Mathematics Courses Research Articles

Comparison of three large language models as middle school math tutoring assistants

Middle school math forms the basis for advanced mathematical courses leading up to the university level. Large language models (LLMs) have the potential to power next-generation educational technologies, acting as digital tutors to students. The main objective of this study was to determine whether LLMs like ChatGPT, Bard, and Llama 2 can serve as reliable middle school math tutoring assistants on three tutoring tasks: hint generation, comprehensive solution, and exercise creation. Our first hypothesis was that ChatGPT would perform better in completing all three tutoring tasks than Bard and Llama 2 due to its largest model size (175 billion parameters). Our second hypothesis was that Bard would perform better than Llama 2 in generating comprehensive correct solutions due to its relatively higher model size (137 billion parameters) than Llama 2 (70 billion parameters). We curated medium-difficulty, word-based middle school math problems on algebra, number theory, and counting/probability from The Art of Problem Solving and Khan Academy. A human tutor evaluated the LLMs' performance on each tutoring task. Contrary to our first hypothesis, results showed that ChatGPT didn't perform uniformly better than Bard and Llama 2 on all the tasks. ChatGPT outperformed both Bard and Llama 2 only in the comprehensive solution task. Bard didn't perform better than Llama 2 in the comprehensive solution task which does not support our second hypothesis. We conclude that middle school math teachers can use a combination of ChatGPT, Bard, and Llama 2 as assistants based on the specific tutoring task.

The Exploration of Curriculum Ideology and Politics in Advanced Mathematics from the Perspective of the Three-Wide Education

For advanced mathematics courses for science and engineering students, the course guided by three-wide education (TWE) explores the ideological and political teaching in the curriculum, analyzes the relationship between TWE and curriculum ideology and politics (CIP), and determines the course objectives. The course is related to the ideological and political elements of the curriculum, establishes the feelings of home and country, integrates into educational activities, creates a collaborative education classroom, and formulate assessment and evaluation standards. Finally, through the questionnaire survey and feedback on the implementation effect, it is concluded that integrating ideology and politics into advanced mathematics can stimulate learning motivation, realizes all-round education throughout the process, and well implement the task of building morality and cultivating people.

Solving word problems involving triangles and implications on training pre-service mathematics teachers

<p>Triangles and trigonometry are always difficult topics for both mathematics students and teachers. Hence, students' performance in solving mathematical word problems in these topics is not only a reflection of their learning outcomes but also an indication of teaching effectiveness. This case study drew from two examples of solving word problems involving triangles by pre-service mathematics teachers in a foundation mathematics course delivered by the author. The focus of this case study was on reasoning implications of students' performances on the effective training of pre-service mathematics teachers, from which a three-step interactive explicit teaching-learning approach, comprising teacher-led precise and inspiring teaching (or explicit teaching), student-driven engaged learning (or imitative learning), and student-led and teacher-guided problem-solving for real-world problems or projects (or active application), was summarized. Explicit teaching establishes a solid foundation for students to further their understanding of new mathematical concepts and to conceptualize the technical processes associated with these new concepts. Imitative learning helps students build technical abilities and enhance technical efficacy by engaging in learning activities. Once these first two steps have been completed, students should have a decent understanding of new mathematical concepts and technical efficacy to analyze, formulate, and finally solve real-world applications with assistance from teachers whenever required. Specially crafted professional development should also be considered for some in-service mathematics teachers to adopt this three-step interactive teaching-learning process.</p>

An analysis of number sense skills of Syrian immigrant students by gender and duration of stay

Considering the negative situations faced by the migrating societies, it is known that the language and culture factors exert a stronger influence on the mathematics course than the other undesirable conditions. From this perspective, it is known that the mathematical performance of individuals is likely to increase by placing the concept of number sense in the center. Therefore, the present study aimed to examine the number sense skills of Syrian immigrant students with reference to gender and duration of stay as an immigrant as well as to determine their conceptual awareness of number sense-related components. The descriptive correlational design was used in this study in which 152 immigrant students participated. Web-based two-tier test was used in the data collection process, and descriptive statistical values and t-test for independent samples in the analysis of the data. As a result, it was found that male students compared to female students, as well as those who had been immigrants in Turkey for a long time compared to those for a shorter time showed higher number sense performances, though most of the students were at a low number sense level. In addition, the differences appeared significantly in relation to the variables of gender and duration of stay as an immigrant. A surprising result is that most students preferred number sense-based solutions as the basis for their answers. It can thus be concluded that the number sense performances of Syrian immigrant students are lower than expected and that future studies are needed not only to focus on teachers but also on teaching methods and materials in order to take immigrant problems under control and to come up with solutions with a view to overcome such challenges.

Evaluation of Recommended Learning Paths Using Process Mining and Log Skeletons: Conceptualization and Insight into an Online Mathematics Course

Evaluation of Recommended Learning Paths Using Process Mining and Log Skeletons: Conceptualization and Insight into an Online Mathematics Course

Reflections on the Teaching Reform of Basic Mathematics Courses in Higher Education in the New Era

Reflections on the Teaching Reform of Basic Mathematics Courses in Higher Education in the New Era

ЖОҒАРЫ МАТЕМАТИКА ЭЛЕМЕНТТЕРІН ОҚЫТУ КЕЗІНДЕ ОҚУШЫЛАРДЫҢ АНАЛИТИКАЛЫҚ-СИНТЕТИКАЛЫҚ ҚЫЗМЕТІН ДАМЫТУ

The relevance of the research work is related to the development by students of methods of mental activity, mental operations, the integrative compatibility of which manifests itself as analytical and synthetic activity, the development of a culture of thinking, increasing its productivity. Based on the research of educational psychologists, the development of analytical and synthetic activity in the educational process is considered as a unity of the processes of analysis and synchronization, as well as conscious mastery of the operations of analysis, synthesis and generalization, as an indicator of critical thinking. Mental operations and actions based on them reflect the procedural nature of thinking, since they act as generalized methods for solving cognitive tasks. The knowledge gained in the course of analytical and synthetic activities will be classified as qualitative. Students develop the skills of active and independent cognitive activity. Cognitive actions such as analysis, synthesis, comparison, generalization and abstraction form analytical and synthetic actions. When studying a mathematics course at a school of elements of higher mathematics, it is difficult to study the abstractness of the educational material, the complex logical structure in their definition. Many teachers did not consider the method of presentation to be correct, and promoted the principles of education and activity. The students wrote that the ready-made truth should be rejected, and the truth itself should be revealed in the process of solving applied problems. Solving problems of an applied orientation contributes to the formation and development of analytical and synthetic activities.

The application of interactive learning technologies to teach the mathematical analysis course for students of the specialties 014 Secondary education (information) and 122 Computer sciences

The application of interactive learning technologies to teach the mathematical analysis course for students of the specialties 014 Secondary education (information) and 122 Computer sciences

Navigating Mathematical Basics: A Primer for Deep Learning in Science.

We present a gentle introduction to elementary mathematical notation with the focus of communicating deep learning principles. This is a "math crash course" aimed at quickly enabling scientists with understanding of the building blocks used in many equations, formulas, and algorithms that describe deep learning. While this short presentation cannot replace solid mathematical knowledge that needs multiple courses and years to solidify, our aim is to allow nonmathematical readers to overcome hurdles of reading texts that also use such mathematical notation. We describe a few basic deep learning models using mathematical notation before we unpack the meaning of the notation. In particular, this text includes an informal introduction to summations, sets, functions, vectors, matrices, gradients, and a few more objects that are often used to describe deep learning. While this is a mathematical crash course, our presentation is kept in the context of deep learning and machine learning models including the sigmoid model, the softmax model, and fully connected feedforward deep neural networks. We also hint at basic mathematical objects appearing in neural networks for images and text data.

Enactment and impact analysis of active learning strategies utilized for the basic science courses in the evaluation of engineering students

The new era of teaching learning process demands more clearance of theoretical aspects utilizing visual strategies. Accordingly, this research focuses on usefulness of student team achievement division (STAD) and project based learning (PjBL) as active learning strategies for comprehensive understanding of basic science courses. The study revealed increased effectiveness of learning, encouraging equal participation, active engagement and supportive learning environment for better understanding of concepts in basic science courses. The usefulness of active learning strategies has been studied by conduction of STAD & PjBL activities for the Engineering Mathematics and Engineering Chemistry courses respectively. The appropriate evaluation and comparative analysis done before and after activity allows to elaborate the efficacy of visual strategies utilized for understanding theoretical concepts. Keywords—Active learning tools, Basic Science Courses, Evaluation Rubrics, Project Based Learning, Student Team Achievement Division

Relationship Between Self-Efficacy and Technology-Based Teaching Styles in Mathematics Education Among Pre-Service Teachers in UPSI

Self-efficacy is defined as a task-specific belief in a person’s potential and ability to master a skill or a task. As the technology is getting sophisticated, teachers are encouraged to apply the technology as teaching aid tool in the class. This research is done to investigate the relationship between the self-efficacy and the technology-based teaching styles of Mathematics pre-service teachers among Sultan Idris University of Education (UPSI) undergraduates. The research design used in this study is correlational study at where 148 AT14 Bachelor of Education (Mathematics) course and AT48 Bachelor of Science (Mathematics) with Education students are the sample. The statistical method used in this study is descriptive statistic which is mean and inferential statistics through Pearson’s correlation were used to study the relationship. The findings show that the level of self-efficacy and practice of technology-based teaching of pre-service teachers is significantly high. The results showed that there was a strong positive significant correlation between the self-efficacy and the technology-based teaching styles of those pre-service teachers (r=0.656, p=0.00, p<0.05). In conclusion, this study unequivocally demonstrates that UPSI’s pre-service teachers are well prepared to train themselves with higher self-esteem and hence applying technology-based teaching style while teaching Mathematics.

Creating and Performing Educational Gymnastics Using Computational Thinking Skills

Purpose: This study examined how physical education majors used computational thinking (CT) skills in a movement concept course. Method: Twenty-two physical education majors were tasked to create two gymnastics routines (i.e., algorithm design), analyze their routines (i.e., decomposition and abstraction), create and follow a personalized fitness plan (i.e., abstract), revise the routines (i.e., debugging), and perform the routines at the end of the semester. Data were analyzed as a single case study with embedded units using structural coding. Results: The participants demonstrated strengths with debugging and algorithm design; however, they struggled with decomposition and abstraction, which was congruent with previous research regarding these two concepts as the most difficult and important CT skills to master. Discussion/Conclusions: The findings underscore the value of CT skills in a non-STEM (i.e., science, technology, engineering, and mathematics) course, expending the instructional appropriateness to expose CT to undergraduate students with little to no interest or previous experience in STEM.

A Study on Optimizing Teaching Assessment Methods in Mathematical Modeling Courses by Combining Big Data Analytics Techniques

A Study on Optimizing Teaching Assessment Methods in Mathematical Modeling Courses by Combining Big Data Analytics Techniques

新工科背景下高等数学课程分类与分层体系研究

新工科背景下高等数学课程分类与分层体系研究

Exploring the Relevance of Advanced Mathematical Knowledge for Secondary-Level Instruction

The usefulness of advanced mathematics in teaching is referred to as its relevance for secondary-level mathematics instruction. This paper is based on research that explores teachers' views on the relevancy of advanced mathematics and their expectations from advanced mathematics courses for teacher preparation programs. Ten secondary-level mathematics teachers participated in this study. semi-structured interviews with open-ended questions and focus group discussions were utilised for data collection and thematic for data analysis. The finding indicates that advanced mathematics is relevant for developing mathematical proficiency, mathematical, and logical thinking, knowledge of mathematical context mathematical activities and increased problem-solving skills and professional competencies. Along with advanced mathematical knowledge, technological and research knowledge, and skills are expected from undergraduate teacher preparation courses. Therefore, it is suggested to incorporate the expected form of knowledge in the teacher preparation program.

Motivating Students to Learn Mathematics in the iGrowMaths Classroom: An Innovative Adaptive Classroom in Business Mathematics Education

The COVID-19 pandemic has exacerbated the inequalities in educational attainment and achievement, especially for students from disadvantaged socio-economic backgrounds. The teaching and learning process has become more complex as students are increasingly diverse in terms of prior knowledge and learning pace. Hence, this study proposes and designs the iGrowMaths Classroom, an innovative adaptive learning classroom for Business Mathematics course at a public polytechnic in Malaysia. The purpose is to create an adaptive learning environment that builds on the level of prior knowledge and learning pace in order to promote motivation and improve achievements in mathematics. The case study design was employed to investigate the effectiveness of iGrowMaths Classroom, with the adoption of a triangulation method that involved questionnaires, interviews, and formative assessment. The findings reveal that the iGrowMaths classroom is effective in fostering the students’ motivation towards learning mathematics and thereby enhancing the learning outcomes.

Needs Analysis and Design of Martapura Kingdom Numerical Teaching Materials based on Android with the help of I-Spring suite for Elementary School students in Samarinda City.

The advantage of the mobile learning concept is that learning can be accessed at any time because it is installed on a smartphone and can be applied to mathematics courses in ethno-mathematics-themed elementary schools. elementary school students in Samarinda City. This research is part of Research and Development (R&D) to develop teaching materials using the ADDIE (Analysis, Design, Development, Implementation, and Evaluation) model. These five stages the researcher uses the Analysis and Design stage. Data collection used a questionnaire filled out by elementary school students and interviews with teachers. The data analysis technique used in this study is a qualitative descriptive data analysis technique and a quantitative descriptive data analysis technique. The research results obtained the results of the stages of needs analysis, from stakeholders and development design. Based on the needs analysis conducted, it was found that 51.6% did not know the oldest kingdom in the archipelago, 19% of learning media still used PowerPoint, 19% visual aids, 20% videos. Regarding gadget or cellphone ownership, 100% of students have their own cellphone and still use it to play online games. The results of the subsequent questionnaire 100% did not know the figure of Raja Mulawarman, 57.1% of students stated that they had never been taught mathematics related to cultural history (ethnomatematics). Teacher interviews in the mathematics learning process tend to use power point and have never used android media. The teacher has never delivered ethnomathematics-based mathematics material. The results of the design stage, the researcher designed math teaching materials (island numbers) based on android applications.

Exploring Students’ Achievements in Differential Equations Courses and Their Feelings Towards Mathematics Courses

Differential equations are a fundamental area of mathematics that is widely used in various fields, including physics, engineering, economics, and more. However, many students find this course to be particularly challenging and struggle to achieve success in differential equations courses. Therefore, this study aims to investigate the relationship between students' achievements in midterm and final exams differential equations courses and their feelings towards mathematics courses, to provide a more comprehensive understanding of the factors that contribute to success in this challenging course. The results of this study indicate a positive correlation between students' achievements in differential equations courses and their feelings toward mathematics. Male students performed slightly better than female students for marks above 50. Additionally, students who enjoyed all the mathematics courses had higher grades in differential equations courses, which was statistically significant. These findings also highlight the importance of midterm exams as preparation before seating for the final exam of differential equations.

Relationships of Abstraction and Application Complexity in the Attainment between Mathematics and Electrical Engineering Modules in Diploma Courses of South Africa

In South Africa, universities are under pressure to meet increasing targets for student enrolment in engineering disciplines and fields. This has resulted in many students being enrolled in engineering programs without possessing the minimum required mathematical skills and understanding to tackle the challenging engineering disciplines. Hence, the engineering disciplines have a high student attrition and failure rate. This study aimed to evaluate the complex relationship of abstraction and application between mathematics attainment and principles of electrical engineering attainment by the students enrolled in diploma courses in technical universities of South Africa. A blend of quantitative and qualitative data was used. Legitimation code theory (LCT) was used to determine the complexity of higher learning levels. The relationships between six core courses in the Electrical Engineering curriculum were investigated to analyze the knowledge building from mathematics modules to principles of electrical engineering modules. The problem-solving, analytics, and abstract mathematical skills developed in these modules impact the overall progression into principles of electrical engineering courses at different levels for diverse students. The research examines the theoretical foundation, student performance, and practical application of mathematical ideas in electrical engineering using curriculum documents, student academic records, and interviews with electrical engineering lecturers. The study found a weak correlation between the two modules and examined how resources, cultural attitudes, and pedagogy affect student achievement. The results indicate an unexpected negative and fragile correlation between the lower mathematics and engineering modules at high levels. The LCT analysis showed the disconnect between the mathematics courses and the principles of electrical engineering in both the level of abstraction used in the studies and the extent of application principles taught.

Analyzing the difficulty level in learning mathematics online using a quantile regression approach

Online learning is a difficult type of educational process due to its limitations, particularly in college mathematics courses. The essential aim of this article is to elucidate the students' difficulty level in learning mathematics amid online learning and predict its statistically significant influencing factors. The data used in this study is secondary from a paper in the mathematics education literature on the form of cross-sectional. The data were summarized employing some descriptive measures and regression modeling as an inference. The result of the study showed that, on average, students are facing "difficulty" in learning their mathematics lessons during distance learning due to some problems. The quantile regression revealed that younger and female students are experiencing higher levels of difficulty. Plus, students who spent more money on the internet are facing higher difficulty in learning. In addition, a not conducive learning environment and social distractions are predictors of difficulty in learning. Conclusively, the difficulty in learning mathematics which adversely affects their performance is due to the distractions and problems in the learning environment, low coping mechanisms, and unprecedented educational process in the form of online setup. Hence, the study suggested that teachers must be flexible with students and provide digital simulations of mathematical problems, and use interactive models in their classes.