Algebra I Teachers’ Beliefs and Knowledge of Algebra For Teaching

Research indicates that teachers’ mathematical beliefs and mathematical knowledge for teaching impacts practices in the classroom. Research also suggests that success in Algebra I is the gatekeeper to higher-level mathematics. With the increased number of certification pathways in some states, it is important to identify those Algebra I teachers’ beliefs and knowledge of algebra for teaching. A study of current Algebra I teachers revealed that regardless of certification pathway, mathematical beliefs are not significantly different. Additionally, significant differences did exist in regards to the certification pathway and Knowledge of Algebra for Teaching (KAT) levels.

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.

The phenomenon of complex knowledge in teaching mathematics as a factor of mathematical literacy forming of school students

Introduction. Mathematics teaching based on the development of complex knowledge generalized constructs (for example, modern achievements in science) becomes an effective direction for the formation of school student’s mathematical literacy with a significant applied and mathematical-informational potential of personal development. The purpose of the study: to develop a technology for student’s mathematical literacy formation during the development of complex mathematical knowledge and in the context of universal educational actions actualization by means of mathematical and computer modeling. Materials and methods. The research materials are based on the historiogenesis and actualization of mastering processes of complex mathematical knowledge by students as an effective mechanism for personal development. A synergetic approach, digitalization tools and visual modeling methods are being implemented to adapt the mastering processes of complex knowledge to school mathematics with the effect of student’s mathematical literacy forming. The choice and justification of methods for personal experience founding create the effect of core actualization of universal educational actions, manifest themselves in the processes of students ' activities individualization. The results of the study. For the first time, a technology for student’s mathematical literacy formation based on the symbiosis of mathematical and computer modeling in mathematics development of complex knowledge has been developed. The founding clusters and research and adaptation technology of hierarchies of complex multi-level knowledge (including modern achievements in science) to school mathematics are constructed. The stages and means of visual modeling and personal experience founding with the effect of student’s mathematical literacy forming in a rich information and educational environment are clarified. Conclusion. Educational practices have shown the high efficiency of this method to school student’s mathematical literacy forming in the process of modern achievements mastering in science. Such didactic solutions and practices are characterized by the ability to fully meet the needs of each school student in self-education and self-actualization when complex knowledge constructs mastering and set the value imperative of personal development, including mathematical literacy.

COMPUTER ANIMATION IN 7TH GRADE ALGEBRA LESSONS: RESULTS OF EXPERIMENTAL WORK

Statement of the problem. The article deals with the problem of visualization in teaching mathematics using animated drawings. The purpose of the article is to present the analysis of the experimental work on computer animation in the GeoGebra environment as a means of improving mathematical education at school. Research methodology. The methodological foundations of the research include activity-based, informational and visual approaches to teaching mathematics, a synthesis of the author’s work experience in testing computer animation at school. Research results. The results of the experimental work confirmed the expediency of using computer animation in the process of teaching algebra in the 7th grade (educational activity of students increased, as well as interest in research work and quality of mastering mathematical knowledge and skills). Conclusion. The use of computer animation in math lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clear illustrations of mathematical concepts and statements. The analysis of experimental work using the animation capabilities of computer environments shows an increase in the technological equipment of modern mathematics teachers, which help them achieve higher educational results.

Virtual Mathematics Education during COVID-19: An Exploratory Study of Teaching Practices for Teachers in Simultaneous Virtual Classes

The current study has aimed to identify the status of teaching mathematics in simultaneous virtual classes, in the light of the Covid 19 pandemic, by uncovering the teaching practices in the fields of lesson planning, teaching the new mathematical knowledge, classroom management, and raising the level of interaction, and that of evaluation. The descriptive approach was used in this study, and a random sample, which consisted of 385 mathematics teachers in the Qassim Education Department, was chosen during the first semester of the academic year 2020/21. The questionnaire was the tool used to collect the data after confirming the validity and the reliability thereof. The results of the study showed that the status of teaching mathematics in simultaneous virtual classes in the light of the Covid 19 pandemic was at a high level (3.80/5), according to the respondents' point of view. The results were respectively as follows: planning "high" 3.87; teaching new mathematical knowledge high "3.81"; the evaluation at a high degree of 3.80; and class management, as well as raising the level of interaction at a high degree of 3.67. The results of the study have revealed that there is a discrepancy in some practices, a matter which requires the identification of the training needs of mathematics male and female teachers in the field of e-learning in virtual classes, such as diversifying the methods of receiving students' responses to activities (chatting - WhatsApp --... etc.); the use of electronic participatory learning strategies in building and organizing the work of cooperative learning groups, employing electronic communication applications in providing reinforcement and feedback to students, employing electronic sports activities in presenting the lesson, and by using virtual engineering tools, while solving mathematical problems.

Exploring Mathematical Concepts and Philosophical Values in Jember Batik

Ethnomathematics are different ways of doing mathematics taking into account the academic mathematical knowledge developed by different sectors of society as well as taking into account the different modes in which different cultures negotiate their mathematical practices (ways of grouping, counting, measuring, designing tools, or playing). Based on this research, this study aims to describe the results of ethnomathematics exploration in Jember batik motifs. The method of analysis used in this research was a qualitative approac with an ethnographic design. Data collection techniques were observation, documentation, and interviews. This research was conducted at Rumah Batik Rolla Jember and Rezti'z Batik Tegalsari Ambulu Jember. The research was conducted for one week. The results of this study indicate that the ethnomathematics in the Jember batik motif has a philosophical value that describes the natural wealth of Jember Regency in each of its motifs, and there are mathematical concepts in the form of geometric transformation concepts (reflection, translation, rotation, and dilation) along with the concept of number patterns.

Methodological recommendations for conducting control work in mathematics teaching

The importance of mathematics as a subject in building intellectually strong personalities, creating and nurturing work habits in students, training them for independent work, are undoubtedly important for acquiring permanent and active mathematical knowledge as a basis for studying mathematics at the next level of education. There is an undoubted need to improve the teaching practice, the current teaching, which only transfers knowledge to the degree of recognition and reproduction.

Methodological knowledge of mathematics as a necessary condition for the formation of professional competencies of future teachers of mathematics

The article deals with the problem of preparing a future mathematics teacher for professional activity in the conditions of digitalization. The requirements for the mathematical training of a future teacher are highlighted and one of the ways to improve mathematical and methodological competencies is proposed. The main idea of the article is to analyze and describe the experience of solving the problems of filling the content of online courses to involve students in an independent research search, the experience of correlation of methods of organizing the educational process in the conditions of offline and online student learning. The author, based on the analysis of the content of methodological knowledge in mathematics and mathematical knowledge proper, reveals the content and essence of the methodological component in the professional activity of a future mathematics teacher. The purpose of the article is to determine the strategies of organizing a course in which future mathematics teachers receive not only mathematical, but also methodological training using different.

What Mathematical Knowledge Do Prospective Teachers Reveal When Creating and Solving a Probability Problem?

The teaching of probability is conditioned by teachers’ mathematical knowledge. In this paper, an exploratory study is carried out with prospective teachers. A training task was designed requiring them to create and solve a probability problem using the values of euro coins, which was adapted to students aged 11 to 12. The study aimed at determining what mathematical knowledge prospective teachers show when dealing with the task. The data were collected through the Moodle online Campus. We framed the data analysis in the Mathematical Knowledge for Teaching model and we used content analysis as the methodological approach. The results indicate that, despite finding evidence of adequate common and specialised mathematical knowledge, in approximately half of the prospective teachers participating in the study, too many of them still show a lack of knowledge in both subdomains. There was also little evidence of knowledge of the curriculum. The main finding of the research is that, when prospective teachers get involved in complex creative tasks, they mobilised together specialised and common mathematical knowledge, working into different mathematical processes such as problem posing and solving, communication, and argumentation, which reinforces the need to continue working on these types of complex tasks.