Mathematics Courses Research Articles

Combat modelling using Lanchester equations

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Using mathematical modelling to provide students with a contextual learning experience of differential equations

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a contextual environment. Teaching mathematics in context has the potential of giving students something to anchor the mathematics to and hence act as cognitive roots With this in mind, in what ways can lecturers use mathematical modelling to provide students with contextual learning experiences of differential equations? A New Zealand study was carried out involving three case studies. Each case study comprised of a mathematical modelling course, lecturer participant and student participants. Modelling examples and activities that involved differential equations were part of all course content. In this paper, I will present information on each course, the main modelling activities each course used, and examples of students' use of differential equations for these activities. Insights discovered into the common practices of the three lecturers regarding using mathematical modelling to teach differential equations will also be presented.

Pursuing Stem Careers: Challenges of Senior High School Students during Distance Learning

The COVID-19 pandemic required the educational sector to implement countermeasures in order to continue educating students amidst the pandemic, this may have resulted in a gap in the number of people entering the STEM (Science, Technology, Engineering, and Mathematics) field. This study determined the challenges of senior high school students in learning in STEM through distance learning. The respondents were 85 Grade 12 STEM students from the six (6) selected public and private educational institutions in the province of Zambales who were chosen through stratified random sampling. Results revealed that STEM 12 students often encountered challenges in terms of Learning Environment (LEC), Student Isolation (SIC), and Workload, simultaneously, it was noted that they sometimes encountered challenges in terms of Self-Regulation (SRC), Technological Sufficiency (TSC), and Technological Literacy and Competency (TLCC).Statistically significant differences were noted on the challenges encountered by Senior High School Students during distance learning in terms of school and age, but there were no significant differences that were noted regarding the other profile variables. The study suggests that the education sector should create program interventions to address the challenges such as curriculum development, to encourage or institutionalize special training courses in mathematics and science, and to develop learning continuity plans to empower teachers and students.

A Mathematics Educator Walks into a Physics Class: Identifying Math Skills in Students’ Physics Problem-Solving Practices

AbstractOne of the main goals of lower division “service” mathematics courses is to provide STEM-intending students with opportunities to engage in activities and contexts that can support their efforts to apply the mathematical ideas they are learning to successive major courses. The Mathematics Association of America has supported many mathematicians’ efforts to ask partner discipline faculty what topics and habits of mind they feel should be covered in mathematics classes to prepare them for their subsequent classes. We add to this work with a twist: Instead of asking physics faculty what they want students to know, we analyzed videos that students in an introductory physics class created so that we could ask ourselves what mathematical practices were most and least prevalent in the students’ physics problem-solving efforts. A qualitative analysis of the results, which we present here, indicated that most students were proficient in math practices involving problem setup and that the majority were able to apply mathematical concepts such as trigonometry and the solving of algebraic equations. However, only 44% of the student groups concluded their explanations by discussing answer reasonability and only 18% conducted a unit analysis to determine if their answers were applicable to the context of the problems assigned, even though both of these elements are important components of the overall sensemaking process. This report presents examples that illustrate these results and concludes with implications for teaching both entry-level mathematics and physics courses by modeling productive problem-solving and sensemaking practices.

FEATURES OF TEACHING HIGHER MATHEMATICS IN THE CONTEXT OF FUTURE PROFESSIONAL ACTIVITIES OF TECHNICAL UNIVERSITY STUDENT

Peculiarities of teaching a higher mathematics course at a technical university for engineering students are considered. Methods of algorithmic learning, problem-based learning, and research learning are analyzed in the context of the future professional

Evaluation of Students' Difficulties in Learning Mathematics in Complex Variable Material

Prospective mathematics teachers are required to be able to master facts and be able to give examples that exist in everyday life. A prospective mathematics teacher is expected to be skilled and mature in using media when operating, explaining and demonstrating direct objects that exist in any complex variable material. The aim of this study is to analyze the obstacles and difficulties of students in Mathematics. Two indicators for assessing mathematics learning outcomes: 1) Direct objects (Facts, Concepts, Skills, and Principles), and 2) Indirect objects (Internet and friends). Mixed methods research method. The subject of the complex variable mathematics course and the student object. Qualitative data collection techniques by observation, interviews, documentation and quantitative survey method collection techniques by distributing instruments. Analysis with, presentation, reduction, presenting bar charts, data synchronization and drawing conclusions. The findings, students' difficulties lie in the direct object, namely mastery of mathematical facts 95.55% and concept difficulties 91.11%, principle (formula) difficulties 91.11% and algorithms 75.55%. Students who get good grades online are assisted by indirect objects, namely the internet and other student discussion partners. In conclusion, students' obstacles and difficulties lie in the direct objects of fact indicators (definitions) and concepts. Material design, facts and concepts with group discussion models are learning solutions.

Determination of Mistakes Made by Pre-Service Mathematics Teachers in Fermi Problem-Solving Performance and Solutions

One of the reasons why students fail in mathematics courses is that the problems used in the lessons are abstract. In this context, it is important to embody the problems used in the lessons. Fermi problems are open-ended problems, a type of problem that reflects real-life situations that are solved by making a series of predictions. In the future, with these problems involving real-life situations, it is today’s pre-service mathematics teachers who are primarily responsible for carrying out an effective teaching process in school mathematics. This research was carried out within the scope of the case study design, which is one of the qualitative research designs, which aims to determine the errors made by primary school mathematics teacher candidates in their performance and solutions to solve the Fermi problem. The study group of the study consisted of 44 pre-service teachers studying in the 4th grade in the department of primary school mathematics teaching in a province located in the southern region of Turkey in the 2022-2023 academic year. As a result of the research, it was concluded that the scores obtained by the pre-service mathematics teachers from the solutions of Fermi problems were not at the desired level, and the performance of the teacher candidates was at a medium level. From the error detection, it was find that the source of this situation is mostly due to the weakness in the dimensional estimation process.

Research on automatic matching of online mathematics courses and design of teaching activities based on multiobjective optimization algorithm.

The teaching of the optimization algorithm is a new kind of swarm intelligence optimization technique, which is superior in optimizing many simple functions. Still, it is not evident in processing some complex problems (group and teaching classification). Achieving automatic matching and knowledge transfer in online courses is imperative in mathematics education. This study proposes a design scheme MTCBO-LR (multiobjective capability optimizer-logistic regression), based on multitask optimization, which enables precise knowledge transfer and data interaction among many educators. It incorporates the standard TLBO algorithm to optimize, provides a variety of learning tactics for students at different stages of mathematics instruction, and is capable of adaptively adjusting these strategies in response to actual teaching needs. Experimental results on various datasets reveal that the proposed method enhances searchability and group diversity in various optimization extremes and outperforms similar methods in resolving to multitask teaching problems.

ON SOME APPLICATIONS OF DIVERGENT PROBLEMS

The paper is devoted to identifying possible effective applications of divergent problems in school courses in mathematics and physics. The article first outlines the essence of the divergent task, its contributing role in the formation and development of the logical and creative thinking of students, after which the varieties of divergent tasks are interpreted, and then, for each variety, examples of divergent tasks found in school courses in mathematics and physics are discussed in detail. The first kind of divergent problems are problems that allow different solutions. As an example, this paper discusses one mathematical problem of determining the largest value of an expression. In addition to the standard method, as a means of stimulating the creative abilities of students, three more options for solving the problem are proposed, which, differing significantly from each other, contribute to a comprehensive consideration of the problem. The next problem discussed in the article is from the "Mechanics" section of the school physics course. Three different approaches to solving this problem are presented. At the same time, these approaches differ not so much in mathematical solutions as in the accepted physical ideas. The next type of divergent problems are problems that have ambiguity, freedom or uncertainty in their conditions. The article analyzes in detail the mathematical problem of motion and the non-standard problem of dynamics, as divergent problems of the second type. The study provides guidelines, the use of which will contribute to the search for ways to solve divergent problems, and will allow you to protect as much as possible from mistakes made in the preparation or solution of such problems, which is the scientific and pedagogical novelty of the article

Importance of Academic Legacy on Student Success in First- and Second-Semester General Chemistry

This investigation sought to elucidate the influence of students' academic legacy on their prior knowledge and course outcomes providing crucial insights for educators who teach general chemistry. This six-semester analysis involved 6,914 students enrolled in classes across nine Texas universities. Explored were personal circumstances associated with students' successes and failures that influenced performance in on- and off-sequence, first- and second-semester general chemistry (Chem 1 and Chem 2). Students' academic legacy based on their categorization as first generation (neither grandparent nor parent/guardian with a 4-year bachelor's degree), second generation (at least one grandparent or parent/guardian with a bachelor's degree), or third generation (at least one grandparent and at least one parent/guardian hold a bachelor's degree) was investigated. Of the students in the dataset 33.8% (<i>n</i> = 2,340) self-identified as Hispanic. Results for Hispanic and non-Hispanic students indicated that first-generation students struggled more with Chem 1 and Chem 2 than students in the other two legacy groups. As students' academic legacy extended, they were more apt to succeed in general chemistry. Second- and third-generation students demonstrated stronger prior high-school chemistry backgrounds and were enrolled in more advanced mathematics courses. As expected, students with stronger academic backgrounds in chemistry and mathematics scored higher on the diagnostic MUST (Math-Up Skills Test), had greater self-efficacy relative to their preparation to succeed, and reported fewer paid work hours. First-generation students on the average entered with lower diagnostic MUST scores, felt less prepared to succeed, and disclosed a greater need to be employed.

Ortaokul matematik öğretmen adaylarının model oluşturma etkinliği tasarlama yeterlikleri, problem çözmeye yönelik inançları, problem kurmaya yönelik öz-yeterlik inançları ve aralarındaki ilişki

This study aimed to determine the change and the relationship between elementary school mathematics teacher candidates' competence to design model-eliciting activities, their beliefs towards problem-solving, and their self-efficacy beliefs towards problem posing according to gender and overall academic grade point average (GPA). Modeling activities designed by 64 elementary school mathematics teacher candidates in Turkey were evaluated by means of a grading key created in the context of "compliance with MEA design principles". In addition, a scale consisting of 24 items was applied to determine the beliefs of the teacher candidates towards problem-solving, and a 26-imoetem scale was applied to determine their self-efficacy beliefs towards problem-posing, and the responses were analyzed by quantitative methods (one-way multiple variance analysis, correlation analysis, multiple regression test). The findings reveal that elementary school mathematics teacher candidates' proficiency in designing model-eliciting activities is generally at a high level, while their belief in problem-solving and self-efficacy beliefs in problem posing is generally at a moderate level. Based on the studies that concluded that modeling competencies develop as they work on modeling problems and that the experience of mathematical modeling affects their mathematical modeling competencies, it was concluded that modeling problems were used to solve mathematical problems and teach these solutions in the mathematical modeling course they took. It was determined that the linear combinations of teacher candidates' proficiency in designing model-eliciting activities, beliefs in problem-solving, and self-efficacy beliefs in problem-posing did not show a significant difference. The fact that pre-service teachers' beliefs about problem solving and posing are not related to their MEA design competencies is thought to be due to their previous routine mathematical problem solving experiences being more dominant. On the other hand, since the mathematical modeling process is basically considered as a problem-solving process, it was expected that these beliefs of pre-service teachers would be related to MEA design proficiency. It is important to conduct qualitative research with teacher candidates in order to examine this situation in more detail and to reveal the underlying causes.

Benefits and Challenges of Peer Interaction in Calculus Group Exams: Perspectives of Latina/Hispanic & Mixed Race Women

Collaborative assessment techniques are needed to align with shifting approaches to learning that center peer interaction. Furthermore, it is critical to understand how collaborative assessments work for students belonging to historically marginalized groups. This study reports the perspectives of four mixed race and Latina/Hispanic women regarding peer interaction and group exams in university mathematics courses. Three primary themes emerged from interviews: (a) benefits of communication during group exams, (b) challenges of working with peers during group exams, and (c) consideration of gender balance when assigning exam groups. These findings have implications for how college instructors implement collaborative exams in intentional ways that benefit students.

First Year Engineering Students’ Difficulties with Math Courses- What Is the Starting Point for Academic Teachers?

The discussion about first-year engineering students’ difficulties in mathematics is continuous in the fields of engineering, mathematics and higher education. The present study aimed to examine the initial barriers academic math teachers need to have in mind if they want to improve students’ performance in engineering math courses through appropriate teaching practices in order to face their initial interindividual differences. During the first phase of the study, we examined first year engineering students’ initial beliefs about the nature of mathematics, their self-efficacy beliefs about mathematics and their basic mathematical knowledge. The math school grade was used for their previous mathematical performance. Results indicated the predominant role of the previous mathematical knowledge and the important role of the formalistic disposition toward mathematics. The lack of experience of using mathematics for problem-solving situations within an engineering framework prevented students from recognizing and appreciating the value of mathematical courses during the engineering studies. The second phase of the study examined, through an interview with a group of students, their perceptions of the teaching practices which were introduced after their teacher attended a training program. The discussion concentrates on how academics can use teaching processes for equity and not equality in order to motivate their students.

Effect of Mobile Instructional Design on Student Perception of Distance Learning

Learning through mobile applications has become more relevant as mobile tools have evolved. The COVID-19 outbreak that spread across the globe in 2019 promoted to a brief period of distance learning. The purpose of the study was to investigate how the students' perceptions of distance learning were affected by the use of a mobile application designed for a seventh-grade mathematics course. The research was performed using quasi-experimental design. The study was conducted in the distance education process with 7th grade students studying in a secondary school in the 2020-2021 academic year. The mobile application was used to deliver the instruction to the students in the experimental group, whereas the control group received instruction based on the textbook. To collect the data for the study, Yıldırım et al. (2014) designed the "Student Opinions Scale for Distance Education". T-tests were used to assess the data for dependent and independent samples, respectively. The study revealed a substantial difference in the post-test results of the students in the experimental and control groups. It was discovered that there was no significant difference between the pre and posttest scores of the control group students' opinions on distance education and that there was a substantial increase in the experimental group students' attitudes on distance education between the two assessments. According to the findings, it has been suggested that by creating mobile applications in various ways and including them into the distance learning process, the impacts of using them for mathematics classes on distance learning can be studied.

ANALISIS KESULITAN MAHASISWA DALAM MENYELESAIKAN SOAL DIFERENSIAL PADA MATA KULIAH MATEMATIKA DASAR

Its research is a descriptive qualitative research. The sampling method in this study used purposive sampling with 10 Informatics Management students in the first semester of the 2022/2023 academic year as subjects, who took Basic Mathematics courses. These students have difficulty solving differential problems, especially material on chain rules and high-order derivatives. The results of the Mid Semester Examination (UTS) obtained were only able to be answered by 20% of students. The purpose of this study was to analyze students' difficulties in answering differential questions, done by looking at learning outcomes and by collecting information obtained during interviews, based on four aspects of expertise, namely: 1) Information skills, 2) Arithmatics skills, 3) Language skills, and 4) Number fact skills. The method of information analysis is carried out by: collecting information, reducing, presenting information, and drawing conclusions. Data collection in this study used a triangulation procedure, namely by equating the information on the test results with the results of the interviews. The results of this study are that students have difficulty solving differential problems when viewed from the four aspects of expertise. Factors causing difficulties in this ability are 1) students are not able to analyze the correct method that will be used to solve the differential function reduction, 2) students do not understand mathematical operations well, and 3) students make mistakes reading and interpreting questions.

Investigating the Impact of Gamification on Student Motivation, Engagement, and Performance

In the academic context, the use of innovative learning techniques that can have a positive impact in the classroom is becoming increasingly common; gamification is one such technique. This study compared the effects of gamification on engagement, cognition, metacognition, and academic performance when university students used a gamified platform to when they did not in a mathematics course. Using the statistical technique of structural equation modelling (SEM) for both cases, the results show that motivation was the construct with the largest effects, influencing behavioral dissatisfaction, cognition, and metacognition. When students used the gamified platform, motivation influenced behavioral dissatisfaction, which in turn influenced academic performance. On the other hand, when the gamified platform was not used, motivation had a negative effect on academic performance. Therefore, the use of gamification learning strategies can help to reduce student demotivation.

Extensions to the theorems of Pappus to determine the centroids of solids and surfaces of revolution

Extensions to the first and second theorems of Pappus are presented, whereby the centroid of a surface or solid of revolution can be determined using only the geometric properties of the generating plane curve or figure and the arc of revolution. The derivations are well suited to first-year-level courses in mathematics and engineering. From a didactic perspective, the resulting formulas are simple to apply, especially since the required geometric properties are typically available in standard tables of plane sections or relatively routine to derive. Furthermore, the formulas provide a general scaffold for students to attempt problems involving axisymmetric bodies while also reinforcing and embedding their knowledge of the properties of the generating plane shapes. A selection of illustrative problems is discussed that are generally regarded to be challenging for introductory mechanics courses but for which the formulas derived in this article provide straightforward solutions.

A Taxonomic Analysis of the Questions Prepared by Prospective Primary Teachers for Primary School Mathematics and Turkish Language Courses

The aim of this study is to investigate the cognitive process dimension of the revised Bloom’s taxonomy in the question preparation of prospective primary school teachers in fourth grade Turkish and mathematics courses. This research is a descriptive study carried out following the survey model, one of the quantitative research methods. The study group consisted of 85 prospective teachers in their final year of the undergraduate programme in primary education at a state and foundation university in Turkey. The data were obtained through questions prepared by the prospective teachers through question preparation forms on Turkish and mathematics courses. These data were analyzed using the descriptive analysis method. The study concluded that the majority of questions prepared by prospective primary teachers in both courses were in the lower levels of the cognitive process dimension of revised Bloom’s Taxonomy (remember, understand and apply). It was found that the questions in the Turkish language course were mostly prepared in the remember and understand dimensions and in the mathematics course were mostly prepared in the apply and understand dimensions. In light of these results, it can be suggested that the preparation of high-level questions in terms of the revised Bloom’s taxonomy should be included more in undergraduate education.

Performance Evaluation of Computer Science Students in Mathematical Courses Over Prgramming Language Courses

Abstract: The low level of performance observed among many computer science students in mathematical and computer programming courses served as the motivation for this work. The prediction of computer science students’ overall performance in mathematical courses over programming courses was done using WEKA and machine learning algorithms. Dataset of students performance from Yaba College of Technology, Lagos, Nigeria and Lagos State Polytechnic, Lagos, Nigeria, for both National Diploma and Higher National Diploma were used. These data set were studied and analyzed using WEKA and Random Forest, J48, Naïve Bayes and Logistic Regression algorithms. The algorithms were applied for the HND and ND dataset and there was comparison based on their accurancy, learning time and percentage of correctly classified instances. This comparison showed that there is direct relation between the execution time in building models and volume of data records. This shows that the predictor did not only predict the number of students that are likely to be in distinction, upper credit, lower credit, pass and fail but also show the relationship between having the knowledge of mathematics and programming language for an overall performance in computer science. The knowledge pattern represented further satisfies the exertion that it is imperative for students to have a standard knowledge of mathematics as this will help in being the best in their chosen profession.

Analysis of Competitive Strategy Innovations: Case A Course and Training Institutes AHA Smart Matematika Jakarta

This study aims to find out and explain the innovation strategies taken by LKP aha smart Mathematics. This research method is qualitative, namely, the research procedure produces descriptive data, both in the form of speech, behavior, and phenomena found when jumping directly into the field to observe the Objects and Subjects to be studied. The data collection technique is carried out through observation, interviews, and documentation. Data analysis is carried out by selecting answers obtained from informants and then collected for analysis and conclusions. The data analysis used is data triangulation. The results of the research were obtained, competitive strategy innovations taken by aha smart mathematics course and training institutions using Michael E Porter's generic strategy, namely low-cost strategies: the fees set by the smart mathematics course and training institutions are Rp 250,000 / month for regular, and Rp 300,000 / month for intensive, differentiation strategies: aha smart mathematics course and training institutions create a unique method that is a differentiator from other LKPs that Similar, and strategy focus: AHA Smart Mathematics course and training institutions focus on market segmentation, focus on optimal products and services, and focus on organizational structuring.