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Lie Group Method for Constructing Integrating Factors of First-Order Ordinary Differential Equations
Feng, Yuqiang; Yu, Jicheng – International Journal of Mathematical Education in Science and Technology, 2023
This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…
Descriptors: Equations (Mathematics), Mathematical Concepts, Problem Solving, Algebra
Ismael Cabero; Carl Winsløw – International Journal of Mathematical Education in Science and Technology, 2025
The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…
Descriptors: Mathematics Instruction, Mathematical Models, Teaching Methods, Secondary School Mathematics
Richard F. Melka; Hashim A. Yousif – International Journal of Mathematical Education in Science and Technology, 2023
In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…
Descriptors: Mathematical Concepts, Mathematical Applications, Problem Solving, Computation
Fukushima, Takumi – International Journal of Mathematical Education in Science and Technology, 2023
This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…
Descriptors: Mathematical Models, Mathematics Instruction, Teaching Methods, Problem Solving
Brian John Winkel – International Journal of Mathematical Education in Science and Technology, 2024
We present a complete, soup to nuts, modeling activity of a falling column of water. Many colleagues have used this material in teaching applications of first order separable differential equations. We describe how the material can be presented with students collecting their own data from online videos. One can then either offer the differential…
Descriptors: Calculus, Learner Engagement, Video Technology, Mathematical Concepts
Alonso Ogueda-Oliva; Padmanabhan Seshaiyer – International Journal of Mathematical Education in Science and Technology, 2024
In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…
Descriptors: Mathematical Models, Equations (Mathematics), Mathematics Instruction, Learning Modules
Ala' J. Alnaser; Justin Hoffmeier – International Journal of Mathematical Education in Science and Technology, 2024
Differential equations are widely used tools for modelling the world around us, making a course in differential equations a natural place for students to connect concrete mathematical applications to abstract concepts. Since students grasp the concepts better by applying them, introducing differential equations through modelling becomes essential.…
Descriptors: Mathematics Instruction, Mathematical Models, Advanced Courses, Mathematical Concepts
Paola Iannone; Athina Thoma – International Journal of Mathematical Education in Science and Technology, 2024
Programming is becoming increasingly common in mathematics degrees as it is a desirable skill for new graduates. However, research shows that its use is mostly restricted to computational or modelling tasks. This paper reports a study on students' perceptions of and difficulties with Lean, an interactive theorem prover introduced as part of a…
Descriptors: Programming, Mathematics Instruction, Computer Science Education, Student Attitudes
Kertil, Mahmut; Küpcü, Ali Riza – International Journal of Mathematical Education in Science and Technology, 2021
This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…
Descriptors: Preservice Teachers, Mathematics Education, Elementary Education, Secondary Education
Rodríguez-Nieto, Camilo Andrés; Rodríguez-Vásquez, Flor Monserrat; Moll, Vicenç Font – International Journal of Mathematical Education in Science and Technology, 2022
The goal of this research is to make a theoretical reflection about connections that contributes to the development of the model for mathematical connections originally proposed by Businskas, and extended with the contributions of other researchers. This model is used in the most relevant investigations in this field. As a consequence of the…
Descriptors: Mathematics Instruction, Teaching Methods, Reflection, Mathematical Models
Abernethy, Gavin M. – International Journal of Mathematical Education in Science and Technology, 2018
A simple discrete-time two-dimensional dynamical system is constructed and analyzed numerically, with modelling motivations drawn from the zombie virus of popular horror fiction, and with suggestions for further exercises or extensions suitable for an introductory undergraduate course.
Descriptors: Mathematical Models, Mathematics, Equations (Mathematics), Mathematical Concepts
Olteanu, Constanta – International Journal of Mathematical Education in Science and Technology, 2018
This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…
Descriptors: Arithmetic, Mathematics Instruction, Mathematical Models, Problem Solving
Cortez, L. A. B.; de Oliveira, E. Capelas – International Journal of Mathematical Education in Science and Technology, 2017
Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…
Descriptors: Thermodynamics, Calculus, Mathematical Concepts, Mathematical Models
More, M. – International Journal of Mathematical Education in Science and Technology, 2018
We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…
Descriptors: Mathematics Education, Engineering Education, Mathematical Models, Competition
Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas – International Journal of Mathematical Education in Science and Technology, 2017
The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…
Descriptors: Problem Solving, Mathematics, Physics, Foreign Countries