Promoting engineering students’ learning with mathematical modelling projects

Mathematics constitutes a key component in engineering education. Engineering students are traditionally offered a number of mathematics courses which provide the knowledge needed at the workplace. Unfortunately, many students perceive mathematics as a discipline that teaches mostly procedures not relevant to their future careers and often view it as one of the main obstacles on their way to an engineering degree. In this paper, we discuss how introducing university students in a standard Differential Equations course to mathematical modelling (MM), a powerful strategy for solving real-life problems, contributes to the development of their mathematical competencies, motivates their interest to mathematics, promotes the use of advanced mathematical thinking, methods of applied mathematics, and digital computational tools

Promoting conceptual understanding of differential equations through inqiury tasks

Courses in Differential Equations (DEs) have been an important part of engineering education for decades. However, students experience difficulties with the understanding of main concepts including differential equation itself and diverse types of solutions (general, particular, stationary). In this paper, we discuss how the work on non-routine problems on the Existence and Uniqueness Theorems (EUTs) helps students to make sense of DEs and their solutions thus contributing to the development of advanced mathematical thinking

Dynamics of a single species in a fluctuating environment under periodic yield harvesting

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sanchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameter sigma associated with the intensity of harvesting is explored. As sigma grows, the number of periodic solutions drops from two to zero. We provide bounds for the bifurcation parameter whose value in practice can be efficiently approximated numerically

On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations

By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument, our criteria improve a number of related results reported in the literature.publishedVersio

Development of students' mathematical discourse through individual and group work with nonstandard problems on existence and uniqueness theorem.

Research shows that students’ learning is affected by the types of tasks. We explore how the use of nonstandard problems influences understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students. The focus is on the development of students’ mathematical discourse during the individual and group work with nonstandard problems. We present the evidence indicating that students developed new mathematical routines gaining a deeper understanding of EUTs and appreciated the experience

Individual and group work with nonstandard problems in an ordinary differential equations course for engineering students

We explore understanding of the Existence and Uniqueness Theorems (EUTs) by a group of engineering students working on nonstandard problems. Students presented three sets of solutions: individual solutions produced in the first tutorial, individual solutions submitted as a homework, and solutions submitted after the discussion with peers in small groups during the second tutorial. The focus of the study is on the role of individual and group work with nonstandard problems. The results show that students gained a deeper understanding of EUTs and appreciated the experience

Oscillation Theorems for Second-Order Nonlinear Neutral Delay Differential Equations

We analyze the oscillatory behavior of solutions to a class of second-order nonlinear neutral delay differential equations. Our theorems improve a number of related results reported in the literature

Advancing engineering students’ conceptual understanding through puzzle-based learning: a case study with exact differential equations

Current views on the teaching of differential equations (DEs) are shifting towards the use of graphical and numerical methods. Motivated by recent research suggesting that puzzle-based learning (PzBL) can improve the teaching and learning of STEM subjects and by the lack of relevant studies for DEs, we designed two tasks—sophism and paradox—to explore undergraduate engineering students’ conceptual understanding of a classical topic—exact DEs—and to analyse the process of meaning-making during collaborative learning in small groups. One hundred and thirty-five undergraduate engineering students from a public university in Iran participated. In response to recent research signalling the tendency of the students to procedural learning of DEs, we analyse how the students in our study engaged in small group work on puzzle tasks, gaining a more conceptual understanding of exact DEs and acknowledging the efficiency of PzBL in their responses to a questionnaire and in interviews.publishedVersionPaid Open Acces

A New Tool for the Assessment of the Development of Students’ Mathematical Competencies

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