Mathematical Preparation Research Articles

On the Activity of Students in Mathematics Lessons the Effect of the Pygmalion Effect

The application of mathematical sciences has a great role in the development of society. Mathematical education is a necessary and important part of general education. Therefore, strengthening the mathematical preparation of students is considered the most important task facing secondary schools. Mathematics is taught in a wide range of programs at every level of education in secondary schools. However, it is not perceived in the same way by all students. While some students find mathematics easy to understand, others find it very difficult. There are several reasons for this: poor mastery of mathematical concepts from primary classes, genetic influences, student's lack of independent work, concepts becoming more complex from class to class, age level, environment. We must keep in mind that it is impossible to succeed in life without understanding mathematics. Therefore, it is necessary to look for the cause of difficulties and try to eliminate them. The purpose of the research is to study the impact of the Pygmalion effect on students' performance in mathematics lessons in secondary schools. Using the Pygmalion effect directs students with a poor understanding of mathematics to positive thinking and creates interest in learning mathematics. Many empirical studies also support the predictions of the Pygmalion effect, but it has been found that its effect sizes can vary from low to moderate. As a result of the research, we concluded that applying the Pygmalion effect in teaching mathematics is one of the best ways to achieve success. The research will be useful for mathematics teachers and parents as well as a contribution to the relevant literature.

Realization of the humanitarian potential of a higher mathematics course in the professional training of technical university students

Introduction. The next stage of globalization of relations is being formed – the creation of a digital economy, including smart manufacturing, smart finance, telemedicine, etc. The UNESCO Science Report: the Race Against Time for Smarter Development – Executive Summary, published in 2021, calls this phase the “fourth industrial revolution.” The development and basis of this revolution in the fields of science and engineering is directly related to digital technologies such as artificial intelligence, robotics, blockchain technology, which intersect with nano- and biotechnologies, and cognitive sciences. Scientific institutions and higher education systems are actively involved in this process as direct participants and as training institutions. Mathematical training is rightfully considered the methodological basis of most educational and special disciplines. The purpose of the study is to reveal the humanitarian potential of a higher mathematics course in the professional training of a technical university student. Materials and methods. In accordance with the provisions of the system-activity and information approaches, the authors have developed a questionnaire to identify preferences in realizing the humanitarian potential of the higher mathematics course at a technical university. Respondents are asked to rank the proposed six statements that characterize the mathematical preparation of students. 368 people took part in the survey, among them students of bachelor's degree (136 people), specialty (124 people), master's degree (78 people) and postgraduate studies (30 people) of St. Petersburg Mining University. The method of summarizing and grouping statistical observation materials was used. Results. The highest rating of 3.74 was occupied by the contradiction between the awareness of the leading role of mathematics in the development of logical thinking and at the same time the predominance of theoretical facts over their practical application in the university course of higher mathematics. This statement was noted as the most significant by 20% of students, 27% of undergraduates and 24% of graduate students. The other two, in terms of the severity of the contradiction, have a rating of 3.55 (mastering the content of a higher mathematics course is accompanied by objective difficulty due to the high abstractness of the subject) and 3.56 (insignificant inclusion of heuristic methods in the content of the course). In the context of constantly increasing requirements for the quality of engineering education, the problem of increasing the role of mathematical knowledge can be solved through didactic support of the educational and cognitive process in the classroom and as part of students’ independent work. In a multi-component educational activity, the basic dominants (spatial, logical, numerical and symbolic) are highlighted and the methodological features of their implementation in the student’s mathematical preparation are revealed. Conclusion. The humanitarian potential of the higher mathematics course presupposes a system of measures aimed at the priority development of intellectual and general cultural qualities of students. The realization of humanitarian potential involves the formation of a student's value attitude towards himself, the world around him and his activities in it. The realization of the humanitarian potential of the discipline in the training of a future engineer is possible through the organization of symbolic activities by means of practice-oriented tasks and educational cases of an applied nature.

Професійна спрямованість математичної підготовки студентів технічних спеціальностей у контексті фундаменталізації освітнього процесу

The article examines the peculiarities of mathematical training of future technical specialists in the context of fundamentalization of the educational process. The study of the definitions of fundamentalization, mathematical preparation was carried out, the main characteristic features of mathematical preparation, proposed by the researchers of the problem of mathematical preparation, were singled out. An analysis of the work of scientists dedicated to the selected research problem was carried out. It has been established that the mathematical training of future technical specialists is a dialectical combination of formed mathematical skills and abilities for their applied application and the direct process of forming these skills. The fundamentalization of mathematical training is considered to be the concept of improving mathematical training, in which basic mathematical invariants are selected for their further application in professional activities. To implement the approach of professional orientation of mathematical training of students of technical specialties, it is recommended to take into account the peculiarities of the construction of the course of higher mathematics and courses of special disciplines in order to enable the integration of educational material, as well as the organization of the educational process in higher education institutions. Based on the analysis of educational programs for students of various specialties of the Vinnytsia National Technical University, a conclusion was made about the difference in program results in mathematics for students of the same lecture stream. On the basis of which it is proposed to unify tasks of professional content. Examples of professional tasks from the "Theory of Probability" section are given.

Generative Artificial Intelligence on Mobile Devices in the University Preparation of Future Teachers of Mathematics

The integration of artificial intelligence (AI) is revolutionizing the field of education. The possibilities of AI in education range from providing intelligent tutoring to facilitating computational thinking, a key skill in an AI-based society. As education systems around the world adapt to technological advances, the need for teachers to develop AI skills becomes crucial. This paper explores the use of AI on mobile devices to improve the preparation of future mathematics teachers. We acknowledge the need for teachers to be skilled in the use of AI tools to foster collaborative, effective, and ethical learning environments. We also provide a case study of our implementation of the generative AI ChatGPT in the preparation of future mathematics teachers at the Faculty of Mathematics, Physics and Computer Science at Comenius University in Bratislava. After this implementation, we analyzed students’ opinions on the application of AI in selected areas. We present the results of this analysis and the implications for the practical use of AI in the university education of future mathematics teachers. Finally, based on our study results, we highlight the possibilities of the successful use of AI in different aspects of teaching and its temporary limitations, which are likely to be reduced by further technological developments.

Women’s Participation in Engineering between 2011 - 2019

Despite much effort by engineering education scholarships to make engineering more inclusive, women are still underrepresented in engineering. Women earn less than 30% of the bachelor’s degrees in engineering. However, when we examine the intersectionality between gender and race/ethnicity, the lack of representation in certain groups of women tells us that some women are more underrepresented than others. There is no question barriers within and outside educational forums still prevent women, and in particular women of color, from entering the world of engineering. The barriers include poor advising, lack of mathematics preparation, poor pedagogy, a difficult curriculum, lack of preparation, an unwelcoming culture for women and minorities, and lack of mentorship. The more systemic barriers include the history of exclusion of women from engineering until the 1970s, and past and present systemic racism in United States education which has influenced the experiences of women across different racial and ethnic groups in engineering. Women earn less than 30% of the bachelor’s degrees in engineering. From 2011 to 2019, the percentage of women who earned a bachelor’s degree increased by 6% from 20.4% in 2011. Therefore, in 2019, women represented 50.8% of the U.S. population, but only 26.4% of the engineering bachelor’s degree holders. Moreover, not all ethnic and racial groups of women experienced an increase in degree attainment. Within this period, American Indian or Alaska Natives have experienced a slight decrease, while Asians, African Americans, Hispanics, and White women have experienced increases in varying degrees. White women have experienced the most gains in bachelor’s degrees, but all categories of women, except for Asian, represented a lower percentage of engineering bachelor’s degree holders compared to their percentage representation within the U.S. population. Fortunately, much is known about factors that make women leave engineering. More effort is needed to remove these know barriers to make engineering more inclusive and to allow more women to successfully complete their engineering bachelor’s degrees.

Math Skills as a Key Determinant of Success in Competitive Exams

The present article explores the significance of math skills as a key determinant of success in competitive exams. By analyzing question papers from UPSC Prelims (General Studies Paper 2), SSC, RRB, TNPSC Group IV, TRB, and TNURSB over the past three years (2021-2023), the study highlights the critical role of mathematical proficiency. The study explores the structure of these question papers and the proportion of math aptitude and attitude questions included each year. By highlighting the consistent presence and evolving complexity of math-related questions, this analysis underscores the importance of robust mathematical preparation for aspirants. The findings suggest that a strong foundation in math not only enhances performance but also boosts overall confidence, thereby increasing the likelihood of success in these exams. The article aims to provide valuable insights for educators and students, emphasizing the need for targeted math skills development in competitive exam preparation.

A Survey Study on the Maturity of Schooling of Young Children in Rural Sichuan Province:Taking the Rural Area of Meishan City,Sichuan Province as An Example

The admission maturity level of preschoolers can predict their performance after entering schools to a certain extent. Therefore, how to prepare for children’s admission to primary school has become a key issue of social concern. In order to improve the admission maturity level of rural preschoolers in Sichuan Province, it is necessary to understand the admission maturity level of 5-6-year-old children in Sichuan Province, so as to provide theoretical and practical basis for taking targeted measures. In this study, the measurement method was used to investigate the admission maturity level of children in rural areas of Meishan City, Sichuan Province as the research sample. It was found that rural children's motor coordination ability did not differ significantly from the national average, and their scores in visual perception ability, auditory perception ability, motor coordination ability, perceptual conversion ability, mathematical preparation ability, verbal communication ability, social adaptation ability and learning quality were significantly lower than the national average, but in auditory perceptual ability, rural children's scores were significantly higher than the national average. The differences in eight abilities between males and females were compared. Except for motor coordination, perceptual conversion ability, and verbal communication ability, there were significant differences in all other aspects, and girls scored higher than boys in all abilities. In addition to this, there is also some discussion on mother's occupation and young children's maturity in school. Based on the findings, targeted improvement measures were proposed to provide a reference for home and school to improve children's admission to primary school.

Третьеклассник и математика: освоение учебного предмета в рамках требований действующего стандарта

The article discusses the organization of education taking into account the requirements of the updated educational state standard, federal educational and work (subject) programs for the mathematical preparation of third-graders. Some features of the updated content of the third year of study and methodological approaches to strengthening the work of the teacher in developing in younger schoolchildren the ability to construct and verify the truth of statements, justify their point of view, understand practical problems, and apply educational and subject-related actions when working with different course contents are presented. Methodological approaches are characterized that allow schoolchildren to ensure better mastery of updated subject content: the ability to work with mathematical text, conduct independent testing and evaluate the results of the solution. Thus, the article substantiates the possibility of taking into account the standard requirements for student independence when organizing the learning process.

The Road Less Travelled: Examining Alternative Routes to Elementary Teacher Preparation in Mathematics

The Road Less Travelled: Examining Alternative Routes to Elementary Teacher Preparation in Mathematics

FEATURES OF THE APPLICATION OF THE SCILAB MATHEMATICAL PACKAGE IN THE PROCESS OF TEACHING THE DISCIPLINE «HIGHER MATHEMATICS»

The article notes that the choice of software is of great importance in teaching the discipline «Higher Mathematics». The complexity and type of tasks to be solved depend on the functionality of the selected program. It is emphasised that the methods of approximate, primarily numerical, solution are used. The methods of numerical solution of mathematical problems have always been an integral part of mathematics and have always been part of the content of natural-mathematical and engineering education. This article uses the Skilab math package as software. It is a multi-functional package designed for performing engineering and scientific calculations, which allows you to perform complex algebraic calculations, solve problems of differentiation and integration. All this contributes to the successful use of the Scilab mathematical package in the process of teaching the discipline «Higher Mathematic». The author draws attention to the fact that Skilab is a computer mathematics system designed to perform engineering and scientific calculations, such as: solving nonlinear equations and systems; solving linear algebra problems; solving optimization tasks; differentiation and integration; processing of experimental data (interpolation and approximation, method of least squares); solution of ordinary differential equations and systems. Skilab provides wide opportunities for creating and editing various types of graphs and surfaces. The Skilab system contains a sufficient number of built-in commands, operators and functions, and its distinctive feature is flexibility. The user can create any new command or function and then use it alongside the built-in ones. The article states that the use of modern mathematical packages significantly increases the intensity of cognitive activity, raises the level of mathematical preparation, improves the knowledge control system, and promotes learning motivation. The perspective of the development of the study of the use of mathematical packages is the development of a database on the issues of their use during the educational process, which should take into account the professional orientation of future activities. This approach provides a more effective application of interdisciplinary connections, which contributes to the in-depth study of the material and the expansion of opportunities for independent learning.

On the interplay of cognitive, tactile, and computational approaches to number theory in teacher education

This paper focuses on topics from elementary number theory used by the author in the mathematical preparation of K-12 teacher candidates by juxtaposing concrete materials, digital technology, and formal reasoning. The topics include triangular numbers, their connection to trapezoidal numbers, and their extension to other figurate numbers. The paper shows how problem solving may be based on the integration of modern-day approaches to mathematics supported by the creation of images, their numeric interpretation, followed by algebraic generalization, and computational verification of general statements in symbolic form. Digital tools used in the paper include spreadsheets, Wolfram Alpha, and Maple. Solicited comments by teacher candidates about their use of digital tools are shared.

Investigation of Secondary School Mathematics Teachers’ Processes of Preparing Mathematical Modelling Activities

In this study, it was aimed to investigate the mathematical modelling activity preparation processes of secondary school mathematics teachers who participated in mathematical modelling training. The study was conducted with six mathematics teachers working in secondary schools. In the study designed as action research, two action plans were applied to the teachers. The first activity forms collected from the teachers before the application, the second activity forms collected as a result of the theoretical training about modelling and the activity forms collected at the end of the active participation of the teachers in the modelling activities constitute the data source of this study. An activity evaluation form was used in data analysis. The results of the study showed that teachers initially had deficiencies in preparing modelling activities in accordance with all criteria. After the theoretical training given, it was determined that teachers’ competencies in preparing modelling activities improved very little. In addition to theoretical training, it was seen that the learning environment prepared to ensure teachers’ active participation in modelling activities affected their activity preparation competencies more positively. The results show that teachers’ theoretical knowledge deficiencies should be eliminated in modelling teaching and learning environments should be prepared for their active participation in mathematical modelling activities.

Interdisciplinary connections of Mathematics and Literature in the preparation for External Independent Assessment of Humanities students

This article examines the issue of finding new methodological approaches to the development of problems that can contribute to the preparation of ‘Humanities’ students to pass the state final certification in the format of External independent assessment (EIA). The study analyzes the existing development of methods of qualitative mathematical training of students of humanities classes who study Mathematics according to the basic level program. In particular, the authors of the article were interested in the use of interdisciplinary connections between Mathematics and humanitarian disciplines. The authors of the article identified cross-curricular problems as a means of forming students’ motivation to study Mathematics, as well as a toolkit for measuring their level of readiness to solve typical problems of EIA. The researchers set a goal to develop cross-curricular problems following the EIA program based on the plot of Bulgakov’s novel ‘The Master and Margarita’. An experiment was conducted to confirm the effectiveness of the use of the system of interdisciplinary problems in the preparation for the EIA of humanitarian students. The obtained results confirmed that the implementation of problems in which the intersubject connections of Mathematics and Literature are realized has a more significant effect on both increasing the motivation of students to study Mathematics and their mathematical preparation.

Mathematics Attitude of Future Teachers of Stem Subjects

Aim. This paper presents research aimed at testing the mathematical self-efficacy of mathematics and computer science student teachers. The aim of the presented phase of the research was to verify the effectiveness of the chosen research instrument after translation into Czech, its applicability within the specific environment of the preparation of future teachers and the design of a shorter version of the questionnaire. Methods. 97 students of the first and second year of Bachelor's degree studies at the Faculty of Education of Charles University, specialising in mathematics and computer science, were interviewed either in a single-subject form or in combination with a second subject. Subsequently, the data was processed and evaluated using quantitative methods. Results. The results confirmed that the test, even when translated into Czech, fully met the claim of high reliability (Cronbach's Alpha = 0.965). Using the Principal Axis Factoring method with Varimax with Kaiser Normalisation in 11 iterations, convergence to the four basic components, which were characterised as Motivation and Enjoyment, Anxiety, Self-confidence and Value, was achieved. Conclusion. The research has shown that the chosen research instrument, the ATMI questionnaire, is fully functional after translation into English and use in the environment of preparation of future mathematics and science teachers. The first measurement data also confirms that attitudes towards mathematics are very different among future mathematics and science teachers. It also confirmed the assumption that the questionnaire has the potential to identify students who have problematic attitudes towards mathematics and are therefore at risk of dropping out.

Characterizing Secondary Teachers’ Structural Reasoning

The Common Core State Standards for Mathematical Practice asks students to look for and make use of structure. Hence, mathematics teacher educators need to prepare teachers to support students’ structural reasoning. In this article, we present tasks and rubrics designed and validated to characterize teachers’ structural reasoning for the purposes of professional development. Initially, tasks were designed and improved using interviews and small pilot studies. Next, we gave written structure tasks to over 600 teachers in two countries and developed and validated rubrics to categorize responses. Our work contributes to the preparation and support of mathematics teachers as they develop their own structural reasoning and their ability to help students develop structural reasoning.

Evaluating a University-Wide Mathematics Assessment for Use in Introductory Statistics Course Performance

Students’ prior math skills are a strong indicator of potential for success in introductory statistics courses regardless of the emphasis on mathematical ability necessary for the course. Thus, many undergraduate instructors utilize some form of math skills assessment as a review for students or for students to identify weak areas in their mathematics preparation. Such evaluations may provide instructors and students with an early indication of the student's chances for success in a course and if additional assistance is required. This study illustrated the efficacy and importance of a standardized math assessment developed and administered as a university-wide mathematics placement test in student success prediction from several modeling approaches.

Task Design for Klein’s Second Discontinuity

Since the 19th century, studies of mathematics at university have been a main component of the usual preparation for teaching at secondary level. Already around 1900, Klein pointed out that specific measures are needed to ensure that the university mathematical preparation becomes useful to the teacher, and he insisted that universities themselves must take responsibility for these measures. In this paper, we discuss this problem, as it presents itself in 2022, and we present and exemplify some principles of task design which are intended to support students’ mobilisation of university mathematical knowledge in relation to specific mathematical challenges for high school teachers.
 

Making university mathematics matter for secondary teacher preparation

Internationally, questions about the perceived utility of university mathematics for teaching school mathematics pose an ongoing challenge for secondary mathematics teacher education. This special issue is dedicated to exploring this topic and related issues in the preparation of secondary mathematics teachers—by which we mean teachers of students with ages, approximately, of 12–18 years. This article introduces this theme and provides a semi-systematic survey of recent related literature, which we use to elaborate and situate important theoretical distinctions around the problems, challenges, and solutions of university mathematics in relation to teacher education. As part of the special issue, we have gathered articles from different countries that elaborate theoretical and empirical approaches, which, collectively, describe different ways to strengthen university mathematics with respect to the aims of secondary teacher education. This survey paper serves to lay out the theoretical groundwork for the collection of articles in the issue.

DIRECTIONS OF DIGITIZATION IN THE PROFESSIONAL PREPARATION OF FUTURE MATHEMATICS AND PHYSICS TEACHERS: INTERNATIONAL AND UKRAINIAN EXPERIENCE

The article highlights the international and Ukrainian experience of incorporating elements of digitization into the preparation of future modern mathematics and physics teachers. The article analyzes international experience, which includes advanced approaches to using digital technologies in the educational process. It also examines Ukrainian experience, focusing on the implementation of various programs to improve the accessibility of educational materials and communication between teachers and students.The significance of preparing teachers for the effective use of digital technologies in the educational process is emphasized. Furthermore, the article emphasizes the advantages that digitization brings to the preparation of future mathematics and physics teachers. A detailed analysis of international experience demonstrates successful examples of using digital technologies in the educational process. The Ukrainian experience also offers interesting solutions for integrating digital technologies into the preparation of mathematics and physics teachers.The overall conclusion of the article underscores the necessity of integrating digital technologies into the professional preparation of future mathematics and physics teachers, which will contribute to improving the quality of education and preparing graduates for the modern digital world.It has been analyzed that the implementation of programs increases studentsʼ interest, improves the accessibility of educational materials, fosters creativity and analytical skills, and prepares students for the demands of the modern digital world.
 Keywords: digital modernization; professional training; future math teachers; future physics teachers; digital technologies; computer programs; online courses; innovative approaches; effectiveness of the learning process; improvement of education quality.

Formation of students' mental activity by improving the applied focus of learning a geometric

Prerequisites for the study the problems of implementing the applied direction of teaching the topic of geometric construction in the geometry course of secondary school are most relevant, since there are no clear basic methods for the formation of students' thinking activities in this direction. This article discusses the results of a scientific study aimed at obtaining theoretical knowledge in any section of school geometry, which aims to give the student the skills to use the means of drawing the properties of geometric shapes and relationships. For this purpose, students were given a review of the literature on the implementation of the applied direction of geometry, focusing on mathematical statements in order to improve the applied direction of geometry. In the framework of the topic, the analysis was carried out in the course of improving this topic, due to the fact that mathematics teachers did not pay enough attention to the problems of construction in the geometry course of secondary school due to lack of time, students did not develop skills in solving problems of the applied direction of geometry. As a result of research, geometric construction problems are an important element of the mathematical preparation of schoolchildren. Using the problems of geometric construction, its application points were determined. The ways of implementing the applied direction in teaching geometry to students are described. Also, when teaching the geometry course, problems of the applied direction were collected in the school's geometry textbooks, ways to solve them were considered, and plot geometric tasks were prepared in order to increase the creativity of students. The stages of solving the practice-oriented geometric construction problem and the principles of implementing the applied direction of teaching mathematics, defined as a special type of plot problem, reflecting the use of geometric means in practical situations, are also studied. In the future, it can be used as a methodological tool for mathematics teachers in teaching construction problems.