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Clark, Thomas J. – PRIMUS, 2019

The first day of many mathematics classes is filled with the formalities of the syllabus and a lecture introduction to the course content. Here, an alternative is presented where modeling is placed as the centerpiece to orient students to the work of differential equations; namely, to capture as beautifully and compactly as possible through the…

Descriptors: Equations (Mathematics), Calculus, Mathematical Models, College Mathematics

Bissell, J. J. – International Journal of Mathematical Education in Science and Technology, 2021

The ability to distinguish between exact and inexact differentials is an important part of solving first-order differential equations of the form Adx + Bdy = 0, where A(x,y) [not equal to] 0 and B(x,y) [not equal to] 0 are functions of x and y However, although most undergraduate textbooks motivate the necessary condition for exactness, i.e. the…

Descriptors: Validity, Mathematical Logic, Equations (Mathematics), Calculus

Hyland, Diarmaid; van Kampen, Paul; Nolan, Brien – International Journal of Mathematical Education in Science and Technology, 2021

This paper reports on an intervention as part of which direction fields were introduced to students learning ordinary differential equations (ODEs). The intervention was designed and implemented to address issues with students' conceptions of the solutions of ODEs. These were identified by a diagnostic survey and through a review of the…

Descriptors: Mathematics Instruction, Teaching Methods, Student Attitudes, Intervention

Henriksen, Mel – PRIMUS, 2021

Reflections are presented on the first time flipping of an introductory Ordinary Differential Equations course. Assessment results, student motivation, and student attitudes are compared between flipped and traditional learning pedagogies in this course over two terms at a small technical university in the northeast United States. Assessments and…

Descriptors: Reflection, Flipped Classroom, Calculus, Mathematics Instruction

Tu, Tao; Li, Chuan-Feng; Zhou, Zong-Quan; Guo, Guang-Can – Physical Review Physics Education Research, 2020

Upper-division physics students solve partial differential equations in various contexts in quantum mechanics courses. Separation of variables is a standard technique to solve these equations. We investigated students' solutions to midterm exam questions and utilized think-aloud interviews. We also applied a framework that organizes students'…

Descriptors: Science Instruction, Physics, Equations (Mathematics), Quantum Mechanics

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, Robin claimed to introduce clever innovations ('wrinkles') into the mathematics education literature concerning the solutions, and methods of solution, to differential equations. In particular, Robin formulated an iterative scheme in the form of a single integral representation. These ideas were applied to a range of examples involving…

Descriptors: Problem Solving, Equations (Mathematics), Mathematics Education, Mathematics Instruction

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2019

Recently, Wilmer III and Costa introduced a method into the mathematics education research literature which they employed to construct solutions to certain classes of ordinary differential equations. In this article, we build on their ideas in the following ways. We establish a link between their approach and the method of successive…

Descriptors: Mathematics Instruction, Problem Solving, Equations (Mathematics), Teaching Methods

Bibi, Aisha; Zamri, Sharifah Norul Akmar Syed; Abedalaziz, Nabeel Abdallah Mohammad; Ahmad, Mushtaq; Dad, Hukam – Malaysian Online Journal of Educational Sciences, 2018

In this study, role of context familiarity in students' differential equations (DEs) solving was explored at pre-university level. An assessment test containing three self-developed DEs tasks were distributed among 430 students, studying in intercolleges. Collected responses were analyzed using a scoring rubric containing three main stages…

Descriptors: Foreign Countries, Mathematics Instruction, Calculus, Problem Solving

Tisdell, Christopher C. – Teaching Mathematics and Its Applications, 2019

In this work we critically examine a mnemonic designed for the pedagogy of first-order ordinary differential equations. The particular mnemonic takes the form of the SHIELDS acronym. We perform a critical analysis on mnemonics, outlining some of their benefits and limitations from the literature. As a result, we propose a general mnemonic model…

Descriptors: Calculus, Mnemonics, Mathematics Instruction, College Mathematics

Winkel, Brian J. – International Journal of Mathematical Education in Science and Technology, 2012

This article offers modelling opportunities in which the phenomena of the spread of disease, perception of changing mass, growth of technology, and dissemination of information can be described by one differential equation--the logistic differential equation. It presents two simulation activities for students to generate real data, as well as…

Descriptors: Mathematical Models, Calculus, Diseases, Class Activities

Tisdell, C. C. – International Journal of Mathematical Education in Science and Technology, 2017

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Descriptors: Calculus, Mathematics Instruction, Mathematical Models, Biology

Starling, James K.; Povich, Timothy J.; Findlay, Michael – PRIMUS, 2016

We describe a modeling project designed for an ordinary differential equations (ODEs) course using first-order and systems of first-order differential equations to model the fermentation process in beer. The project aims to expose the students to the modeling process by creating and solving a mathematical model and effectively communicating their…

Descriptors: Undergraduate Study, College Mathematics, Mathematics Instruction, Equations (Mathematics)

Khotimah, Rita Pramujiyanti; Masduki – Online Submission, 2016

Differential equations is a branch of mathematics which is closely related to mathematical modeling that arises in real-world problems. Problem solving ability is an essential component to solve contextual problem of differential equations properly. The purposes of this study are to describe contextual teaching and learning (CTL) model in…

Descriptors: Calculus, Mathematics Instruction, Problem Solving, Teacher Improvement

DeDieu, Lauren; Lovric, Miroslav – PRIMUS, 2018

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which…

Descriptors: Mathematics Instruction, College Mathematics, Undergraduate Study, Equations (Mathematics)

Tisdell, Christopher C. – International Journal of Mathematical Education in Science and Technology, 2017

For over 50 years, the learning of teaching of "a priori" bounds on solutions to linear differential equations has involved a Euclidean approach to measuring the size of a solution. While the Euclidean approach to "a priori" bounds on solutions is somewhat manageable in the learning and teaching of the proofs involving…

Descriptors: Mathematics Instruction, Calculus, Geometry, Geometric Concepts