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Teaching Mathematics and its Applications: An International Journal of the IMA Current Issue

Published: Fri, 09 Sep 2016 00:00:00 GMT

Last Build Date: Tue, 03 Oct 2017 12:58:27 GMT


How well do engineering students retain core mathematical knowledge after a series of high threshold online mathematics tests?


In the Dublin Institute of Technology, high threshold core skills assessments are run in mathematics for third-year engineering students. Such tests require students to reach a threshold of 90% on a multiple choice test based on a randomized question bank. The material covered by the test consists of the more important aspects of undergraduate engineering mathematics covered in the first 2 years of the Honours degree programme and the 3 years of the Ordinary degree programme. Students are allowed to resit the assessment as frequently as required until they pass. In order to measure the effectiveness of such an exercise, a follow-up assessment was given to students on their first day of their fourth year. A comparison is made with the level of basic mathematical knowledge of these students on their first day in third year, exactly a year previously. For the majority of the students we see a significant decrease in the performance of the students from the beginning of third year to the beginning of fourth year. In addition, students were surveyed for their perception of both how much knowledge had been retained and how effective they felt that this approach had been. Overall the students felt positive about the process of online testing and that it would make it easier for them to regain this information in the future.

The construction of a square through multiple approaches to foster learners’ mathematical thinking


The task of constructing a square is used to argue that looking for and pursuing several solution routes is a powerful principle to identify and analyse properties of mathematical objects, to understand problem statements and to engage in mathematical thinking activities. Developing mathematical understanding requires that students delve into mathematical objects’ properties to formulate questions as a way to identify and explore mathematical relationships that eventually are supported through visual and geometric arguments. In this process, the use of a Dynamic Geometry System, such as GeoGebra, becomes important to represent and examine dynamically some attributes (area, lengths and perimeter) and properties of embedded objects. As a result, some of GeoGebra’s affordances (dragging or moving objects orderly, finding loci, quantifying parameters, using sliders, etc.) become important in detecting invariants and patterns and ways to validate mathematical relationships.

Gaining modelling and mathematical experience by constructing virtual sensory systems in maze-videogames*


This work is part of a research project that aims to enhance engineering students’ learning of how to apply mathematics in modelling activities of real-world situations, through the construction (design and programming) of videogames. We want also for students to relate their mathematical knowledge with other disciplines (e.g., physics, computer science or electronics) and adapt it as necessary, as is usually part of the practice of an engineer. The design of the activities, and their implementation, is framed in the constructionism educational paradigm, which considers that learning is facilitated through engagement in the construction of external objects. Each activity integrates three aspects: the mathematization of a physical or digital system, programming simulations and the construction of a videogame. Students work both individually and collaboratively, and record their progress in a logbook. Here, we present the work carried out by six university engineering students during an activity that required building a videogame where a virtual mobile robot has to navigate a maze; this required the modelling of combinational logic circuits, which in turn needed Boolean algebra and the simplification of logic equations. The programming of the videogame involved brainstorming and experimentation in a meaningful and motivating activity, where students were able to apply the theoretical mathematical knowledge in the design of the real-world project (in this case of a digital systems model). We found that students gained insights and expertise on how to apply their interdisciplinary knowledge and skills in different contexts related to the practice of engineering, within the videogame design (e.g., they were able to apply their mathematical and technical skills for developing functional simulations of mobile robots, and even include aesthetic and narrative features).

Emphasizing visualization and physical applications in the study of eigenvectors and eigenvalues


This article presents a teaching proposal that emphasizes on visualization and physical applications in the study of eigenvectors and eigenvalues. More concretely, these concepts were introduced using the notion of the moment of inertia of a rigid body and the GeoGebra software. The proposal was designed after observing architecture students difficulty grasping the meaning of eigenvectors and eigenvalues from a geometric point of view. The aim of this research is to determine whether the designed teaching proposal allows students to give a geometrical meaning to the concepts of eigenvectors and eigenvalues. To this end, the responses given to a test by the students attending the teaching proposal and others attending a traditional course with no emphasis on visualization were analysed. A classification of the students reasoning was established in order to check differences between both groups. As our findings show, the students who attended the course, where the teaching proposal was developed, obtained better results in questions formulated from a visual point of view than those attending the traditional course. Moreover, it was observed that in the traditional group, no responses reasoned in the embodied world of mathematics were found, whereas in the group attending the teaching proposal responses were found in each of the three worlds of mathematics provided by Tall: embodied, symbolic and formal.