dat die ontwikkeling van getalbegrip 'n fokus van primêre voordiensonderwyseropleiding behoort te wees. Die data in hierdie gemengde metode navorsing is verkry uit 'n Getalbegrip, 'n Skriftelike Berekeninge en 'n Hoofrekene Vraelys. Hierdie vraelyste is gebaseer op die instrumente wat ontwikkel is deur Professor Der-Ching Yang vir graad 6 en 8 leerlinge in Taiwan. Onderwyservertroue is gemeet deur die McAnallen Confidence in Mathematics and Mathematics Teaching Survey. Ses ewekansig geselekteerde voordiens-onderwysers is ondervra om te bepaal watter sinvolle strategieë hulle gebruik om vrae oor getalbegrip te beantwoord. Die korrelasie-analise toon 'n sterk verband tussen getalbegrip en hoofrekene; tussen getalbegrip en vertroue in die vermoë om wiskunde te doen en te leer, en tussen vermoë om hoofrekene en skriftelike bewerkinge te doen. Die algehele resultate van hierdie studie dui daarop dat die finale jaar primêre voordiens-onderwysers oor beperkte getalbegrip en baie min van die aanwysers van getalbegrip wat deur Kalchman, Moss en Case (2001) beskryf is, beskik. Die bevindinge toon ‘n gebrek aan begrip van die domein van getalle en bewerkings, veral in die domein van rasionale getalle en die bewerkings vermenigvuldiging en deling. Die voordiens-onderwysers beskik oor min of geen soepel strategieë om probleme op te los en hoofrekene te doen nie. Hulle beskik nie oor die vlotheit in basiese feite en bewerkings om skriftelike berekeninge doeltreffend en korrek uit te voer nie. Die vertroue wat voordiens-onderwysers uitgespreek het in hulle vermoë om wiskunde te doen en onderrig staan in sterk teenstelling met hierdie bevindige. Dit word aanbeveel dat hoofrekene en skatting 'n fokus van primêre skool wiskunde-onderwys behoort te wees. Instansies gemoeid met onderwyseropleiding behoort die getalbegrip van voordiensonderwysers te onwikkel en navorsing te doen oor effektiewe en lang-termyn programme vir professionele ontwikkeling. Onderwysers se vertroue en bereidwilligheid om te leer kan as 'n belangrike hulpbron gebruik word.

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.

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.

This study aims to explore four grade 3 teachers’ understanding of teaching reading in Rukwangali, a home language in Namibia in Kavango region and to observe the strategies they use as well as the activities they set for their learners. During my School Based Studies (SBS), I noticed that learners were not reading with understanding. My interest was also stimulated by a study carried out in Namibia that found that the literacy levels for Namibian learners were poor compared to those of other African countries. This is a qualitative case study carried out within an interpretive paradigm. It seeks to understand the meaning that people attached to human actions. I selected the participants purposefully and in terms of convenience, as all three schools selected are situated in Rundu, the town in which I work as a college lecturer. The research tools I employed were semi-structured interviews, document analysis, classroom observation, and stimulated recall discussions on the lessons I observed. I used a variety of methods to triangulate data and enhance validity. This study reveals that teachers use multiple methods to teach reading. These methods include phonics and syllabification to help struggling learners to decode difficult and long (polysyllabic) words and the look-and-say method for whole word recognition and meaning making at word and sentence level. In addition, they also use the thematic approach to teaching and learning to expand learners’ vocabulary and enhance their understanding of the texts they read and to make their lessons learnercentred. However, the problems of language, lack of reading books written in Rukwangali and large class sizes constrain the teachers from teaching in a more learner-centred way. Therefore, the study gives some tentative recommendations to remedy this situation.

AbstractTeaching multiplication is a compulsory topic in elementary education mathematics programs. Much time is dedicated to teaching multiplication tables and algorithms, obtaining mediocre results. Recent investigations in neuroscience suggest that our way of teaching is not congruent with how the brain works and, as such, important changes should be made in teaching of numerical facts and algorithms. Additionally, other kinds of calculation, like mental calculation and calculations with a calculator, have not yet reached the level of importance of their use in education that citizens require in a contemporary society.

In this chapter a model is outlined for using asynchronous online discussions in a mathematics content course for preservice elementary teachers. The model integrates conversational discussion threads as a component of a traditional, face-to-face course. This successful approach is based on elements of the variation theory of learning, and derives from a comprehensive dissertation study examining its effectiveness.

Problem-solving digital games that make sense of mathematics do not happen by accident but by careful design. This chapter looks at a popular design framework, Game Network Analysis (GaNA), and examines how teachers can use it to turn popular digital games into strong mathematical experiences grounded in effective teaching practices that use play, purposeful explorations, and focused dialogue to make mathematical concepts more meaningful. The chapter involves a careful study of the GaNA framework in comparison with the eight Mathematics Teaching Practices of Principles to Actions: Ensuring Mathematical Success for All. The findings encourage further analysis of the GaNA framework in terms of specific academic areas. Explicit clarification is needed to use the framework to effectively move mathematics education toward its future potential.

The affordances offered by modern Internet technologies provide new opportunities for the pre-service and in-service training of teachers, making it possible to overcome the restrictions of shrinking resources and geographical locations and to offer high quality learning experiences to geographically dispersed teachers. The focus of this chapter is the question of how information and communication tools made available online could be effectively exploited to build and study network-based services with the aim of fostering online communities that promote teacher learning and development. The chapter presents an overview of the main experiences gained from a study which investigated the forms of collaboration and shared knowledge building undertaken by a multinational group of teachers participating in EarlyStatistics, an online professional development in statistics education targeting European elementary and middle school mathematics teachers. Findings from the study provide insights into the factors that may facilitate or hinder the successful implementation of an online community of teaching practitioners.

The purpose of this chapter was to investigate pre-service teachers' noticing of children's critical thinking and views towards eliciting and using students' critical thinking in mathematics teaching. A mixed method study was used to provide a range of perspectives on pre-service teachers' views towards mathematics. The results indicated that the pre-service teachers initially held beliefs that mathematics teaching and learning consist of transferring information and students absorbing and memorizing information. The pre-service teachers based their instructional responses on experiences they had as students in elementary mathematics classrooms. The pre-service teachers described what they had observed about teaching mathematics as the ideal without regard for how the teaching behaviors they observed might influence children's critical thinking about mathematics. After completing a mathematics methods course, the pre-service teachers held beliefs more consistent with a reform-oriented classroom and demonstrated growth in their ability to notice children's mathematics thinking.

Providing a study on mathematics teachers' technological pedagogical content knowledge (TPACK), the goal of this chapter is to investigate the predictive value of teachers' beliefs (e.g., self-efficacy) and mathematical knowledge for teaching (MKT) on their level of TPACK. Background variables, gender, ethnicity, certification, experience, and mathematics degree were all controlled for in this study. Two-step regression analysis results by school level (K-5, middle, and high) indicate that standards-based mathematics teaching beliefs positively predict mathematics teachers' level of TPACK for all teachers. Having a college/graduate mathematics degree is more predictive of TPACK for K-5 and middle school teachers while MKT is more predictive of TPACK for high school teachers. In addition, elementary teachers' mathematics self-concept and pedagogical preparedness and middle school teachers' mathematics teaching interest were significantly related to their level of TPACK. The implications for school districts and teacher preparation programs to develop TPACK for teachers are discussed.

This chapter provides an overview of interactive remote clickers and how they can be used in an elementary school classroom as a tool for formative assessment in mathematics. The authors share the perspective of a university professor, two teachers, and an elementary school student about the benefits of these types of devices in mathematics classrooms. To this end, they present two vignettes from two fourth grade classrooms and findings from an exploratory study that examined the influence of clickers on teaching and learning in classrooms. Implications and recommendations for using these devices in elementary mathematics classrooms are also provided.

This chapter shares the findings from a study that examined primary grades teachers' fidelity of implementation during a year-long professional development program on formative assessment in mathematics. The project provided over 80 hours of professional development to elementary school teachers regarding their use of an internet-based formative assessment system for their students' mathematics achievement. This study examined teachers' online reflections and data in the internet-based assessment system to identify themes that lead to either a high fidelity or low fidelity of implementation. High fidelity teachers expressed beliefs that formative assessment supported their mathematics teaching, improved their students' learning, and was feasible to carry out in their classrooms. Low fidelity teachers' reflections were associated with numerous barriers to implementation as well as a lack of buy-in that the formative assessment system could benefit their teaching.

This chapter shares the findings from a study that examined primary grades teachers' fidelity of implementation during a year-long professional development program on formative assessment in mathematics. The project provided over 80 hours of professional development to elementary school teachers regarding their use of an internet-based formative assessment system for their students' mathematics achievement. This study examined teachers' online reflections and data in the internet-based assessment system to identify themes that lead to either a high fidelity or low fidelity of implementation. High fidelity teachers expressed beliefs that formative assessment supported their mathematics teaching, improved their students' learning, and was feasible to carry out in their classrooms. Low fidelity teachers' reflections were associated with numerous barriers to implementation as well as a lack of buy-in that the formative assessment system could benefit their teaching.

This chapter describes how the author leveraged asynchronous online instruction to develop elementary school teacher-leaders' knowledge of elementary school mathematics content and pedagogies in a graduate program in the United States. This chapter provides the theoretical framework of learner-centered professional development and explains how the six courses in the program embody the framework and support teachers' development of knowledge and skills related to mathematics teaching and learning. This chapter also shares the findings of a study that evaluated teacher-leaders performance on five student-learning outcomes in the program as well as feedback on course evaluations and end-of-program surveys. Data analysis indicated that every teacher-leader demonstrated proficiency on each student-learning outcome. Implications for the design of asynchronous online programs are also shared.

The present work was created from the need to develop educational tools that can be used in the Multimedia Resource Rooms of the Bagémunicipal education network, especially with children with autism. The software requirements were defined from meetings with the team of teachers and professionals who work in the Specialized Educational Service of General Emilio Luiz Malletschool, chosen as pilot of this project because it is one of the first schools to be contemplated with the classroom. resources. Among the listed requirements was prioritized to attend students aged 8-12 years and activities related to the four fundamental operations of mathematics: addition, subtraction, multiplication and division. As the purpose of the app is to support the teaching of students in the early grades of elementary school with autism. Thus, after the definition of the contents and the type of application, began to study the autistic universe and its particularities so that it was possible to design and develop an attractive game for this student