The Relation between the Teaching of Mathematics and Statistics in the Republic of South Africa

The purpose of this study is to explore the relation between the teaching of Mathematics and the teaching of Statistics at high school level in the South African Context. The study also examines and analyses examples of statistical teaching situations from both a mathematical and a statistical perspective with view to reveal the links between the teaching of Mathematics and teaching of Statistics. A non-empirical method or conceptual method was followed to achieve the purposes of the study. The study reveals the cardinal links between the teaching of Mathematics and teaching of Statistics. Hence the call to educators to acknowledge the symbiosis to enhance the teaching and promote an awareness of the ways in which Statistics is presented and aligned in the South African Mathematics high school Curriculum. Keywords: teaching mathematics, teaching statistics, high school, South Africa context

João Antonio Coqueiro: sua produção e expertise docente

Apresentamos o professor maranhense João Antonio Coqueiro como um expert no ensino de matemática no final do século XIX e início do século XX, na província/estado do Maranhão. Pautados teoricamente em Hofstteter et al. (2017), Morais (2017) e Valente (2016), buscamos responder ao questionamento: como João Antonio Coqueiro sistematizou saberes matemáticos objetivados na formação de professores de matemática e no ensino de matemática no Maranhão? Constatamos que João Antonio Coqueiro participou, de modo decisivo, da produção de saberes no ensino de matemática e da formação de professores que ensinavam matemática, em vários níveis de ensino no Maranhão, configurando, assim, a sua expertise.João Antonio Coqueiro: his production and teaching expertiseWe present the Maranhão teacher João Antonio Coqueiro as an expert in the teaching of mathematics at the end of the 19th century and beginning of the 20th century, in the province/state of Maranhão. Theoretically guided by Hofstteter et al. (2017), Morais (2017) and Valente (2016), we sought to answer the question: how did João Antonio Coqueiro systematized mathematical knowledge aimed at training mathematics teachers and teaching mathematics in Maranhão? We found that João Antonio Coqueiro participated, in a decisive way, in the production of knowledge in the teaching of mathematics and in the training of teachers who taught mathematics at various levels of education in Maranhão, thus shaping his expertise.Keywords: Mathematics; Expertise; Maranhão.

A expertise em educação de Carleton Washburne na produção de saberes sobre o ensino de aritmética

O objetivo deste texto é analisar, em perspectiva historiográfica, a constituição de saberes sobre o ensino de matemática a partir da emergência da figura do expert no âmbito escolar. Trata-se, em específico, de analisar as ações pedagógicas de Carleton Washburne, importante pedagogo estadunidense da educação progressista. Para tanto, utilizou-se como ferramenta de análise os conceitos de expertise e expert advindos dos estudos desenvolvidos por Hofstetter et al. (2017). Os resultados da análise indicam que ao ser convocado para transformar as escolas públicas de Winnetka em escolas de excelência, Washburne produziu e sistematizou saberes específicos sobre o ensino de aritmética, resultando na reestruturação dos conteúdos matemáticos, em novas práticas, novos materiais didáticos, nova relação aluno-professor-saber, novos saberes pedagógicos, de modo a garantir que o aluno seguisse seu próprio ritmo de desenvolvimento. A esse tempo, não basta mais ao professorado saber os conteúdos aritméticos e os métodos pelos quais ensiná-los, mas o que, como, por que e quando e isso depende da produção de novos saberes escolares sobre o ensino de aritmética na escola primária.Carleton Washburne's pedagogical expertise in the production of knowledge about the teaching of arithmeticThe objective of this text is to analyze, from a historiographic perspective, the constitution of knowledge about the teaching of mathematics from the emergence of the figure of the expert in the school environment. It is specifically about analyzing the pedagogical actions of Carleton Washburne, an important American pedagogue of progressive education. For this purpose, the concepts of expertise and expert arising from the studies developed by Hofstetter et al 2017 were used as an analysis tool. The results of the analysis indicate that when invited to transform Winnetka's public schools into schools of excellence, Washburne produced and systematized specific knowledge about the teaching of arithmetic, resulting in the restructuring of mathematical contents, in new practices, new teaching materials, new student-teacher-knowledge relationship, new pedagogical knowledge, in order to ensure that the student followed his own pace of development. At this time, it is no longer enough for teachers to know the arithmetic contents and the methods by which to teach them, but what, how, why and when, and this depends on the production of new school knowledge about the teaching of arithmetic in primary school.Keywords: Arithmetic made to mesure; Teaching individualization; Expert in education; Winnetka system; Teacher training.

THE CONCEPT OF TEACHING MATHEMATICS IN THE 1ST GRADE OF A GENERAL EDUCATION SCHOOL

The teaching of mathematics should reflect the global trends in the development of mathematical and pedagogical scientific thought. The authors develop guidelines for studying mathematics in the 1st grade based on the Federal State Educational Standard. Thus, the structure and the form of the textbook content are described by chapter. The theoretical part should allow students to complete screening questions, univariate and multivariate tests, problems, and exercises. Each chapter of the developed textbook is divided into paragraphs, and each paragraph is divided into items. One item of theoretical material contains either a new idea to study or a set of interrelated concepts that define a new idea. According to this, it is possible to form mathematical knowledge trajectories. So, there are broad opportunities to transform knowledge elements into multimedia forms, including presentations, videos, test modules, and other newly emerging means of representation and visualization, using the achievements of artificial intelligence. It is possible to define main themes such as natural numbers counting, acquaintance with geometric shapes, comparison of objects in the value and quantity, acquaintance with a squared paper and measurement standards, the study of objects position, the sets consideration, introduction to the algorithm concept can. The authors’ conceptual directions of teaching mathematics in the 1st grade provide the foundation for mathematical education in general education schools for all the years of study.

Implicaciones de la gamificación en educación matemática, un estudio exploratorio

Las aplicaciones tecnológicas ofrecidas para la educación son variadas, brindando nuevas posibilidades de aprendizaje. Se debe estar en constante vigilancia de las propuestas de gamificación para el aula, dado que su desarrollo y uso no asegura un éxito en la enseñanza. Estudiamos el impacto de la gamificación en la enseñanza de la matemática, analizando su papel en el tratamiento de las figuras geométricas cono y cilindro con estudiantes de 13 y 14 años. Desde un enfoque cuantitativo descriptivo de tipo cuasi-experimental, con grupo control y piloto y aplicación de test, se realiza un análisis estadístico clásico e implicativo, evidenciando un mayor porcentaje de respuestas correctas del grupo piloto, en el ítem sobre la relación entre el volumen del cono y el cilindro, con un 96,3%, en contraste un 73,08% que obtuvo el grupo control. Además, se muestra un comportamiento con alto nivel de similaridad (84,4%) entre el uso del videojuego y responder satisfactoriamente los ítems. Esto nos sugiere que este medio educativo puede provocar mejoras en los aprendizajes del alumnado, quien parece ser proclive a su uso. The technological applications offered for education are varied, providing new learning possibilities. Gamification proposals for the classroom must be constantly monitored, since their development and use does not ensure success in teaching. We study the impact of gamification in the teaching of mathematics, analyzing its role in the treatment of geometric cone and cylinder figures with 13 and 14 years old students. From a descriptive quantitative approach of quasi-experimental type, with a control and pilot group and test application, a classical and implicative statistical analysis is carried out, showing a higher percentage of correct answers from the pilot group, in the item on the relationship between the volume of the cone and the cylinder, with 96.3%, in contrast to 73.08% obtained by the control group. In addition, a behavior with a high level of similarity (84.4%) is shown between the use of virtual games and satisfactorily answering the items. This suggests that this educational medium can cause improvements in the learning of students who seem to be prone to its use.

Mediating Wor(l)ds: Teaching and Learning of Mathematics in English in Malaysia

<p>This study investigates the implementation of ETeMS (English for the Teaching of Mathematics and Science) policy in Malaysia. Teachers, who learnt mathematics and were trained to teach mathematics in Bahasa Melayu, have had to teach mathematics in English since the implementation of ETeMS. This study observes two teachers and their teaching of mathematics in English to ten-year-old students. The study draws on sociocultural and sociolinguistic theories of classroom research which strongly advocate that education is a process of interaction. Both theories place importance on the joint construction of meaning through classroom interaction. The research mainly seeks to understand how teaching and learning is mediated in classrooms through the new medium of instruction. Adapting Erickson’s (1982) proposed constructs: academic and social participation structures, the study investigates the academic world and social world of linguistically altered mathematics classrooms. Sinclair and Coulthard’s (1975) discourse analysis tool has been adapted to study the teaching and learning of mathematics in English. Principles from conversation analysis and critical discourse analysis have been drawn upon to study the social world of linguistically altered classroom. Analysis of the classroom interaction showed that the academic world of linguistically altered classrooms is still heavily reliant on triadic dialogue. Despite that, teacher talk, through various discursive practices, was found to be an important mediating tool for mathematical content and mathematical English. Mathematical content and mathematical English were also shown to be jointly constructed through the use of several other mediating tools. The study revealed that there is more of an emphasis on teaching for testing than teaching for understanding, hence more attention to procedural fluency than to conceptual understanding, thus more emphasis on calculation discourse than on conceptual discourse. However, once the content and concept has been jointly constructed, students take some ownership of the classroom interaction. As well as the academic world, the study investigates how the new language of instruction mediates the social world of the classroom. The study found that the new medium (re)creates the social world of the classroom as teachers and students position and (re)position themselves and each other, and (re)establish their identities and sense of agency through the new language. From the insights gleaned from this study, the inter-relationship between ETeMS policy on paper and ETeMS policy in practice is explored. Some important implications for policy, practice and inter-disciplinarity in mathematics education and applied linguistics are discussed. The thesis concludes by proposing an adapted and extended model of mathematics education and directions for future research.</p>

Mediating Wor(l)ds: Teaching and Learning of Mathematics in English in Malaysia

<p>This study investigates the implementation of ETeMS (English for the Teaching of Mathematics and Science) policy in Malaysia. Teachers, who learnt mathematics and were trained to teach mathematics in Bahasa Melayu, have had to teach mathematics in English since the implementation of ETeMS. This study observes two teachers and their teaching of mathematics in English to ten-year-old students. The study draws on sociocultural and sociolinguistic theories of classroom research which strongly advocate that education is a process of interaction. Both theories place importance on the joint construction of meaning through classroom interaction. The research mainly seeks to understand how teaching and learning is mediated in classrooms through the new medium of instruction. Adapting Erickson’s (1982) proposed constructs: academic and social participation structures, the study investigates the academic world and social world of linguistically altered mathematics classrooms. Sinclair and Coulthard’s (1975) discourse analysis tool has been adapted to study the teaching and learning of mathematics in English. Principles from conversation analysis and critical discourse analysis have been drawn upon to study the social world of linguistically altered classroom. Analysis of the classroom interaction showed that the academic world of linguistically altered classrooms is still heavily reliant on triadic dialogue. Despite that, teacher talk, through various discursive practices, was found to be an important mediating tool for mathematical content and mathematical English. Mathematical content and mathematical English were also shown to be jointly constructed through the use of several other mediating tools. The study revealed that there is more of an emphasis on teaching for testing than teaching for understanding, hence more attention to procedural fluency than to conceptual understanding, thus more emphasis on calculation discourse than on conceptual discourse. However, once the content and concept has been jointly constructed, students take some ownership of the classroom interaction. As well as the academic world, the study investigates how the new language of instruction mediates the social world of the classroom. The study found that the new medium (re)creates the social world of the classroom as teachers and students position and (re)position themselves and each other, and (re)establish their identities and sense of agency through the new language. From the insights gleaned from this study, the inter-relationship between ETeMS policy on paper and ETeMS policy in practice is explored. Some important implications for policy, practice and inter-disciplinarity in mathematics education and applied linguistics are discussed. The thesis concludes by proposing an adapted and extended model of mathematics education and directions for future research.</p>