Journal articles 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.

Using a Mixed Methods approach, this study investigated changes in levels of self-efficacy among elementary preservice teachers following a semester course on teaching elementary students’ mathematics. Participants in this study included 347 preservice elementary teachers at a mid-size regional university who had just completed an elementary mathematics methods course. The data were collected from several semester groups. The instruments used were the Mathematics Teaching Efficacy Beliefs Instrument, interview data, and observation data collected during the clinical experience. The focus of this study was to compare the changes in teacher self-efficacy following a methods course that emphasized hands-on mathematics instruction with manipulatives by means of the 5E instructional format. The results of the paired-samples t-test indicated that there was a significant difference in the preservice elementary teachers’ self-efficacy for teaching mathematics after engaging in the elementary methods course. Preservice teachers reported that their understanding of various instructional practices changed significantly from a “tell, show, and do” model to an approach utilizing interactive and engaging activities. They also reported that their attitude toward mathematics had improved significantly and that there had been a direct impact on their confidence for teaching mathematics as a result of the structure of the elementary math methods course.

<span>This research was aimed at finding out the effectiveness of experiential learning-based teaching material in Mathematics on the Mathematics cognitive ability of the fifth-grade student in elementary school. This research used quasi-experimental design involving two sample groups: experiment and control group. The sampling technique in this research used simple random sampling. The subject of this research was 54 students </span><span lang="IN">from</span><span> the fifth-grade elementar</span><span lang="IN">y</span><span> school in Gunungpati Sub-district in the academic year 2017/2018. This study involved 28 students of the fifth-grade elementary school Nongkosawit 02 as the experimental group and 26 students of the fifth-grade elementary school Sadeng 03 as the control group.</span><span lang="IN"> The instrument used in this research was multiple choice test consisting of 30 questions. The test was used to obtain pretest and posttest score.</span><span lang="IN">The data analysis in this research used T-independent test to examine the hypothesis. The result of the study shows the significance level of 0.000 is less than </span><span>α = 0.05</span><span lang="IN"> which means that there is different cognitive ability between the experimental and control group. Thus, the use of experiential learning-based teaching material in Mathematics is effective to improve the Mathematics cognitive ability of the fifth-grade student in elementary school</span><span>.</span>

n the process of teaching and learning it will be fun if students have self-efficacy and the teacher has high creativity in teaching. The purpose of this study is to find out how much the relationship between teacher teaching creativity and self-efficacy of fifth grade students at SDN Sukamaju 03 District Cigudeg, Bogor Regency. This type of quantitative research is a functional relationship between variable X with variable Y, the subjects in this study were 1 group teacher that was sampled only grade V teachers who numbered 20 and class V students of SDN Sukamaju 03 totaling 20 students and the data obtained from questionnaires, Data collection techniques by questionnaire, observation, interview and documentation. Based on the results of testing using product moment, the correlation between teacher teaching creativity (X) with student self-efficacy (Y) obtained a value of rcount = 0.790 and rtable for 20 is 0.444 at level significance of 5% thus rcount > rtable (0.790> 0.444) then H0 is rejected, which means there is a significant correlation between creativity teaching self-efficacy of teachers with students. The significance of the regression equation obtained the Fcount of 29.840 and the Ftable of 4.41 with a sig value of 0.000, so that Fcount > Ftable, then there is a significant relationship between teacher teaching creativity (Variable X) and student self-efficacy (Variable Y). And this research is to get R2 = 0.624 62.4% showed their creativity variables affect self-efficacy of teachers to teach students, the remaining 37.6% influenced by other factors not an analysis in this study.

This research is to develop mathematics teaching materials that are integrated with elementary school thematic learning. The purpose of the development is to obtain mathematics teaching materials that prioritize the local wisdom of the Acehnese people. This teaching material is helpful for fifth-grade elementary school students in which there are character values for learning mathematics. This study uses a qualitative descriptive research method with the ADDIE model development research design. This research focuses on analyzing elementary school teachers who face the problem of integrated mathematics-based character education in thematic learning, then making initial designs and developing character education-based mathematics teaching materials that are integrated into the learning theme. The results showed that character education-based mathematics teaching materials were compatible with elementary students' thematic learning. Mathematics teaching materials focused on solving math problems for elementary students, integrating character values in mathematics with various themes in thematic learning by integrating each mathematics material into themes. The mathematics teaching materials developed were designed with various activities related to daily activities with straightforward language to be understood and made into a mathematical model.

<em>Teaching material is a collection of material and images compiled by the teacher. Learning mathematics in elementary school (SD) really needs to provide content between mathematics in the daily world of students based on local culture with school mathematics. One of the innovative mathematics learning in elementary school can be done by linking the material with culture or ethnomatematics. Ethnomatematics-based teaching materials in elementary schools can be defined as a collection of special elementary materials compiled by teachers in facilitating the process of learning mathematics in class related to culture, either in the form or form that is often encountered by students. The advantages of teaching materials consist of: 1) Study From Anywhere, Anytime; 2) No Commuting; 3) Flexibility to Choose. While the shortcomings of teaching materials consist of: 1) High Chances of Distraction in the Class; 2) No Social Interaction; 3) Takes A Lot of Time and Money. The research method used is the Library Study (Library Research). The data analysis technique used in this study is the Content Analysis method.</em>

The aim of this study is four fold: (a) to investigate the beliefs of elementary (grades 1-3) and middle school (4-6 grades) math teachers about teaching, learning and nature of mathematics; (b) to explore their teaching practices of mathematics; (c) to study the impact of their educational qualifications, years of experience, major on their beliefs toward teaching, learning and nature of mathematics, and; (d) to explore the relationship between their beliefs about teaching learning and nature of mathematics and their teaching practices. Data were collected using two questionnaires: the Math Teacher Beliefs Scale and the Mathematics Teaching Practices Scale. The study sample consisted of 101 teachers who teach in 11 private schools located in Amman, Jordan. The result of this study showed that teachers’ beliefs towards teaching and learning mathematics are more inclined towards being constructive or mixed in between. It was also concluded that the teaching practices lean towards constructivism. There were no significant differences attributed to years of experience, academic level, major, or at what stage they teach, whether it revolves around the their beliefs towards teaching and learning mathematics or towards teaching practices (from teachers’ perspective). The study results revealed a statistically significant correlation between what the teachers believe and what teaching practices they put into use.

I have never yet heard of a high school teacher's being satisfied with the first-year pupil's knowledge of common fractions, and the other day a 1. A. [a specific grade level] girl frankly admitted that she could not multiply 12 2/3 by 15 3/4 because she had skipped one grade, had then had algebra and geometry, and the review didn't touch on mixed numbers. Of course, this was not the fault of any teacher, but the fault of a system which is trying to crowd too many things into too small a space. The real efficiency of the schools does not depend upon their being housed in million-dollar buildings, under a well-organized administrative force, excellent equipment, etc.; it depends on two things,—what is taught, and how it is taught; and more especially upon the latter; for every teacher of mathematics knows that a pupil can derive as much permanent good from the study of a few topics or theorems, so presented as to be pleasing to the pupil, or at least interesting, and at the same time make him think, as he can from ten times the amount of material “rammed home” with the sole object of being reproduced at examinations. The policy of standardizing everything by examinations is doing our expensive school system an untold injury; the report of the city superintendent compares the schools according to the number of their pupils who pass the examinations, and the principal warns the teacher that he is rated according to the number of his pupils that pass, and this pressure is passed on to the pupil. Until some method of close class-room observation and supervision is introduced with a view to allowing free rein to a teacher's individuality and originality even at the expense of his pupil's failing the conventional examinations, it is hardly worth while suggesting other changes.

Abstract Students who are proficient academic language (AL) users, achieve better in school. To develop students’ AL register teachers’ AL input is necessary. The goal of this study was to investigate the extent of AL features in the language input first and second grade teachers give their students in whole class mathematics instruction. Five key features could be distinguished: lexical diversity, lexical complexity, lexical specificity, syntactic complexity and textual complexity. Teachers used all features, but the amount in which they used them varied. While all teachers used lexical specific language when teaching mathematics, they did not use very complex language input. The academicness of teachers’ input was significantly higher in grade 2 than in grade 1 with respect to lexical diversity and lexical specificity. The input during explanation and discussion only differed with regard to textual complexity, which was higher during explanation.

In this article, Amanda Jansen, Dawn Berk, and Erin Meikle investigate the impact of mathematics teacher education on teaching practices. In their study they interviewed six first-year teachers who graduated from the same elementary teacher education program and who were oriented toward teaching mathematics conceptually. They observed each teacher teaching two lessons: one on a mathematics topic that was developed in their teacher education program (target topic) and one on a mathematics topic that was not addressed in their program (control topic). Based on their observations, the authors identified four instructional practices for teaching mathematics conceptually that the participants used in their classroom practice and found that these teachers were more likely to enact two of these instructional practices when teaching target topics: use of mathematical language to support students' sense making and use of visual representations. They also found that the teachers enacted two other instructional practices—use of story problems and pressing students for mathematical explanations—in both target and control topic lessons but did so with limitations in control topic lessons. For teacher education to influence teaching, the authors assert, it is important to develop content knowledge for teaching and pedagogical knowledge in tandem with developing beliefs.

In this exploratory study, teachers’ use of standards-based, discourse practices and their students’ mathematics learning in inclusive elementary mathematics classrooms were examined. Two beginning teachers (one third-grade teacher, one fourth-grade teacher) and six students identified with disabilities or as low performing in mathematics participated in this study (three students from each classroom). Six classroom observations of teachers took place over 4 months focusing on a subset of indicators associated with Walshaw and Anthony’s framework of mathematics classroom discourse practices. Follow-up interviews were also conducted. Curriculum-based and state-accountability measures were collected on the six target students in these settings. Different patterns of student performance emerged across the two classrooms in which teachers were observed using different types and degrees of standards-based discourse practices during mathematics lessons. Findings suggest indicators of effective mathematics teaching in inclusive general education classrooms to be validated by future research efforts.

This study uses the knowledge structure of the adaptive learning platform to explore the model of elementary school students' self-regulated learning of mathematics. The research objects are 85 students who are in grade five. In the two experimental groups, students are divided into groups to carry out scaffold-support self-regulated learning and experimental teaching. The control group conducts traditional teaching. The results of the study show that: 1) The self-regulated learning model supported by multiple scaffolding performs better than the traditional teaching models in learning mathematics. And it is also superior to the traditional narrative of only teaching materials provided by the digital learning platform. 2) The learning performance of high achievement students is higher in Experimental Group 1 compared to all the other groups. 3) Students in Experimental Group 1 have more confidence in themselves as compared to those of Experimental Group 2 with regards to these five aspects including self-regulated learning/planning, self-monitoring, evaluation, reflection, and effort.

Most of the prospective teachers who enter my methods courses assume that teaching mathematics to elementary students will be easy. For example, Jenny wrote, “I thought, ‘I can teach math. How can it be so hard? It's elementary math!’ But I have been proven wrong.” Based on comments such as Jenny's, I realized the importance of giving prospective teachers opportunities to understand that effectively teaching mathematics to elementary students is complex and challenging. I recognized that field experience in my mathematics methods courses had to make the complexities of teaching more visible for prospective teachers. In other words, prospective teachers must study teaching practices. Such study would not only require viewing, analyzing, and discussing practices but also include the opportunity for prospective teachers to practice and analyze their own teaching.

This study investigated how elementary teachers in a mathematics lesson study made sense of student learning, teaching, and content, as related to using representations in teaching multidigit subtraction, and how changes occurred over time in their talk and practice. The lesson-study process paved a group talk path along which teacher talk shifted from superficial to deeper consideration of student learning. By providing a context in which interactions of diverse ideas drove teacher learning, lesson study facilitated teachers making connections between the craft knowledge of teaching and scholarly knowledge. Individual teacher talk paths varied within the group path, and one teacher's learning path and the interaction of different learning paths is discussed.

<div><p>This study aims to examine the relationship between epistemological beliefs, teaching-learning beliefs and assessment beliefs in mathematics education. This research is a quantitative study with a correlational study. Data collection using the survey method with a cross-sectional design. The participants were 71 pre-service elementary school , mathematics teachers. The data on beliefs were collected through means of a questionnaire. The data collected from the questionnaire were then analyzed quantitatively through descriptive and inferential statistics. Descriptive statistics utilizes the mean value, maximum value, and standard deviation values. Inferential statistics use the product-moment correlation as well as path analysis. The research results show that there is a positive and significant correlation between static and dynamic beliefs on epistemology of mathematics, and the constructivist beliefs on mathematics teaching and learning, with the productive beliefs on mathematics assessment. In addition, there is seen to be a functional influence between both epistimological beliefs (both static and dynamic), as well as beliefs on teaching and learning (constructivist) and beliefs about mathematic assessment (productive). The results of this research signify the importance of considering one’s beliefs about the epistemology of mathematics and mathematics teaching and learning when constructing their beliefs regarding mathematics assessment.</p></div>

This research was the first four parts of the Borg and Gall version of RnD research, (1) preliminary research and studies, (2) research planning, (3) initial product development, and (4) limited field testing. The purpose of this study is to explain the importance of using traditional games in teaching mathematics in elementary schools using a realistic mathematical approach. The method used is qualitative. Data obtained through interviews and teacher response scales. The subjects of this study were 15 elementary school teachers teaching elementary mathematics in Salatiga which were selected by purposive sampling technique. The results of this study is the steps to develop traditional games with a realistic mathematical approach in elementary mathematics learning.

This study focused on understanding the evaluation of the area of a rectangular region as a multiplicative relationship between the lengths of the sides. The analysis of data from a whole-class teaching experiment involving prospective elementary teachers resulted in the development of a description of the quantitative reasoning involved. Important aspects of this reasoning include the anticipation of a rectangular array of units as the structure of the area quantity and the subsequent constituting of the units based on the linear measures. The analysis of the prospective teachers' understandings proved useful in generating additional problems. The teachers' engagement with these problems resulted in their developing more complete understandings of the constitution of area units.

Math is often taught poorly emphasizing rote, procedural methods rather than creativity and problem solving. Alberta Education developed a new mathematics curriculum to transform mathematics teaching to inquiry driven methods. This revised curriculum provides a new vision for mathematics and creates opportunities and requirements for professional learning by teachers. Conventional offsite, after school, or weekend professional development is typically “sit and listen, maybe try on Monday”. Professional development that is embedded, responsive, and personalized is known to be more effective at changing teaching practice. Alberta teachers are geographically dispersed making online professional learning a desirable alternative to on-site workshops. As access to and use of the Internet gains momentum in schools across the country, opportunities for collaborative, online professional development become more viable. The online professional development in this hermeneutic study maps on to the new vision promoted in Alberta’s math curriculum, and addresses the challenge of a distributed teacher population. Thirteen geographically dispersed participants, including 10 teachers, a PhD mathematician, and two mathematics education specialists, collaborated in an online professional learning community to build knowledge for teaching mathematics. This paper describes and interprets the shared experiences of learners within an online, synchronous learning community that focused on discipline rich, focused inquiry with mathematics. Findings show that the nature and quality of the mathematics task impacted the quality and nature of the online interaction. Mathematics problems that incorporated easily drawn symbols and minimal text worked best in the online collaborative space. Members of this learning community discovered how to assert their identity in the online environment.

Abstract This article is aimed at elementary teacher attitudes towards using educational technologies in education, especially in teaching elementary mathematics. The data used were collected by a questionnaire which was created on the principle of semantic differential. Basic statistical characteristics were calculated and a graph of the semantic space was plotted for all of the respondents participating in the study. In general, it is surprising that how differently teachers perceive the use of computers in education on the one hand, and the use of computers in teaching mathematics on the other. The results show that teachers are not convinced that it is meaningful to implement computers into primary mathematics education or that employing multimedia in teaching mathematics might bring educational benefits. Keywords: Mathematics, computer teaching assistant, education.

One of the basic abilities in learning mathematics is the ability of students to understand mathematics. Mathematical comprehension ability will develop other mathematical abilities, including communication, connection and problem-solving abilities. To be able to hone students 'mathematical abilities, a learning model is needed that is appropriate to the students' character and the material being taught. One learning model that can improve student learning outcomes is the Contextual Teaching and Learning (CTL) model. The method used in this study is Classroom Action Research (CAR). Subjects in this study were fifth grade in Elementary School. The instruments used in this study were tests and observation sheets of teacher and student activities. Based on the analysis of research data, it is concluded that CTL can improve the ability of mathematical understanding of fraction concept for elementary students. Thus, the use of CTL learning models can be used as an alternative learning to be applied to learning mathematics in elementary school especially on learning concept of fractions.

The aim of this research is to develop a media for learning mathematics in "Opung HAN" elementary school based on Interactive Audio Instruction (IAI) for students majoring in UNIMED elementary school teacher education. The IAI-based "Opung HAN" fraction media was compiled based on observations during the learning and analysis conducted on the dictates of high-class mathematics education courses and interviews conducted with elementary school teacher education students, where teachers were very difficult to convey material related to fractions, The teacher does not know what media to use in teaching broken material. On the other hand, in the high school mathematics education textbook, there is also no media / teaching aids that can be used to teach fractional material. The specific purpose of this research is: developing IAI-based "Opung HAN" fraction media which will later be used by students majoring in primary school teacher education in teaching fraction material when they later become a teacher. This research uses development research (Developmental Research). The subjects of this study were students majoring in primary school teacher education at the State University of Medan. In the initial stage, observations were made during the learning process, analysis of the dictates of high-level mathematics education courses and continued with interviews with students. From the results of these observations and interviews, an initial draft of the IAI-based "Opung HAN" fraction was compiled. Furthermore, the initial design of the IAI-based "Opung HAN" fraction media was validated by a team that aimed to assess the quality of these elementary mathematics learning media fractions so that the fractional media became effective learning media which would later be used by lecturers and students in the lecture process.Keywords : IAI, Fraction media, math learning.

This study investigates relationships between a beginning elementary school teacher's beliefs and mathematics teaching practices. A proposed model of relationships between beliefs and practice provided a conceptual framework for the examination of factors that influence beliefs, practice, and the level of inconsistency between them. Data were gathered over 10 months through audiotaped interviews, observations, document analysis, and a beliefs survey. Analyses included the categorization and comparison of beliefs and practice and the development of a revised model of relationships between beliefs and practice. Findings indicate that this teacher's beliefs and practice were not wholly consistent. Rather, her practice was more closely related to her beliefs about mathematics content than to her beliefs about mathematics pedagogy. Her beliefs about mathematics content were highly influenced by her own experiences as a student and her beliefs about mathematics pedagogy were primarily influenced by her own teaching practice. However, the extent to which her teacher preparation program influenced either her beliefs or practice was limited.

This mixed-methods study explored the pedagogical practices of Prospective Elementary Mathematics Specialists (PEMSs) as they completed a university K-5 Mathematics Endorsement program. Participants were 13 elementary teachers at an urban, high-needs charter school. Data were collected via individual interviews, written reflections on enacted teaching practices, two observations of classroom teaching practices, and a 36-item Cognitively Guided Instruction Teacher Knowledge Assessment. The findings show the PEMSs were connecting their learning during program courses with instructional practices in their classrooms, as 85% were implementing standards-based learning environments (SBLEs) at a high level, with the classroom event of providing their students opportunities to make conjectures about mathematical ideas as a relative struggle. The PEMSs described pedagogical shifts across the program, providing insights into these changes, along with how particular program components contributed, with the emergent themes of skepticism, trying it on, shifters, and need more support.

Using the lens of Gutiérrez's framework for equity-based teaching, this study examines how two clinical practice experiences supported elementary education teacher candidates' development of mathematics pedagogies. Findings indicate that clinical experiences with teachers who demonstrate equity-based practices were associated with candidates' confidence to implement equity-based teaching. Further, in classrooms that did not promote equity-based teaching candidates were still able to implement equity-based practices when teaching small groups of students. Implications include the need for teacher educators with specific content expertise to form partnerships and clinical practice experiences with schools to ensure that equity-based practices are present.

Four case studies of preservice teachers enrolled in a STEM-focused elementary teacher preparation program are used to document changes in mathematics and science teaching efficacy over the course of one academic year. Qualitative analysis revealed that all four case studies experienced changes in their mathematics and science teaching efficacy beliefs over the course of the year. Participants described unique ways of understanding their growth (or lack thereof) in teaching efficacy, the trajectory of teaching efficacy over the course of the year, and the role of teacher training in changing their efficacy beliefs.

The present research focuses on developing mathematics comic as a teaching material that integrates the moral value of discipline and hard work for elementary school students. This character-building comic development method was made based on the ADDIE model, which includes analysis, design, development, implementation, and evaluation. Twenty-nine grade four students were recruited as samples, consisting of a small group of students in the limited trial group and a big group of students in the field trial group. The data collection technique used was a questionnaire. The development of mathematics comic teaching material containing discipline and hard work character-building has successfully resulted in a comic that met the feasibility standards. The field trial showed a significant increase of 0.76 and 0.74 in students’ character development in terms of discipline and hard work, respectively. The results indicate the effectiveness of mathematics comics in instilling Pancasila moral values in elementary mathematics teaching in Indonesia.

The purpose of this study has been to determine the views of elementary mathematics teachers on the applicability of modeling in mathematics courses. A case study was conducted with 17 elementary mathematics teachers working in various provinces in Turkey. An interview form consisting of open-ended questions was designed for the purpose of collecting data, which was obtained through semi-structured interviews. From the categories constituting the themes developed via the views of the teachers, four major conclusions and one minor conclusion were reached at the end of the study. Study results showed that the elementary mathematics teachers’ knowledge of the process and teaching performance had an impact on their views of the applicability of modeling.

This article reviews research on the achievement outcomes of three types of approaches to improving elementary mathematics: mathematics curricula, computer-assisted instruction (CAI), and instructional process programs. Study inclusion requirements included use of a randomized or matched control group, a study duration of at least 12 weeks, and achievement measures not inherent to the experimental treatment. Eighty-seven studies met these criteria, of which 36 used random assignment to treatments. There was limited evidence supporting differential effects of various mathematics textbooks. Effects of CAI were moderate. The strongest positive effects were found for instructional process approaches such as forms of cooperative learning, classroom management and motivation programs, and supplemental tutoring programs. The review concludes that programs designed to change daily teaching practices appear to have more promise than those that deal primarily with curriculum or technology alone.

Abstract: The perspective of teaching in rural area led this study to investigate non-indigenous teacher's teachings in an indigenous classroom of one of rural elementary schools in Hualien, Taiwan. The teacher's views on indigenous students' grade and how it related to the teacher’s teaching were explored also. This study was a case study. Data was collected and analyzed by applying qualitative method. It implemented classroom ethnography approach. It revealed that although the teacher had demonstrated a great deal of passion in teaching indigenous students, involvement the students in some indoor and outdoor activities, and using various media to get students’ attention, but he was concerned about his students’ low academic achievement. In Hualien, there are annual provincial examinations on the subjects of Chinese, Mathematics and English in May, which all the elementary students are required to take. To improve the student academic performance he used some classroom time to practice drills rather than spending time on exploratory activities. When indigenous students' underperformance in standardized tests are considered as reflecting poor quality of teaching, preparing students for the sit-in tests will continue to be a part of classroom teaching. This study suggests that teachers have to understand the educational context in which teaching and learning take place. Knowing this would provide teachers a more meaningful teaching and learning. Keywords: Teaching, grade, non-indigenous teacher, indigenous students, rural elementary school

Teaching students to self-regulate enhances their mathematics performance, yet few studies have investigated the long-term differential impact of particular self-regulation strategies specifically for low-achieving students. This quasi-experimental study evaluates the effect of teaching different self-regulation strategies on mathematical problem solving in low-achieving students. The participants were 69 sixth-grade elementary school students randomly assigned to one of three experimental groups (and taught predominantly cognitive, metacognitive or volitional strategies, while verifying intervention fidelity) or a control group for 16 sessions. Mathematical problem-solving skills were evaluated prior to the intervention, upon completion, and two months later. While all three intervention groups obtained significantly better results compared to the control group immediately after the intervention, volitional and metacognitive strategies showed the strongest and most lasting positive effects. We conclude that low-achieving students could benefit from learning self-regulation strategies, particularly when these strategies take into account the affective and motivational dynamics of learning.

In this study, it was tried to determine teaching activities that elementary preservice mathematics teachers exhibited in a micro teaching session. Preservice teachers are required to prepare and later present a sample micro teaching session. First of all, they were advised to freely select a topic (or an attainment) of their own intention within 5-8 middle school mathematics subjects. Then, every one of them planned their own special session. While they were planning the sessions, they were advised to take into account of all perspectives and practices of the theoretical subjects covered via the course of Special Teaching Methods 1 and the experiences that they gained during the other courses of the mathematics teacher education program. After that, each one performed tasks in the classroom environment related to their own planning. No intervention was made to the preservice mathematics teachers by the lecturer during the sessions. After each session, the remaining candidates and the lecturer made critique about the candidate’s performance. The study was conducted with 50 preservice teachers who take Special Teaching Methods II course. A systematic observation form has been prepared and used for data collection. Descriptive analysis and content analysis based on observations were used as mixed methods in the study. Findings show that preservice mathematics teachers have some misconceptions regarding the lectured subject, besides the deficiencies and mistakes in the course planning and performance.

In the scenario of discussions about the didactic and epistemological obstacles that 'haunt' the teaching and learning processes of Mathematics content in Elementary School in the early years, we find among other Santos theorists (2007; 2014; 2015; 2017). In this study, we aim to present the importance of challenging the Pedagogy graduate to leave his 'comfort zone', where he reproduces the mathematical contents/models, and provoke him to deconstruct/reconstruct/discover the mathematical concepts, to the detriment of a paralytic reproduction, and thus, we contribute to the thinking/questioning, from challenging situations. This practice has also contributed to the pedagogist's perception that his knowledge must exceed that of the student; and, above all, it has made it possible for the pedagogist to reflect more on his praxis, in order to constitute himself within the process as an epistemic subject, providing him with a rethinking of his action in a vision of what it is to teach. The actions have awakened us to the need for a more innovative teaching formation that overcomes challenges and difficulties in the exercise of teaching with excellence.

Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS.

Research on mathematics teacher education indicates that offering an appropriate constructivist-based teaching model of mathematics instruction to preservice elementary teachers enhances their teaching abilities and confidence in future teaching. The purpose of this study was to investigate preservice elementary teachers' decisions about teaching strategies and their attitudes toward mathematics and computer-related technologies in a constructivist-centered methods course which included the use of problem solving multimedia. The treatment consisted of six hours of multimedia-enhanced instruction over two weeks. This study focused on three mathematics education topics taught to each group of students: problem-solving, technology, and ratios/proportions. The results indicated that constructivist-based instruction using multimedia helped the participants develop more positive attitudes toward computer-related technologies and influenced their decisions to plan more constructivist-based teaching strategies than those participants in the comparison groups.

This study was designed to assess the mathematics teaching efficacy beliefs of undergraduates in elementary education through a manipulative-based course in mathematics. Responses of 106 university undergraduates to the 21-item Mathematics Teaching Efficacy Beliefs administered as pre- and posttest without a control group showed a significant immediate postcourse change in their efficacy beliefs using dependent t test.

Graduate teaching assistants serve as instructors of record for numerous undergraduate courses every semester, including serving as teachers for mathematics content courses for elementary preservice teachers. In this study, we examine 6 teaching assistants' teaching practices in the context of a geometry content course for preservice teachers by focusing on their enactment of reasoning-and-proving tasks. Results indicate that teaching assistants engaged preservice teachers in a variety of reasoning-and-proving activities. For 42 of 82 tasks observed, preservice teachers' engagement in reasoningand-proving processes decreased relative to the potential for reasoning and proving in mathematical tasks. This investigation into teaching assistants' teaching practices identifies factors associated with their enactment of reasoning-and-proving tasks (e.g., generating student participation). This research has implications for professional development to support college mathematics instructors' teaching.

Programming and computational thinking have emerged as compulsory skills in elementary school education. In 2018, Sweden has integrated programming in mathematics education with the rationale that it fosters problem solving and logical thinking skills and motivates students to learn mathematics. We investigated how teachers introduce programming in mathematics education in a Swedish primary school using an explorative case study. We followed four mathematics teachers during the first semester in which programming was mandatory. They taught second-, sixth- and ninth-grade students. Our contributions are threefold: we provide an account of how programming is taught in mathematics education; we discuss how teachers reflect on the challenge of teaching programming in mathematics; and we report on students’ understanding of programming and their view on the relationship between programming and mathematics.