Mathematics Courses Research Articles

Using student projects to enhance learning

The implementation of student projects in undergraduate mathematics and statistics courses is discussed with suggestions and recommendations. Advantages and pitfalls of this teaching tool are presented. A prototypical student project for an elementary mathematics course is described. The features of this sample project serve as models for components of other projects. This illustrative project concerns the locus of intersection points of pairs of tangent lines to a conic section, such that the products of the lines’ slopes are a constant.

The power of feedback in teacher education

PurposeThis qualitative study extends jigsaw lesson study (JLS) by focusing specifically on the impact of feedback on teacher candidates’ (TCs') professional knowledge and instructional growth in the teacher-educator classroom.Design/methodology/approachFor this study, JLS took place in two different methods courses and followed the lesson study (LS) framework using the small group rotations of JLS. In each course, the JLS small group teams taught another team before receiving feedback and revising their lessons. Then they would teach another group. After each iteration, teams debriefed and reviewed the feedback to revise their lessons and prepare for reteaching. Following the JLS process, TCs reflected on the impact of feedback in a post-survey that was analyzed, coded and aligned with their lesson iterations and revisions.FindingsBoth integrated language arts (ILA) and math TCs reported that receiving peer feedback improved their lessons, instructional materials, revisions and student engagement. Through collaboration, TCs valued peer dialog, multiple perspectives and TCs learned to provide and receive constructive feedback professionally. Overall, feedback and collaboration helped strengthen their lesson planning as they considered multiple perspectives. Feedback helped TCs consider differentiation and the diversity of learners as well as student engagement while building their professional knowledge.Originality/valueAlthough a previous study has shown an impact of JLS in ILA teacher-education courses with a broader scope in mathematics courses, this study focused on the JLS process in two teacher-education courses. Furthermore, current research tends to focus on the LS process, but this study focused specifically on TCs’ perceptions of the impact of feedback of their professional and instructional growth.

Students’ ways of using video lectures in a linear algebra course

Abstract Video lectures have become a common element in many university mathematics courses, and students often believe that these support their learning in various ways. However, some studies indicate that students who use such video lectures frequently perform lower in exams. Hence, it is important to investigate how students use video lectures. We interviewed nine students of a linear algebra course about the activities they carried out when watching prerecorded video lectures. In these interviews, all our participants reported in detail lots of activities they engaged in while watching, and our study contextualizes these activities with content-specific examples. However, our study also indicates that even if students are very active while watching video lectures, their cognitive engagement with the actual content might nevertheless be rather low. Possible consequences concerning the implementation of video lectures are then discussed.

Research on the Teaching Design of Advanced Mathematics Courses Based on Outcome-Based Education Concept

This paper first analyzes the characteristics and current situation of the Advanced Mathematics course; secondly, it proposes a teaching model that integrates the outcome-based education (OBE) philosophy and blended teaching method, reorganizing the teaching objectives, teaching content, and assessment evaluation process of the Advanced Mathematics course; lastly, through practice, it is proved that this approach can effectively improve students’ mastery of course content, enhance students’ ability to apply mathematical knowledge, and strengthen teaching effectiveness.

Reflections: enhancing critical thinking in science education by implementing philosophy elements into training.

In this work, I describe the trajectory of philosophy and science as separate disciplines from their early days as quite overlapping fields to their clear divergence in the latest centuries. From personal experience, I discuss the benefits of exposure to philosophy and closely related courses in undergraduate studies and bring to the forefront the positive aspects of integrating philosophy of science courses in graduate science, technology, engineering, and mathematics (STEM) curriculum. I also briefly offer some additional steps institutions can take to foster unity between areas of science and philosophy by incorporating interdisciplinary activities.

Examination of the Delphi Method for Establishing a Quantitative Literacy Framework in Undergraduate Mathematics Course

The increased relevancy and importance of quantitative literacy (QL) have called for educational reform in undergraduate mathematics course offerings. However, lack of clear guidelines has led to wide variability in the content and outcomes of math courses meant to address QL. Therefore, having an expert consensus regarding content and outcomes for an undergraduate mathematics course focusing on QL would advance the quantitative literacy initiative in higher education. The authors propose the Delphi Method to aid in developing a framework based on expert opinions. The authors explain the Method and suggest the result of this process should yield a research-based framework that faculty and institutions can use as a resource for QL math courses.

The General Mathematics Course ‘Mathematics and Life Sciences’ for Non-science and Engineering Students

In modern society, alongside the rapid advancement of science and technology, the role and importance of mathematics are increasingly being emphasized. Such advancements, including data analysis and artificial intelligence development, rely fundamentally on mathematical thinking and theory, which have become essential elements across all academic disciplines. Against this backdrop, the role of university general mathematics education has become undeniably important. It is necessary not only for students in science and engineering, but also for those in the humanities and social sciences, to have access to balanced mathematical education. To this end, universities must focus on developing a variety of general mathematics courses. This paper presents a detailed case study of the design and operation of a basic general mathematics course titled “Mathematics and Life Sciences,” offered to students in the humanities and social sciences at Y University in Seoul. The course is structured to enable students to learn essential basic mathematics theories that are crucial across various disciplines and to apply them to phenomena in life sciences. In doing so, students will gain a better understanding of certain interdisciplinary connections as well as enhance their thinking and problem-solving skills. Additionally, this paper analyzes the educational effects and positive feedback from students obtained through a decade of continuous improvement in the content and operation of this course. Based on this analysis, this paper proposes future directions for development and research tasks in the educational field. This research is expected to contribute to the exploration of the direction in which university general mathematics education should head.

The student self-confidence profile in learning English for Mathematics with the Tiktok application

Speaking is a mentally demanding task for a foreign language learner. One of the aspects that can lessen speaking anxiety is confidence. This research was conducted to expose mathematical students' confidence profiles when speaking using the TikTok application. To reveal the mathematical students' confidence profile, this research used the quantitative analysis research approach comprised of in-depth data analysis in the form of numbers. The data was obtained from the second-year Mathematics students who took English for Mathematics course. The results show the variety of levels of confidence and the aspects of confidence possessed by the students. Teachers can take advantage of the students' confidence profile to improve their teaching. Keywords: English for mathematics; Self-confident; Speaking; TikTok Application

THE RELATIONSHIP OF RESILIENCE WITH BASIC MATHEMATICS LEARNING OUTCOMES OF PGMI STUDENTS

Students still need help learning mathematics and completing assignments. Various things can cause this. One of them is the pressure of facing basic mathematics learning. This research aims to determine the relationship between mathematical resilience and learning outcomes in basic mathematics courses for PGMI UIN Sunan Kalijaga Yogyakarta students. The sample for this research consisted of 33 PGMI UIN Sunan Kalijaga students. The research method used is the correlation research method. Data collection techniques use research instruments in the form of test and non-test instruments. The test instrument used in this research is questions to measure mathematics learning outcomes, while the non-test instrument uses a questionnaire to measure mathematical resilience. The data analysis technique uses descriptive data analysis, prerequisite tests (normality and homogeneity tests), and hypothesis testing using the product moment correlation formula. The results of this research show that there is a significant relationship between resilience and mathematics learning outcomes for class C PGMI UIN Sunan Kalijaga students.

Examination of Mathematics Course Contents Related to Proof in the Educational Informatics Network

This research aims to examine the mathematics course contents related to proof in the Educational Informatics Network. The document analysis method was used in this qualitative research. The data of the study consisted of 35-course contents related to proof in the Educational Informatics Network. These contents were subjected to content analysis. According to analysis results, it has been determined that there isn’t enough proof in the contents of the Educational Informatics Network for all grade levels and in all learning domains. Although not in sufficient numbers, the proofs in these contents mostly consist of proofs belonging to the “Geometry” learning domain. The number of proofs in the “Numbers and Algebra” learning domain is limited. It is seen that no proof of the “Data, Counting, and Probability” learning domain is included. In line with the results of this research, it can be suggested to produce more content related to proof suitable for cognitive developments and grade levels by making the most of the potential of technology for all grade levels and all learning domains.

APPLIED DIRECTION OF THE STUDY OF HIGHER MATHEMATICS BY STUDENTS OF PROFES- SIONAL PRE-HIGHER EDUCATION

The article substantiates the need for a practical, professional focus of studying the course of higher mathematics by students of professional pre-higher education institution. The aim of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the education of students in various specialities of vocational higher education. Modern requirements for the development and reform of higher education require an increase in the professional competence of a bachelor’s graduate in each field of knowledge, the ability to creatively approach and find the solution to emerging professional tasks. Therefore, teachers of higher mathematics have the task of reorienting the teaching of the academic discipline with the use of professional problem solving. The purpose of the article is to highlight the ways of implementing the professional orientation of the content of mathematical disciplines in the training of students of professional pre-higher education in various specialties of the college. In connection with the rapid development of science and technology, the training of competent, competitive, and highly qualified specialists requires a high level of skills in applying mathematical apparatus in professional activities. Mathematics is the basis of studying physics, technology, general technical and special disciplines. At present, mathematical education has a significant impact on the formation of professional qualities of a modern specialist who is able to navigate the directions of development of modern science and methods of learning about the world around them, predict the impact of human production on society and the environment. Modern mathematics is used in the study of economic, humanitarian, biological, physical, technical and other phenomena. This is done by building a mathematical model. It takes into account all essential connections within the phenomenon. Under mathematical modelling we will understand the method of researching processes or phenomena by building their mathematical models and researching these processes. The applied direction of solving problems by students of various specialties is oriented towards future professional activity. This is an effective means of increasing learning motivation, and developing mathematical and professional competences. The results of the research are examples of practical problems of various sections of higher mathematics for students of economic and technical specialties. The applied nature of the given problems aims to combine the study of higher mathematics with special training of future bachelors and to give them the opportunity to gain experience in solving production problems, and to increase their professional competence. This is very important in times of fierce competition in the labour market. Conclusion. Practical skills and the ability to use the mathematical apparatus when solving applied, profession-oriented problems increase the motivation of students of higher and pre-higher education, and aid students to study other courses of professional disciplines, and do coursework and diploma projects, which will contribute to the maximum use of mathematical methods in the educational course of higher education mathematicians in the future professional activity. The obtained results open up prospects for further research in the following directions: development of methods of formation of skills to solve applied problems by students of various specialties, as well as strengthening integration links between fundamental and profession-oriented courses.

Transitioning to proof via writing scripts on the rules of a new discourse

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers’ learning of these rules when being taught them explicitly. Our data come from academically motivated high-school students who took a special course in undergraduate mathematics. The course teacher dedicated three academic hours to introducing and explaining selected rules of proof to support students’ shift to the new discourse. The homework assignment consisted of typical proof-requiring problems and a scriptwriting task, asking students to compose a dialogue between fictional characters about a proof-related mistake of their choice. We analyzed the differences and similarities between the rules discussed in the classroom and those that students addressed and implemented in their proofs. The analysis showed that while students’ solutions to proof-requiring problems required rule implementation, fictitious dialogues opened the space for rule formulation and substantiation. In many cases, the students discussed the rules presented in the classroom, extending, elaborating, and specifying the teacher’s formulations. Furthermore, while the students’ proofs were mainly consistent with the teacher’s expectations, some of their rule formulations were more radical and overgeneralized than expected. These findings suggest that newcomers’ communication about the rules of proof may lag behind their capability to implement those rules to prove mathematical statements.

Learning Theories and teaching Mathematics online: The Case of the Hellenic Open University

The utilization of pedagogical principles and learning theories is essential for improving the quality of education provided in online learning environments. In the field of mathematics, the utilization of the appropriate pedagogical approaches and techniques should be based on grounded and practically established theories. The Hellenic Open University (HOU) has been at the forefront of distance education in Greece, providing students with the opportunity to study a variety of scientific subjects remotely. This study aimed to investigate the extent to which learning theories are utilized by instructors/tutors in mathematics courses of HOU. The research methodology followed the qualitative approach of a case study. Semi-structured interviews were conducted with ten participants (instructors/tutors and instructional design experts). The results revealed that the utilization of pedagogical approaches and techniques based on learning theories was not consistent nor widespread. The findings emphasize the importance of providing training and support to instructors/tutors of HOU as well as clear guidelines integrating pedagogical approaches and learning theories into the learning material, the educational activities and the course structure.

ERROR ANALYSIS IN SOLVING APPLIED MATHEMATICS PROBLEMS BASED ON THE NEWMAN PROCEDURE

The purpose of this study is to describe the various kinds of errors made by taruna when solving applied mathematics problems based on the Newman procedure. Newman divides errors into 5 types, namely reading error, comprehension error, transform error, process skill error, and encoding error. This research uses descriptive qualitative research methods. Data collection techniques were carried out using tests and interviews. Data reduction, data presentation, and verification or conclusion drawing are part of this research. Based on the results of research and data analysis, it can be seen that in solving mathematical problems in land mathematics courses there are 5% of subjects experience errors in reading errors, 16% of subjects experience errors in comprehension errors, 9% errors in transform errors, 26% of subjects experience process skill errors, and 9% errors in encoding errors. Most of the errors were errors in the selection of problem-solving strategies.

The Cultivation of Students' Mathematical Literacy Under the Background of Vocational Education

This article analyzes the problems in the teaching of mathematics courses in higher vocational colleges, elaborates on the relationship between innovative development and mathematics teaching, and points out the special role of mathematics in cultivating high-quality innovative talents, promoting teaching reform in colleges, and assisting the innovative development of higher vocational education. The cultivation of mathematical literacy is a subtle process. Based on the current situation of mathematics education, several suggestions are proposed to provide certain reference for the reform of mathematics education and teaching.

Vocational school students’ use and opinions of voluntary-based online learning solutions presented in a mathematics course

This article focuses on the use made by Finnish vocational upper secondary students, including their opinions, with regard to the voluntary-based aspects and activities of a compulsory mathematics online course. In particular, the study investigated whether the vocational field affects students’ views and actions. There were altogether 313 students from six vocational fields participating in this study, but the number of students who responded to the feedback questionnaires related to the different opportunities and activities varied. Of the opportunities offered, the repetition opportunity was the most used and the most useful from the students’ point of view. Almost 90% of the respondents ended up, either voluntarily or under guidance, taking advantage of the repetition option. The education video was watched by almost 60% of the students responding to the questions related to the video. Students had a positive attitude towards the effects used in the educational video, the length of the video, and the level of explanation of theory. Approximately half of the respondents who were offered an additional practice opportunity took advantage of this, and the opportunity was seen as quite useful. There were only minor, if any, statistically significant differences between the vocational fields regarding the use of the opportunities offered and the opinions related to them. This research will assist in developing online teaching of mathematics at vocational upper secondary level and will also offer guidelines for the development of online education more generally.

An examination of pre-service mathematics teachers’ course-taking, beliefs, and preferred assessment practices

AbstractThis study uses structural equation modeling to investigate the relationships between pre-service teachers’ (PSTs’) course-taking history, beliefs about mathematics, beliefs about students’ mathematical ability, and opinions about (1) how student errors should be addressed when they occur and (2) how much emphasis should be given to various forms of assessment. The results indicate that some types of courses are strongly associated with beliefs about the nature of mathematics. Specifically, PSTs who have taken more mathematics courses are more likely to see mathematics as a set of rules. PSTs’ views about mathematics strongly predict their beliefs about who can do high-level mathematics, how they think student errors should be addressed, and which forms of assessment they think are most appropriate. Implications for teacher preparation programs are discussed.

Mobile Technologies in Teaching Mathematics

Purpose. The article discusses the use of mobile technologies in teaching mathematics to engineering students. The relevance of the paper is due to the need to introduce new methods and means of teaching in connection with the increasing integration of mobile technologies into all areas of life, the interests and characteristics of the new, networked generation of students, the limited possibilities of using innovative methods and means of teaching mathematics due to the conduct of classes outside the computer lab.Materials and methods. The peculiarity of this study is that the integration of mobile technologies into the process of teaching mathematics is considered as a system of three components: technological, informational and social. The analysis of these components made it possible to obtain answers to research questions: where and how mobile devices should be used when studying mathematics; what mobile applications will provide the most effective learning of the discipline; how to organize the educational process using mobile technologies to increase interest and motivation in learning mathematics.Results. The main reasons for the lack of interest in studying mathematics and low motivation include the high level of abstraction of the discipline and the characteristics of the modern, networked generation of students. Analysis of scientific sources and our own observations made it possible to identify such characteristics as problems with understanding complex and long text, the ability to easily read from a small screen and process information in parallel, the choice of sound and images instead of text, the desire for short-term learning and instant results, and attitude towards mobile devices as vital items. Taking into account the interests and wishes of students, and relying on the didactic capabilities of mobile technologies, the paper proposes mobile applications for studying various topics of a mathematical course, assignment options that help increase motivation, develop group work skills and digital literacy. The importance and effectiveness of using social services for visualizing mathematical concepts and calculation schemes, as well as the WhatsApp messenger for instant messaging between students and receiving timely individual and group consultation from a lecturer, is shown. An important characteristic of the messenger is the presence of video communication.Conclusion. The analysis of scientific literature, the study of the requirements of employers and the interests of the modern, networked generation of students, indicated the need to integrate mobile technologies into the process of teaching mathematics. Working with different groups in terms of both the level of mathematical knowledge and the level of proficiency in mobile technologies made it possible to identify and outline ways to solve the main issues of using mobile technologies in teaching mathematics. With limited time to study mathematics, it is difficult for a lecturer to allocate additional time to present the capabilities and effectiveness of mobile applications. A solution to this issue may be to include a section “Mobile Technologies” in a course related to the study of information and communication technologies. It is noted that group work also contributes to a more effective study of the capabilities and techniques of working with mobile applications.

"Four New and Three High" Mathematical Modeling Course Construction

After years of inheritance, innovation and integration, the mathematical modeling curriculum has been reformed from the aspects of education concept, training goal, teaching system, teaching material system, course content, teaching method and learning mode. Teaching "four new" design is to organically integrate the ideological and political elements with professional characteristics into the course teaching, innovate the course content, teaching methods and evaluation methods, enhance the students' independent learning ability, and realize the integration of teaching and ideological and political education. The transformation of "three high" innovation resources into teaching: high-level design, high-quality requirements, high-level implementation, relying on high-level scientific research and innovation resources, timely transformation into teaching resources through classroom teaching, extracurricular science and innovation, school-enterprise exchanges and other ways, and focusing on cultivating students' practical ability and innovation ability.

Can I Eat Melted-Frozen-Melted Bread?: Use of Practical Assignments to Harmonize Mathematics and STEM Courses and as a Measure for Future Technology Studies

Can I Eat Melted-Frozen-Melted Bread?: Use of Practical Assignments to Harmonize Mathematics and STEM Courses and as a Measure for Future Technology Studies