E-Learning of Mathematics- A New Trend of Learning in 21st Century During Covid-19 Pandemic

The goal of this study is to highlight current breakthroughs in digital technology research in the subject of mathematics education. The Covid-19 outbreak in 2020 turned both private and public life on its head. Higher education institutions all across the world were forced to switch their teaching and learning online on very short notice. As a result, many types of software like Google Meet, MS teams, Zoom and WebEx, etc. have been developed to help teachers and students communicate more effectively. Problem-solving is a characteristic of mathematical activity and an essential component of the development of mathematical and analytical skills. The capacity to answer a broad variety of complicated mathematical problems is a major goal of mathematics education and learning. However, the process of problem-solving in online mode has not received the attention it deserves, because many professors are uncomfortable with it. As a result, problemsolving as a method and skill is not taught as an intrinsic component of the mathematics learning process by instructors. Qualitative methodology is a technique used for this study. The purpose of this study is to reveal the roles and significance of mathematics teaching and learning via the use of technology applications (E-learning). Keywords: Mathematics, COVID-19, E-learning, Education

Algebraization Levels in the Study of Probability

The paper aims to analyze how the different degrees of mathematical formalization can be worked in the study of probability at non-university educational levels. The model of algebraization levels for mathematical practices based on the onto-semiotic approach is applied to identify the different objects and processes involved in the resolution of a selection of probabilistic problems. As a result, we describe the possible progression from arithmetic and proto-algebraic levels of mathematical activity to higher levels of algebraization and formalization in the study of probability. The method of analysis developed can help to establish connections between intuitive/informal and progressively more formal approaches in the study of mathematics.

Scientific and Methodological Support for Teachers in the Context of Gamification in Mathematics Study in the Russian System of Additional Education

The relevance of this study is due to the practical significance of the issues of using game mechanisms in the process of teaching mathematics, the lack of research into the issues of symbiosis of game and didactic technologies in mastering complex mathematical knowledge, the need to search for effective technologies to establish how they affect the development of students and the formation of a modern style of thinking. The analysis of global trends and practices of introducing elements of gamification into the education system has shown that the mastering of complex knowledge and patterns of mathematical activity, the solution of problem areas of mathematics at different levels of learning and complexity is carried out by a complex of mathematical and information methods without the integration of game elements. It has been substantiated that gaming technologies in combination with the informatization of mathematical activity give a powerful motivational charge to the study of mathematics, actualize the processes of self-organization of cognitive activity, and contribute to the development of a probabilistic style of thinking. The purpose of the study is to provide a theoretical substantiation and effective methodological support for the process of professional development of mathematics teachers in the context of gamification in mathematics study with the effect of developing a probabilistic style of thinking. The authors have developed an arrangement mechanism and determined the content of scientific and methodological support for teachers working in the constituent entities of the Russian Federation to provide additional educational services in the context of gamification in education. The developed materials, in particular, include evaluative case tests for identifying competence deficiencies in teachers, which ensure the formation of a probabilistic style of thinking based on gamification processes by managing the information saturation of the motivational field of learning. In addition, the authors proposed an additional professional education program for teachers, Mathematics in Gaming Activities (Business, Didactic and Intellectual Games) , and developed new forms of certification and assessment materials (gamification-based didactic solutions and effective practices). Using the concept of gamification, it was possible to demonstrate the activation of cognitive and motivational structures, in particular, the effective development of a probabilistic style of thinking in the process of mastering complex mathematical knowledge through its adaptation to school mathematics. The results of the study allow making it possible to bring the process of teaching students and developing their personalities to a modern qualitative level using current achievements in the field of digitalized education.

Visually impaired student-teachers’ knowledge and use of basic assistive technology tools for mathematics

Studies show that assistive technology tools have provided opportunities for the visually impaired in some developed countries to pursue mathematics programmes and foster inclusive education. However, their counterparts in developing countries sparingly participate in any mathematical activity due to low knowledge and use of these tools. The main purpose of this study was to expose student-teachers with visual impairments to basic assistive technology tools. The knowledge and use of the tools helped to convert, convey and interpret basic mathematical equations. The design was a case study involving five student-teachers who were admitted to the Department of Basic Education, University of Education, Winneba to pursue a Post Diploma in Mathematics programme. A semi-structured interview guide was used to collect the data whose items contained tools for general administration, additional support, STEM, mathematics instruction, polynomials and assessment. These served as the cases of the study and data analysis. The analysis was undertaken in two stages. The first stage explored their knowledge and use of the assistive technology tools. The second stage analysed transcriptions of statements. The two stages helped to corroborate the findings. To ensure the validity and reliability of the findings, the interview guide was validated by post-graduate students of the Department of Special Education and Basic Education. The findings showed that the student-teachers had little knowledge and use of the basic assistive technology tools. However, they were still desirous to learn and use the basic assistive technology tools for mathematics teaching and learning. It was therefore recommended that stakeholders make available and accessible common basic assistive technology tools to schools, and restructure the mathematics curriculum to suit the integration of assistive technology tools.

The Influence of NeoTrie VR’s Immersive Virtual Reality on the Teaching and Learning of Geometry

The use of dynamic, three-dimensional software with virtual reality offers new possibilities for the teaching and learning of geometry. We explore the effects of introducing the immersive virtual reality software NeoTrie VR in real classes. Within a Design Research framework, we present qualitative observational data to report how the collaboration among a software development company, university researchers, and schools produces improvements in the design and updating of the software; the geometrical content, representations, and mathematical activity that students have access to as well as the way teachers conceive and manage the teaching of geometry.

Generating mathematical knowledge in the classroom through proof, refutation, and abductive reasoning

Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this activity and the construction by students of knowledge, such as mathematical concepts and theorems, that is new to them. This issue is significant to seeking a better integration of mathematical practice and content, emphasised in curricula in several countries. In this paper, we address this issue by exploring how students generate mathematical knowledge through discovering and handling refutations. We first explicate a model depicting the generation of mathematical knowledge through heuristic refutation (revising conjectures/proofs through discovering and addressing counterexamples) and draw on a model representing different types of abductive reasoning. We employed both models, together with the literature on the teachers’ role in orchestrating whole-class discussion, to analyse a series of classroom lessons involving secondary school students (aged 14–15 years, Grade 9). Our analysis uncovers the process by which the students discovered a counterexample invalidating their proof and then worked via creative abduction where a certain theorem was produced to cope with the counterexample. The paper highlights the roles played by the teacher in supporting the students’ work and the importance of careful task design. One implication is better insight into the form of activity in which students learn mathematical content while engaging in mathematical practice.

Connecting expectations of Te Whāriki and The New Zealand Curriculum: Examples of mathematical practices

The first year of primary school aims to be closely connected with early childhood education, yet this is often invisible in the curriculum of specific subjects. This paper sets out an approach that uses mathematical practices as a curriculum tool that reconceptualises school mathematics. Using the early childhood mathematics framework of Te Kākano, the strands of mathematical practices are important descriptors of mathematical activity for children. We describe examples of mathematical learning from both early childhood and the first year of school, and make a case for using mathematical practices as a conceptual tool for designing a mathematics curriculum in the first years of school.

Inspiring Children's Mathematical Activity Through Contact with a Picture Book

Children’s literature has a cognitive value and is a source of aesthetic experiences. Picture books with mathematical content are a special type of children’s books. The study aims to show that picture books where mathematical text is combined with images in an aesthetic form provide impulses to create educational situations that inspire mathematical activity. Based on the classification of mathematical activity by Ewa Kozak-Czyżewska, we developed our methodological proposals for stimulating creative and imitative mathematical activity in children. These suggestions are presented on the basis of our work with two books: Numbers written by Jacek Cygan and At our house written by Isabel Minhós Martins and Madalena Matoso. For the purpose of this study, educational classes with the use of mathematical literary texts were conducted for six-year-old children in kindergarten. It has been shown that picture books can inspire creative and imitative mathematical activity in children. By providing positive experiences, these texts can support the processes of learning mathematics, awaken children’s motivation to calculate and use mathematics in everyday life. The presented study may be used as a model of working with picture books with mathematical content in kindergarten.

Entertaining mathematics presented by steam educational approach in teaching preschool and primary school age children

The subject of this article is to clarify the connection between entertainment in Math lessons and educational STEAM technologies, which have the potential to motivate and stimulate the interest of preschool and primary school age in Math and their cognitive logical - mathematical activity. The article discusses the STEAM approach in its essence and teaching Maths using this method. The article also presents some educational technologies in fun Math, which allow children to discover for themselves through the methods of experimentation, exploration and experience, and this acquired independence leads children to an increased interest and motivation to learn.