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

Levels of thinking in computer science : development in bachelor students’ conceptualization of algorithm

How do we know if our students are beginning to think like computer scientists? In a first study we defined four levels of abstraction in computer science students’ thinking about the concept of algorithm. We constructed a list of questions about algorithms to measure the answering level as an indication for the thinking level. This list was presented to various groups of Bachelor computer science students. The mean answering level increased between successive year groups as well as within year groups during the year, mainly from the second to the third level. Student-level estimations provided by teachers fell in the same range as the level measurements, but level growth was not detected in their estimations; level estimation appeared very difficult for lecturers. The reliability of the instrument proved to be satisfactory. To investigate the validity, a follow-up study was done with a small heterogeneous group of Bachelor students. They answered the same questions and were successively interviewed to check whether they understood the terms they used. Their understanding proved to be satisfactory, sustaining the validity of the instrument. In the first study little relation was found between thinking levels and regular test results on algorithm-oriented courses. Supposedly, besides levels on the dimension of abstraction, levels on concretizing, analyzing and synthesizing are also relevant. A broader framework for future research is being proposed

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

Differences in beliefs and attitudes about computer science among students and faculty of the bachelor program

Becoming a (computer) scientist involves more than learning knowledge and skills. The development of the professional attitude towards the discipline and the professional beliefs can be seen as a process of enculturation. In this study attitudes and beliefs of Computer Science students of the first, second and third Bachelor year, are compared with the beliefs and attitudes of the faculty of the department. The study shows enculturation at some aspects: attitudes and beliefs change into the direction of those of the faculty. At some other aspects, however, change occurs in the opposite direction. For a series of aspects, students halfway the first year already have attitudes and beliefs similar to those of the faculty