Fifteen years of experience with modelling courses in the Eindhoven program of applied mathematics

The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Netherlands includes a series of modelling projects: the so-called Modelling Track. This track was introduced in the curriculum fifteen years ago and has a specific educational approach. Mathematics that may be useful in the projects is not necessarily taught in courses preceding the modelling projects. Moreover, during the projects, students have to use their current skills and knowledge or even have to learn (or discover) new techniques by themselves. Overall, this teaching method has been quite successful in terms of students¿ results and satisfaction. Project coaches have always been recruited from the entire department and gradually, the majority of the staff has become pleased with this method of modeling education. Throughout fifteen years, the structure and content of the series of projects have evolved. This article is based on reflections concerning these changes expressed by the coordinator of the mathematical modelling education (the second author) and the educational advisor (the first author), both of whom have been closely involved in the track¿s development over the years. These changes will be described and their external as well as internal causes will be identified. Examples of external causes are developments of technical phenomena in society, university-wide educational innovations, and a change in the overall structure of the university¿s academic calendar. An example of an internal cause is the variety in background of the project coaches. Finally, strengths and weaknesses of the track will be analyzed. The purpose of the article is to share the experiences with this way of teaching mathematical modelling in higher education and give advice to others who want to implement it

Modelling as a foundation for academic forming in mathematics education

The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students build a portfolio during the track and in the new course they reflect on their former modelling activities, especially from a mathematical and a social perspective. Essay writing on these subjects is followed by peer assessment and peer feedback

The Many Faces of the Mathematical Modeling Cycle

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been prompted with a simple three-step representation of the modeling cycle. This representation consisted out of 1) problem translation into a mathematical model, 2) the solution to mathematical problem, and 3) interpretation of the solution in the context of the original problem. The students’ task was to detail and complete this representation. Their representations also showed a great diversity. This diversity is investigated and compared with the representations of the students’ teachers. The representations with written explanations of 77 students and 20 teachers are analyzed with respect to the presence of content aspects such as problem analysis, worlds/models/knowledge other than mathematical, verification, validation, communication and reflection at the end of the modeling process. Also form aspects such as iteration and complexity are analyzed. The results show much diversity within both groups concerning the presence or absence of aspects. Validation is present most, reflection least. Only iteration (one is passing the modeling cycle) more than once is significantly more present in the teachers’ group than in the students’ group. While accepting diversity as a natural phenomenon, the authors plea for incorporating all aspects mentioned into mathematical modeling education

Positie van het vak informatica in havo/vwo

De vraag van dit artikel is: hoe moet het verder met het vak informatica in de bovenbouw van havo en van vwo? Deze vraag is relevant om een aantal redenen. Enerzijds gaat het om een tamelijk marginaal vak; slechts ongeveer 60% van de scholen biedt informatica aan. Anderzijds is er een discussie op gang aan het komen over de positie van het vak. Zo zijn er mensen die zich afvragen of informatica in de huidige vorm moet blijven bestaan, maar ook mensen die vinden dat de maatschappelijke relevantie van informatica zo groot is dat de positie ervan versterkt moet worden. In dit artikel geven we na een beschrijving van de huidige positie van het schoolvak informatica vooral argumenten pro het laatste standpunt en hoe dat vorm kan krijgen

Problem-based teaching in engineering education

The aerospace industry requires highly educated, motivated engineers capable of working with increasingly complex processes and equipment, rapidly-changing requirements, and the need to constantly improve production efficiency. Colleges and universities throughout the world strive to provide training to young professionals for jobs in high-tech industries and to provide not only core technical knowledge, but also training on how to approach problems creatively and to generate novel solutions to problems. Problem-based learning (PBL) contributes to solving this problem. This paper reviews the literature on PBL, studies its benefits and drawbacks, and presents the positive results achieved by its implementation in the training of engineering students at Tomsk Polytechnic University

Incorporating life cycle assessment and ecodesign tools for green chemical engineering: a case study of competences and learning outcomes assessment

Chemical engineers assume a broad range of roles in industry, spanning the development of new process designs, the maintenance and optimization of complex systems, and the production of intermediate materials, final products and new technologies. The technical aptitude that enables chemical engineers to fulfill these various roles along the value chain makes them compelling participants in the environmental assessment of the product in question. Therefore, the introduction of life cycle assessment (LCA) and ecodesign concepts into the chemical engineering curriculum is essential to help these future professionals to face design problems with a holistic view of the technical, economic, social and environmental impacts of their solutions. The teaching of these and other disciplines by means of student-centered methods, based on a holistic structure, have demonstrated better teamwork and communication skills. For that reason, this paper proposes a Micro (Assess-Analyze-Act) (M-3A) model of assessment mainly focused on closing the loop of the learning activities. This model has been applied to an ecodesign case study of the "University master's Degree in chemical engineering" of the University of Cantabria/University of the Basque Country, with positive feedback of the students. They felt that the approach has allowed them to utilize their analytical skills in quantifying a situation before applying other subjective measures, and that the public discussion of the results was a satisfactory element for improving their communication skills. Moreover, the students found that the workload was nicely adjusted, highlighting the acquisition of 4 competences preferentially: teamwork, creativity; relevance of environmental issues and initiative and entrepreneurship. Finally, the students suggest that the application of this methodology into their degree could motivate future students improving their performance

The influence of technology on the mathematical modelling of physical phenomena

A study is presented in which students are asked to model two physical phenomena using applications on electronic tablets : a bounce of a ball and the extension of a spring. The analysis focusses on (a) the influence of characteristics of the applications on the tablets on the decisions that groups of 16-year-old students made during the modelling phases in which reality and mathematics are related, (b) mathematisation of the phenomena and (c) interpretation of the models. The phenomena were recorded using an app that requests users establish a set of references during the mathematisation process, which makes students focus on the way the references have been set to interpret the model properly. Our findings indicated inconsistences between student decisions made during mathematisation and their considerations during interpretation of the model. To conclude we suggest reasons students experience problems in working without a pre-defined reference syste

Co-operative learning and adaptive instruction in a mathematics curriculum

The AGO 12 to 16 Project (the acronym AGO stands for the Dutch equivalent of 'Adaptive Instruction and Co-operative Learning') seeks to develop and evaluate a mathematics curriculum which is suitable for mixed-ability groups in secondary education. The research questions we will address here are, first, whether this curriculum is feasible and effective, and, second, what effects, if any, the context variables time and mean cognitive level of the class have on learning. Many mathematics programmes make insufficient allowance for the differences in intellectual ability that exist in mixed-ability classes. In order to change this situation we developed a mathematics curriculum with adaptive qualities. The evaluation of the experimental curriculum was carried out in two stages. During the first stage the curriculum was used at two schools with the aim of investigating the feasibility of the programme. Experience with the implementation of the programme led to some improvements in the experimental materials. By and large the AGO model appeared to be feasible in secondary classrooms. In the second stage, which was on a large scale, the focus was on the effectiveness of the programme. Six hundred students, 13 teachers and six schools were involved in the research. Teachers in the experimental group were trained in AGO methods and in implementing the new AGO curriculum. Teachers in the control groups worked with the existing programme following their usual methods of teaching. The main conclusion of the study is positive. The AGO model as a whole proved to be practical and effective in learning mathematics. The AGO model has a positive effect on the intercept, which means that the mean scores of AGO classes are higher than the mean scores of non-AGO classes. It may be concluded that, on the average, students benefit from learning in AGO classes as compared with non-AGO classes. AGO does not increase or decrease the differences between students in the same class. As expected, positive effects of two context variables were found: (1) the total amount of time spent in class covering the mathematical content and (2) class composition as indicated by the mean pretest score (aptitude) of the class