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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
Abboud, Elias – International Journal of Mathematical Education in Science and Technology, 2023
In this article, we consider certain minimization problems. If d[subscript 1], d[subscript 2] and d[subscript 3] are the distances of a boundary or inner point to the sides of a given triangle, find the point which minimizes d[subscript 1][superscript n] + d[subscript 2][superscript n] + d[subscript 3][superscript n] for positive integer n. These…
Descriptors: Computer Software, Mathematics Instruction, Geometry, Calculus
de Sá Neto, Olimpio Pereira; Aquino Sousa, Herbert José; da Silva, Rafael Ferreira – Physics Teacher, 2022
We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.
Descriptors: Problem Solving, Science Instruction, Teaching Methods, Physics
Vorob'ev, Evgenii M. – International Journal of Mathematical Education in Science and Technology, 2023
This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…
Descriptors: Teaching Methods, Mathematics Instruction, Internet, Calculators
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
Alves, Alexandre – International Journal of Mathematical Education in Science and Technology, 2023
Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Error Patterns
Dae S. Hong – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
This study explores opportunities to learn definite integrals in three widely used textbooks in the U.S. Definitions, worked examples, and exercise problems were coded using research-based cognitive resources in definite integrals. The results show that limited opportunities for students to explore multiplicative relationship between two…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Mathematical Concepts
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
Dae S. Hong; Jae Ki Lee – International Journal of Mathematical Education in Science and Technology, 2024
This study examined college calculus instructors' preferences in solving two calculus tasks to examine college calculus instructors' use of important cognitive roots in understanding derivatives of function. Our results showed that only one instructor consistently uses cognitive roots while other instructors either focus on algebraic methods or…
Descriptors: College Mathematics, Calculus, College Faculty, Teaching Methods
Wangberg, Aaron; Gire, Elizabeth; Dray, Tevian – Teaching Mathematics and Its Applications, 2022
Students need a robust understanding of the derivative for upper-division mathematics and science courses, including thinking about derivatives as ratios of small changes in multivariable and vector contexts. In "Raising Calculus to the Surface" activities, multivariable calculus students collaboratively discover properties of…
Descriptors: Mathematics Instruction, Teaching Methods, Calculus, Introductory Courses
Gencev, Marian; Šalounová, Dana – International Journal of Mathematical Education in Science and Technology, 2023
The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…
Descriptors: Teaching Methods, Mathematics Instruction, Problem Solving, Geometric Concepts
Richard Velasco; Dae S. Hong – North American Chapter of the International Group for the Psychology of Mathematics Education, 2023
In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…
Descriptors: Mathematics Education, Mathematical Concepts, Mathematics Skills, Mathematics Instruction
Saba Gerami – ProQuest LLC, 2024
In this dissertation I explore instructors' work with instructional tasks as they plan to introduce various representations of derivatives. Drawing on the notion of "framing" from sociology, I adopt a situative lens to study calculus instructors' planning of instructional tasks. I rely on Herbst and Chazan's (2012) notion of…
Descriptors: Calculus, Mathematics Teachers, Mathematics Instruction, Teaching Methods
Hong, Dae S. – International Journal of Science and Mathematics Education, 2023
We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…
Descriptors: Calculus, Mathematics Instruction, Mathematics Teachers, Genetics