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Alberto Gandolfi – International Journal of Artificial Intelligence in Education, 2025
In this paper, we initially investigate the capabilities of GPT-3 5 and GPT-4 in solving college-level calculus problems, an essential segment of mathematics that remains under-explored so far. Although improving upon earlier versions, GPT-4 attains approximately 65% accuracy for standard problems and decreases to 20% for competition-like…
Descriptors: Artificial Intelligence, Reliability, Problem Solving, Mathematics Skills
Shiv Krishna Madi Reddy; Meng Guo; Long Cai; Ralph E. White – Chemical Engineering Education, 2024
A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…
Descriptors: Chemical Engineering, Engineering Education, Computer Software, Mathematics Instruction
Amenda N. Chow; Peter D. Harrington; Fok-Shuen Leung – Teaching Mathematics and Its Applications, 2024
Physical experiments in classrooms have many benefits for student learning, including increased student interest, participation and knowledge retention. While experiments are common in engineering and physics classes, they are seldom used in first-year calculus, where the focus is on solving problems analytically and, occasionally, numerically. In…
Descriptors: Mathematics Instruction, Calculus, Computer Software, Programming
Jaleh Rezaei; Nasim Asghary – International Journal of Mathematical Education in Science and Technology, 2025
Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect…
Descriptors: Calculus, Mathematical Models, Mathematics Instruction, Problem Solving
Manuel Santos-Trigo; Matías Camacho-Machín; Fernando Barrera-Mora – ZDM: Mathematics Education, 2024
The aim of this paper is to review recently calculus curriculum reforms and research studies that document what types of understanding students develop in their precalculus courses. We argue that it is important to characterize what difficulties students experience to solve tasks that include the use of foundational calculus concepts and to look…
Descriptors: Mathematics Instruction, Calculus, Barriers, Problem Solving
Robert J. Fisher – Chemical Engineering Education, 2025
Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…
Descriptors: Chemical Engineering, Mathematics, Problem Solving, Skill Development
Eko Andy Purnomo; Y. L. Sukestiyarno; Iwan Junaedi; Arief Agoestanto – Mathematics Teaching Research Journal, 2024
Students are required to have the ability to implement mathematics in solving everyday life problems. A good solving process will produce an excellent solving ability. The existing problem-solving stages cannot be used in solving problems with the Higher Order Thinking Skills (HOTS) category. The aims of this research are 1) to know students'…
Descriptors: Mathematics Instruction, Problem Solving, Calculus, Thinking Skills
Sunil Dehipawala; Tak Cheung – International Society for Technology, Education, and Science, 2024
The Physics One Mechanics in a community college syllabus usually allocates more time to cover the topics in kinematics, dynamics, energy, momentum, and rotation; with relatively less time for the topics of fluid mechanics and heat diffusion in the creation of a knowledge gap for those students deciding on mechanical and chemical engineering…
Descriptors: Community College Students, Student Projects, Physics, College Science
Fereshteh Zeynivandnezhad; Ramón Emilio Fernández; Yudariah binti Mohammad Yusof; Zaleha binti Ismail – International Electronic Journal of Mathematics Education, 2025
This study explores the effects of a computer algebra system on students' mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students' capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was…
Descriptors: Algebra, Computer Uses in Education, Mathematical Logic, Thinking Skills
Glenn Ledder; Stefano Manzoni – International Journal of Mathematical Education in Science and Technology, 2024
Decomposition of organic matter controls the flow of carbon and nutrients in terrestrial and aquatic ecosystems. Several kinetic laws have been proposed to describe decomposition rates, but they neglect adaptation of the microbial decomposer to environmental conditions. Here we formalise decomposition as an optimal control problem by assuming that…
Descriptors: Microbiology, Calculus, Undergraduate Students, Barriers
The Structure of Students' Mathematical Errors in Solving Calculus Problems Based on Cognitive Style
In Hi. Abdullah; Hery Suharna; Mustafa AH. Ruhama – International Education Studies, 2024
The understanding mathematical concept is an error that often occurs in classroom learning among students when solving mathematical problems. The most difficult part for students is solving problems, because it requires numeracy skills, high concept mastery, as well as the ability to use good language, and so on so that students don't make any…
Descriptors: Error Patterns, Problem Solving, Cognitive Style, Calculus
Thembinkosi Peter Mkhatshwa – International Journal of Mathematical Education in Science and Technology, 2024
This article reports on a qualitative investigation into students' thinking about a differential equations problem posing task; i.e. an initial value problem. Analysis of written and verbal responses to the task indicate that only four of the 34 students who participated in the study were successful in posing problems. Furthermore, only one of the…
Descriptors: Mathematics Skills, Equations (Mathematics), Abstract Reasoning, Thinking Skills
Thembinkosi Peter Mkhatshwa – International Journal of Mathematical Education in Science and Technology, 2024
Contributing to research on undergraduate students' thinking about problem solving tasks, the present study reports on students' reasoning about two initial-value problems i.e. first-order linear ordinary differential equations with initial conditions. A qualitative analysis of task-based interviews and work written by 34 students revealed that…
Descriptors: Problem Solving, Undergraduate Students, Thinking Skills, Student Attitudes
Elien Sijmkens; Nico Scheerlinck; Mieke De Cock; Johan Deprez – International Journal of Mathematical Education in Science and Technology, 2024
Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…
Descriptors: Teaching Methods, Mathematics Instruction, Mathematical Concepts, Comparative Analysis
Peter Klosterman – Australian Mathematics Education Journal, 2024
In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.
Descriptors: Foreign Countries, Calculus, Mathematics Instruction, Problem Solving
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