This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

Some children enjoy playing with the spring-loaded, plastic toy cannon that accompanies many model pirate ships. This cannon pivots in such a way that it can be fired at any angle from about -15 degrees to 195 degrees when viewed from a position directly in front of the cannon. The spring provides each fired projectile with approximately the same…

Using spreadsheets such as Microsoft Excel for building crop models and running simulations can be beneficial. Excel is easy to use, powerful, and versatile, and it requires the least proficiency in computer programming compared to other programming platforms. Excel, however, has several weaknesses: it does not directly support loops for iterative…

Introduction: When talking about knowledge itself, the way it is perceived, understood, learnt, remembered and thought, we are talking about metacognition. It is considered a crucial aspect in the development of reflective thought, autonomous learning and construction of knowledge. There exists several tools in literature to measure metacognitive…

One goal of physics instruction is to have students learn to make physical meaning of specific mathematical expressions, concepts, and procedures in different physical settings. As part of research investigating student learning in statistical physics, we are developing curriculum materials that guide students through a derivation of the Boltzmann…

In short, this is a "master class". The learning and teaching of mathematics can be revolutionised with the creative use of dynamic software is an oft quoted mantra. Here, this mantra is exemplified through the documented experiences of using Autograph to enliven, to extend, and to foster the understanding of differentiation and integration. The…

Calculus is an important tool for building mathematical models of the world around us and is thus used in a variety of disciplines, such as physics and engineering. These disciplines rely on calculus courses to provide the mathematical foundation needed for success in their courses. Unfortunately, due to the basal conceptions of what it means to…

Mathematics teachers constantly encourage their students to think independently. The study of integration in calculus provides an excellent opportunity to encourage inventive investigation. In contrast to differentiation, which is predominately mechanical, integration is a more creative process. One such possibility is offered by the study of the…

As noted in "Beyond Crossroads" (AMATYC, 2006), for today's students, learning mathematics is participatory and depends on the active involvement of students (p. 53). The National Council of Teachers of Mathematics shares the point of view that the teaching and learning of mathematics should include giving students ample opportunity to think…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

Research on writing in mathematics has shown that students learn more effectively in an environment that promotes this skill and that writing is most beneficial when it is directed at the learning aspect. Writing, however, necessitates proficiency on the part of the students that may not have been developed at earlier learning stages. Research has…

In a previous study, the onto-semiotic approach was employed to analyse the mathematical notion of different coordinate systems, as well as some situations and university students' actions related to these coordinate systems in the context of multivariate calculus. This study approaches different coordinate systems through the process of change of…

There has been a national call to transition away from the traditional, passive, lecture-based model of STEM education towards one that facilitates learning through active engagement and problem solving. This mixed-methods research study examines the impact of a supplemental Peer-Led Team Learning (PLTL) program on knowledge and skill acquisition…

The Common Core State Standards (CCSS) provide teachers with the expectations and requirements that are meant to prepare K-12 students for college and the workforce (CCSSI 2010b). The Common Core State Standards for Mathematical Practice (SMPs) emphasize the development of skills and conceptual understanding for students to become proficient in…

This paper presents a method for allowing calculus taught by mathematics faculty to be augmented with real-world engineering problems. The method relies on modules to deliver the problems and required background information. Students complete the modules outside of class and discuss them in mentor-led sessions. To encourage participation, students…