In this contribution we will present an ongoing research project on mathematical practices in electrical engineering. Starting with interesting phenomena we have encountered in our research regarding the relationship of mathematics and engineering, we provide some general thoughts on the notions application and modelling. We then present our own vantage point: Using the Anthropological Theory of the Didactic (ATD), we take an institutional point of view on mathematical practices. This allows us to conceptualise two ideal type mathematical discourses corresponding to different epistemological constitutions of mathematical knowledge in mathematics courses for engineers and in advanced courses in electrical engineering, respectively. We will enrich our presentation with short vignettes of our latest research results to illustrate the kind of insights that the institutional point of view enables us to gain particularly regarding educational issues.
We report from the first iteration of a small-scale project introducing elements of inquiry-oriented education in a first-year engineering Calculus course. In four of the exercise sessions we introduced problem solving in groups, using problems designed to provide alternative viewpoints on central topics of the course, for example limits, differentiation and integration, and containing elements of modelling and numerical methods. The theoretical perspective underlying the design was commognitive theory. We discuss some of the problems used in the intervention, focusing particularly on the numerical differentiation and integration problems. We also report some observations made during the first two iterations of the project, and how these have fed into the continued evolution of the project.
This is a practice report on our teaching practices of mathematical modelling education for humanities and social sciences students at a Japanese university. Our practices were initiated in order to respond to a request from social sciences and psychology departments, and to the growing social demand for such education in Japan. It has been a challenging task because many of these students are not good at mathematics, and some have math anxiety. In this report, we will reflect on our teaching practices over a nine-year period, including the preparation phase, and report our findings.
The authors have developed teaching materials on calculus including multivariable functions for first-course undergraduate students in the science and engineering fields. The materials differ from commonplace textbooks in that they first introduce the topics encountered in engineering and then explain the mathematical aspects. This style aims to help readers understand mathematical concepts smoothly by identifying their interests and offering topics that appeal to intuition.