A straightforward experimental set-up, requiring a two-liter bottle, a ruler and a stopwatch, is used to provide data appropriate for modelling with Torricelli's Law in the simplest case, and a more sophisticated differential equation when losses are taken into account and a pipe extension is considered. With only an exit hole included in the…

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…

Mathematical modelling has garnered national and international interest due to its importance. Mathematical modelling can develop students' mathematical understandings, teamwork and communication practices. The ability for teachers to select appropriate mathematical modelling tasks is important to ensure the benefits listed for students are…

This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

In this paper, I discuss the potential transformations to teach K-12 geometry topics with the technology of 3D Pens, which enabled 3D models to be created instantly via one's moving hands. I draw on an example of using constructionist learning activities with 3D Pens to teach young children, 'how tall is the triangle?'

In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed. This is due to the impossibility of expressing, in terms of simple elementary functions, the solutions of the nonlinear differential equation (NLDE) that models the pendulum, which is why the authors usually choose the linearized…

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was…

Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Over the past decade, many researchers have discussed the effectiveness of clickers and their potential to change the way we teach and interact with students. Although most of the literature revolves around elementary usage of clickers, the deeper questions of how to integrate this technology into teaching are largely unanswered. In this paper, we…

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…

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

In keeping with the national mandate of increasing graduates in the sciences in South Africa, a concerted effort in improving the first year experience becomes imperative. First year mathematics courses commonly provide the base knowledge necessary for progression in different degree programmes at university. Success in mathematics courses…

To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…