Mathematics Courses Research Articles

Choosing science and mathematics programs in college: practical and psychological arbiters in career-pathing

The objective of this exploratory qualitative research is to investigate the practical and psychological factors influencing students’ decisions to pursue science and mathematics-based courses for their career paths. The study will focus on a sample size of 25 second-year students in Calbayog City who have chosen to continue with their chosen course after completing one year of study. To collect data, the study will use one-on-one interviews, a qualitative research method. This method will allow for a thorough investigation of the participants’ experiences, viewpoints, and motives. Through one-on-one interviews, the researchers are able to acquire a thorough understanding of the factors that influence students’ decision-making processes. The findings of this study will provide important insights into the practical and psychological factors that impact students’ selections in science and mathematics courses. This information can be utilized to improve career advising programs and educational systems, as well as to guide students who are exploring comparable career options.

Nurturing prospective teachers noticing skills through argumentation: The case of fractions

This study aimed to investigate the extent to which prospective teachers’ noticing skills develop while they engage in argumentation on students' mathematical thinking regarding fractions. The study consisted of 10 third-year prospective teachers participating in online methods of teaching mathematics course. Classroom teaching experiment design was used where 8 sessions of teaching experiments were conducted. Data involved pre and post-tests, interviews, video recordings, daily reports, and post-discussion reflection papers. Findings revealed that prospective teachers' noticing skills of attending to students' strategies and making sense of their understanding were enhanced after their involvement in the classroom teaching experiment. Findings were discussed within the scope of the noticing literature.

Bioscience Students in Physics Courses with Higher Test Anxiety Have Lower Grades on High-Stakes Assessments and Women Report More Test Anxiety than Men

Test anxiety is beginning to be recognized as a significant factor affecting student performance in science, technology, engineering, and mathematics (STEM) courses, potentially contributing to gender inequity within these fields. Additionally, the management of test anxiety can improve self-efficacy, which is a construct that has been well studied in the physics context. In this study, we investigated the relationship between self-efficacy, test anxiety, and gender differences in performance in a two-semester-long introductory physics course sequence for bioscience students in which women outnumber men. Using validated survey data and grade information from students in a two-semester introductory physics course sequence, we compared the predictive power of self-efficacy and test anxiety on female and male students’ performance on both low- and high-stakes assessments. We found that there were gender differences disadvantaging women in self-efficacy and test anxiety in both Physics 1 and Physics 2, as well as gender differences in high-stakes outcomes in Physics 1. There were no gender differences in low-stakes assessment scores. We also found that self-efficacy and test anxiety predicted high-stakes (but not low-stakes) assessment outcomes in both Physics 1 and Physics 2. Comparison of these findings with prior studies involving physical science and engineering students shows that although women outnumber men in physics courses for bioscience students and the career goals of bioscience students are very different from the earlier researched group, most of the negative trends hold even for this new population. Thus, these findings, in a new context involving bioscience students in physics courses, are very important because they reinforce the systemic nature of women being affected more adversely by anxiety in high-stakes assessments, which is a threat to creating equitable and inclusive learning environments. An important implication is that course instructors should carefully consider how high-stakes and low-stakes assessments are used to determine grades and how to create an overall equitable, inclusive, and low-anxiety learning environment.

Empirical Study on Attitude towards Making Decision to Select Mathematics for First-Degree Program

Recently debatable arguments have existed regarding the perceived lack of numerical skills among the graduates from the Humanities and Social Sciences. In response to this concern, the Faculty of Humanities and Social Sciences, Faculties of Art in national universities in Sri Lanka have taken measures to more opportunities to undergraduates to bolster their numerical proficiency. This is achieved through the incorporation of mathematics course units for their degree programs along with the main subject streams. The study focuses on factors that affect the undergraduates’ attitudes towards making the decision to select the subject mathematics for their first-degree program. A sample survey was carried out using structured questionnaire and stratified random sampling technique was utilized to select a sample size of 352 from the undergraduates belongs to Faculty of Humanities and Social Sciences in University of Sri Jayewardenepura. The binary logistic regression model is utilized, and the study revealed that self efficacy, mathematical anxiety, and interest in mathematics are significantly affected students’ attitudes on counting mathematics course units for their degree program. The student who has self-efficacy is 1.03 times more likely to select mathematics course unit at the first academic year than other students. A unit increase of mathematics anxiety with all other factors remaining constant, the odds of a student selecting the mathematics course decreased by 11.2%. When one-unit increases in the interest in mathematics of students the odds of selecting mathematics course unit is 1.06 times more likely to than other peers. These insights suggest that educational institutes, particularly those in the humanities and social sciences, should prioritize enhancing students ‘numerical skills. This can be achieved by providing valuable consideration aimed at refining their curriculum and support mechanism, increasing awareness programmes about the importance of studying mathematics course units within their degree programmes and conducting programmes to reduce mathematics anxiety while fostering an increased interest in mathematics.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course: A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China, colleges and universities are facing new challenges and impacts in talent training. Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors. Its critical role in cultivating students’ thinking skills and improving their problem-solving skills is self-evident. Course ideological and political education construction is an important link in college talent training work. Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality. At present, the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems, mainly manifested in the lack of attention paid by teachers to course ideological and political education, insufficient exploitation of ideological and political elements, and the simplification of ideological and political education implementation methods. In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching, we should strengthen the construction of teacher teams, improve teachers’ ability to carry out course ideological and political education, integrate educational resources, develop educational resources for ideological and political education, and innovate teaching methods to improve the overall effect of ideological and political education integration.

Mulțimea valorilor unei funcții: aspecte metodice și de calcul

The study of elementary functions is one of the main thematic lines of the pre-university mathematics course. At the same time, the concept of function and related concepts (domain, set of values, graph) represent the most difficult concepts for students. The paper presents the analysis of the formation for the concept of the set of function values and synthesizes its determination methods for different functions. Examples of the use for the set of function values will be useful both for understanding and expanding the concept, and for developing the mathematical capabilities of gifted students.

DEVELOPMENT AND IMPLEMENTATION OF THE TEACHING METHODOLOGY OF THE HIGHER MATHEMATICS COURSE BASED ON PRACTICE

The teaching of higher mathematics has traditionally focused on theoretical concepts, which often creates a gap between students' understanding of the subject and its practical applications. This article explores the development and implementation of a teaching methodology for the higher mathematics course based on practice-oriented learning. The objective is to bridge the gap between theory and application, improving students' problem-solving skills and enhancing their ability to apply mathematical concepts in real-world situations. By integrating practical activities, case studies, and applied projects into the curriculum, this methodology fosters deeper comprehension and equips students with valuable competencies for their future careers.

Analytical and geometric interpretation of the flat arrangement of points by means of metric geometry in the study of metric spaces

Abstract When studying metric spaces, students of higher education often have difficulties with understanding the basic concepts and properties of these spaces. This, to a large extent, is a consequence of the significant level of formalization of such concepts on the one hand, and the preservation of the corresponding formulations and names familiar to students from a school mathematics course. To overcome these difficulties, it is advisable to use methods of geometric interpretation and visualization of these properties. At the same time, it is appropriate to use elements of metric geometry. Its methods make it possible to interpret the geometric features of the mutual placement of points of metric space in Cartesian (rectangular) coordinate systems, which are familiar to students of higher education. Moreover, it becomes possible to visualize these features with the help of graphic editors, since they, as a rule, use numerical values of the coordinates of points to visualize them. Based on the definition of an angle as an ordered trio of points of an arbitrary metric space, and the angular characteristic of this angle, the fact of the flat placement of four points of a non-Euclidean metric space is established, and examples of digital visualization of this arrangement using the dynamic geometric environment GeoGebra 3D are given.

The usage of stochastic matrices while learning the topic “Eigenvalues and eigenvectors of a matrix” in the course of Higher Mathematics

Abstract The article looks into teaching students mathematical modeling during the mastering of the topic “Eigenvalues and eigenvectors of a matrix” in the Linear Algebra. The modeling is based on the usage of matrices built based on Markov chains. The analysis of the researchers’ papers shows that the usage of matrices of this type can be implemented while teaching students of different university specialties. The analysis of the prerequisites for the involvement of stochastic matrices in the consideration of students has helped to determine additional concepts and theorems that should be considered while learning “Eigenvalues and eigenvectors of a matrix”. The theorem on the presence of stochastic vectors in a stochastic matrix can serve as a formula for systematizing problems that can present applications of eigenvalues and eigenvectors of the matrix in real-life situations. The results of the experiment conducted using the developed system of problems for students of different University specialties show the improvement of skills provided by mastering the topic “Eigenvalues and eigenvectors of a matrix”.

Мәтіндік және стандартты емес есептерді шешу әдістері

One of the most important tasks of primary education is the development of logical thinking. Textual and non-standard tasks have a special place in the formation of students' thinking abilities. By mastering the solution of such problems, we form in the student such qualities as search for innovation, self-attitude, perseverance. The article discusses textual and non-standard tasks and solutions found in the course of elementary mathematics, the technology of criterion-based assessment. The concepts of "text task", "non-standard task" were defined. This article presents a methodology for criterion-based assessment of students' academic achievements in mathematics lessons. The peculiarity of this technology is that when solving a task, students create descriptors, which are subsequently used in formative and aggregate assessments. Each descriptor is a step in the algorithm that solves the problem. Particular attention is paid to the use of various methods by primary school teachers in solving text problems, the importance of observing and supporting the child's non-standard ideas. The habit of finding other ways to solve the problem, the ability to use various ways and means of solving the problem plays a huge role in the future work, scientific and creative activity of the student. As a result of the research work, the main recommendations for finding a solution to text and non-standard tasks were developed. The advantages of using the criterion-based assessment system in mathematics lessons are revealed.

Computational Thinking Processes in Solving the Corona Epidemic Model: Pre-service Maths Teachers

In the 21st century, pre-service mathematics teachers are expected to have problem-solving skills that are effective, efficient, and solutive and are in line with the mindset of computer experts. In learning mathematics, the concept of computational thinking (CT) is also needed and at this time, many still have difficulty solving mathematical problems in general, especially in solving problems in epidemic mathematical models. The subjects of this study were twenty-seven pre-service mathematics teacher students who took mathematical modeling courses. The researcher used the purposive sampling technique to select two research samples. The research method used was a descriptive qualitative research method in exploring the thinking process of pre-service mathematics teacher students in solving the problem of modeling the epidemic spread of disease. The results showed that the thinking process of the first subject began with identifying the problem and existing information by writing down the data in the form of a graph so as to get a certain pattern, which was then used as the basis for the process of transforming the problem into mathematical language. By adding assumptions related to the existence of environmental limitations in the next epidemic model, the concept of differential equations, in which there are integral properties and natural logarithms, can be used to find the solution to the epidemic model. The second subject was unable to solve the integral at hand. The researcher discovered that pre-service mathematics teacher students who correctly solved the problem in the mathematical model used CT components, namely decomposition, abstraction, pattern recognition, algorithm and mathematical literacy.

Enhancement of Teaching Methods of Main Mathematical Disciplines in Higher School

Innovations are proposed in the courses of mathematical analysis, linear algebra and discrete mathematics taught in the first year of study. Innovations are aimed at improving methods of teaching basic mathematical disciplines in higher education.

The use of multimedia technologies in the illustrative teaching of the school mathematics course

The article emphasizes the importance of combining traditional teaching methods in the school mathematics course with modern illustrative methods. Traditional methods such as lectures and textbooks play a crucial role in the transfer of basic knowledge and concepts. However, the use of illustrative techniques such as visualization, games, and interactive applications can significantly improve students' understanding and assimilation of mathematical concepts. The combination of these methods allows for a more efficient and modern educational environment, encouraging active student participation and encouraging their creative thinking. In the course of the work, it is proposed to talk about the illustrative method and the traditional method, about the advantages and disadvantages of their application, compare the illustrative method and the traditional method, the results of research and their application. Based on data analysis and pedagogical methods, he proposes strategies for integrating multimedia resources to improve the visual and conceptual understanding of mathematical concepts in the school classroom. Analyzing the results of experiments and teaching methods, the authors discuss the practical use of multimedia resources to increase interest and understanding of mathematical concepts among students. In the course of the work, approaches to learning were considered, the advantages and disadvantages of the illustrative method and the traditional method were identified, analogs were analyzed and recommendations were given.

Centering students’ thinking with the rights of the learner to counter deficit narratives in mathematics

ABSTRACT This article explores the implementation of Olga Torres’s Rights of the Learner (Torres’s RotL) framework in a 100-level undergraduate mathematics course, particularly focusing on assessment practices. Torres’s RotL framework offers a means to center students’ voices, mathematical thinking, and humanity in the classroom. The article delves into the five rights outlined by Torres — the right (1) to be confused, (2) claim a mistake, (3) speak, listen and be heard, (4) write, do, and represent what makes sense to you, and (5) the right to feel safe and respected — and discusses their implications for assessment in the mathematics classroom. Drawing from sociopolitical perspectives in mathematics education, the article emphasizes the importance of rehumanizing the classroom environment and addressing power dynamics and identity issues. Through reflection and alignment with Torres’s RotL, various assessment practices are shared related to small group and individual classwork, whole class discussions, weekly homework, asynchronous choice activities, and exams, highlighting how each can honor students’ rights while fostering a supportive, inclusive learning environment.

Design and implementation of a cloud computing based vocational college course teaching practice platform

In recent years, China’s vocational college education informatization construction has achieved significant results, but there is still a certain gap with the requirements of university informatization construction and education development. Firstly, the foundation for the construction of a public service platform for professional course resources is relatively weak, and there are insufficient shared mathematical professional course resources; Secondly, the construction of information infrastructure in some vocational college lags behind, and there is a shortage of high-quality and shared course resources. In addition, the application rate of information technology in professional course resources in vocational colleges is relatively low, which cannot fully meet the actual needs of China's vocational college reform and development. This article applies the theoretical foundation and practical methods of cloud computing to research and design a cloud computing based vocational college course teaching resource platform.

Pre-service mathematics teachers’ perceptions based on two differing mathematically underpinned debates

This study explores how pre-service mathematics teachers build alternative model simulations of real-world scenarios. Inclusion in the formal structures for wealth generation and accumulation is a fervently debated issue in South Africa. Share owning in companies listed on the Johannesburg Stock Exchange (JSE) in South Africa is one of many wealth-building tools. Related discussions evolved on the spread of share ownership among black and white citizens. Two mathematically motivated positions were reported in a newspaper. In one of their mathematics courses, prospective mathematics teachers were presented with the article and asked to reflect on it with the prompt 'Which of these two methods for determining the "number of Black South Africans holding shares on the JSE" would your group support?' Audio- and video-recorded data were collected and subjected to thematic analysis. The themes that emerged from the analysis were economic empowerment, authority of research and trustworthiness of information. The discussions reflected on the complexities and rationalities involved in decision-making of mathematically driven opposing positions on issues of social importance. The mathematically derived results of such issues will eventually be resolved in the political field. The findings revealed that building of alternative mathematical models by pre-service mathematics teachers begins with an explicit problem setting, followed by the development of mathematical models that included real-world problems.Contribution: This article contributes to pre-service mathematics teacher education by exploring how such teachers deal with the issue of critical engagement of mathematically based arguments, highlighted in the Curriculum Assessment and Policy Standards (CAPS) document for school mathematics.

STEM Enrollment Decision Trees as Graduation Predictors for Community College Students Enrolled in Remedial Mathematics

Objective/Research Question: Community college graduation rates are typically quite low, and developmental mathematics enrollment and coursetaking patterns may constrain academic outcomes. To identify ways in which community college graduation rates may be improved, decision trees were utilized to examine the STEM coursetaking patterns of N = 5,065 students who matriculated in remedial mathematics. Methods: The research design was guided by Tinto’s academic and social integration framework, which provided an analytical lens for identifying how decision trees facilitate academic decision making when academic and social integration is limited. Decision trees identified course sequence rules to predict graduation, which can be used to formulate course pathways for community college advisors and their students. Results: Nine rules from the decision tree were identified, which could be used to advise community college students in coursetaking that aligns with career aspirations. The most important variable predicting graduation was completing College-Level Mathematics, which included Algebra II, Statistics, Precalculus, and survey mathematics courses. General education sciences courses such as Astronomy, Geology, Environmental Science, and Marine Biology were the most important science courses predicting graduation. Conclusions/Contributions: Results suggest the importance of College-Level Mathematics in providing the skills necessary for students to be successful in subsequent STEM coursework and persist to graduation. Designating specific academic pathways may improve social and academic integration and graduation rates, providing continuity as students work with different advisors to choose majors and plan course sequences. Transparent, accessible enrollment planning fosters programmatic consistency and student agency in selecting coursework that will maximize their success.

Designing and Testing a Contextual Factors-Based Teaching and Learning Model for Blended Mathematics Instruction

The study employs design-based research (DBR) to design the mathematics teaching and learning activity model (M-TLAM) for blended learning instruction in a Tanzanian higher education context. This model utilises contextual factors, including ICT tool usage, collaborative learning with metacognitive activities, and local culture, to determine how optimising these factors boosts math students’ motivation and achievement. Two DBR phases were conducted, of which Phase 1 lasted for two weeks and Phase 2 an entire semester. To evaluate M-TLAM in real-life learning settings, experiments were conducted with 225 first-year undergraduate students and seven lecturers at the College of Business Education in Tanzania. Experimental data were collected from pre-and post-tests, interviews, and questionnaires administered to students and lecturers. The study examined the perceptions and motivation of the participating lecturers towards using the M-TLAM in mathematics education and the factors influencing student motivation, academic achievement, and experience towards business mathematics courses. The evaluation results are promising and show that the M-TLAM implementation can potentially improve students’ motivation and academic achievement. In addition, the pedagogical experiences of students were primarily positive, and student’s attitudes towards the business mathematics course through M-TLAM were more favourable than those of students who studied the course via traditional methods. Cultural, technological, and instructional Factors contribute to students’ improved motivation. Lectures demonstrated a cheerful disposition towards the potential of the M-TLAM for enhancing teaching and learning activities. The contributions of this study are highlighted through the implementation of the M-TLAM for blended learning and through the design principles and guidelines provided towards its effective implementation.

Investigating preservice secondary mathematics teachers' skills in posing realistic mathematics tasks

Mathematics tasks situated in realistic situations play a central role in developing and applying mathematical knowledge. However, mathematics educators face difficulties in designing realistic mathematics tasks. This study was conducted to gain deeper insights into the characteristics of mathematical problems that underprepared preservice secondary mathematics teachers pose. This study examined 32 preservice secondary mathematics teachers' problem-posing skills based on three problem-posing situations: structured problem-posing, semi-structured problem-posing, and free problem-posing. As the context of the participants, they did not have learning experiences in designing realistic mathematics tasks. In evaluating the preservice teachers' works, the researchers used several evaluation criteria, namely the compatibility of the problem with the mathematical principles, plausibility and sufficiency of information, the problem text, level of context authenticity, cognitive demand, and the correctness of the solution. The results revealed that most preservice teachers posed problems with the first-order level of context use and low cognitive demand. Additionally, many of them encountered difficulties when attempting to solve the problem. The findings of this study were expected to serve as a basis for developing a curriculum for pedagogic and mathematics courses in teacher education.

Investigation of Middle School Students' Attitudes towards Mathematics Course in the Context of Different Variables (Eskişehir-Türkiye Case)

It is believed that students' motivation and emotions have an important role in their understanding of mathematics teaching. In this context, this study aims to investigate middle school students' attitudes towards mathematics lessons in the light of various variables. A quantitative cross-sectional survey approach was used in the design of the study. It was tried to understand how these variables affect students' attitudes towards mathematics. In the study, various variables such as gender, grade level, school type, technology use, use of concrete materials/activities in lessons and use of Education Information Network (EBA), an online platform for distance education, were taken into consideration. According to the findings of the study, students' attitudes towards mathematics lessons are positively affected by educational policies, curriculum designs and the creation of concrete materials and activities in the classroom. In particular, a detrimental change was observed in the attitudes of students who used EBA less. The perspective provided by this study is crucial for understanding middle school students' attitudes about mathematics in learning environments. It is also recommended that the study be extended to cover more samples and regions, as the findings can serve as a basis for further research.