We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Adjusting the Calculus I curriculum by putting modelling and differential equations literally at its centre leads to a better-organised and better-motivated course. The biggest change is including a section on "qualitative" and "numerical" solutions to ordinary differential equations between the customary sections on…

Epidemiological models have enhanced relevance because of the COVID-19 pandemic. In this note, we emphasize visual tools that can be part of a learning module geared to teaching the SIR epidemiological model, suitable for advanced undergraduates or beginning graduate students in disciplines where the level of prior mathematical knowledge of…

The state mandated College Credit Plus (CCP) program in Ohio has grown significantly for several years. Many general education core courses are being offered to high school students, on-premises or in a partnering university. In mathematics, students can complete pre-calculus courses while in high school. In forming the partnerships with high…

The process of turning a doctoral student into an independent researcher is usually guided by a professor. In this work, the supervisor-supervisee relationship is represented by a scheme inspired by Michaelis-Menten kinetics, which has been used to determine the rate of enzyme-catalysed reactions. Here, the time evolution of the number of…

In this paper, we explain changes made in an introductory Real Analysis classroom that address common challenges and that may allow for all levels of students to meet a high standard of learning and written work. We aim for this goal by fusing elements of a hybrid course with scaffolded collaborative work to improve student learning. The hybrid…

The paper introduces the notion of collateral creativity as an unintended outcome of the appropriate use of technology, both physical and digital, in the teaching of mathematics. The notion is motivated by Dewey's conceptual framework of collateral learning which enables one gaining knowledge beyond the intent of the traditional curriculum.…

Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

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…

In March 2020, COVID-19 restrictions required our university courses to be offered in online mode only. This quick transition meant that lecturers were suddenly tasked with adapting their classroom-based teaching approaches and materials to the online space. For mathematics teacher educators (MTEs), whose on-campus classes were characterized by…

The COVID-19 pandemic meant a move to emergency remote teaching for many university students around March 2020. Two months later, we undertook an online survey to ascertain experiences of university mathematics lecturers. We received responses from 257 mathematics lecturers from 29 countries. In this paper, we consider their responses when asked…

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the…

The following article deals with the possibility of discovering several parameters of the picture when using Google Maps images, e.g. time and date of taking the image. This is possible with all pictures in which buildings, trees, poles ('objects') can be seen with their shadows. In some cases, one can find -- with a bit of luck -- an aircraft…

In Peru, national assessments repeatedly rank Indigenous mathematics students as the lowest performing across the entirety of Latin America and South America. Whereas lack of financial resources often predicts low measures, the history of educational practice teaches us that students' poverty need not predict their educational outcomes -- creative…

We introduce the concept of the "sequence of the ratios of convex quadrilaterals," identify some properties of these sequences and use them to provide new characterizations for some classic quadrilateral families. The research involves aspects of geometry, arithmetic and mathematical analysis, which converge to produce the results.