Jc Jacob Perrenet

Exploring students' understanding of the concept of algorithm: levels of abstraction

How do we know if our students are beginning to think like computer scientists? In this study we have defined four levels of abstraction in the thinking of computer science students 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. Little relation was found between answering levels and test results on algorithm oriented courses. The study was inspired by the tradition of mathematics education research.

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.

Pedagogical Content Knowledge in Teaching Material.

The scope of this article is to understand to what extent Computer Science teachers can find support for their Pedagogical Content Knowledge (PCK) in teaching material. We report the results of a study in which PCK is used as framework to develop a research instrument to examine three high school computer science textbooks, with special focus on programming. PCK is analyzed in this study in its two components: pedagogical knowledge (PK) and content knowledge (CK). The results of the textbooks have been compared with the results of a previous study, in which experienced teachers from various countries were involved in semi-structured interviews to portray the PCK of programming for secondary school. Our expectations to find textbooks relatively strong on the CK, but weak on the PK aspect, is confirmed by the results.

The academic merits of modelling in higher mathematics education: A case study

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively for, or even construct, mathematical knowledge useful for the problem at hand. A detailed analysis of the academic profile of the curriculum is presented, using a framework of competencies and dimensions, developed at this university by the project, Academic Competencies and Quality Assurance (ACQA). The profile is constructed from the perspective of teachers’ ambitions. The research question for the present study is: Are there certain academic characteristics typical for the Modelling Track compared to the characteristics of the other courses in the Eindhoven Bachelor curriculum of Applied Mathematics? The analysis shows that the modelling projects are essential for the development of the designing competencies in the curriculum. Other courses in the curriculum are more intended to develop abstraction capabilities. These results provide supporting arguments for the realistic approach chosen for mathematical modelling education.

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.

Quality Criteria for Mathematical Models in Relation to Models’ Purposes: Their Usefulness in Engineering Education

A taxonomy of eight quality criteria for mathematical models was developed for the common basic modelling course in the innovated BSc curriculum of Eindhoven University of Technology. First year engineering students of all disciplines reflected on their group modelling projects, indicating how their models could be improved, using the criteria. The students were also asked to indicate the purpose(s) of their models from a list of 16 purposes. This study explores the usefulness of the purposes and criteria, defined as relevance combined with understandability. Optimisation proved to be the most relevant purpose, followed by analysis, prediction (what), and verification.Specialisation, genericity, scalability, distinctiveness, and convincingness criteria proved useful; but audience, impact, and surprise did not.

Discussion of Methods for Threshold Research and an Application in Computer Science

The first Dutch dissertation concerning CS education was by Saeli (2012), built on publications with Perrenet, Jochems, and Zwaneveld (2011, 2102a, 2012b). Saeli et al. studied secondary CS education, specifically programming, from the perspective of Pedagogical Content Knowledge (PCK).

Design-Based Learning in Mechanical Engineering Education

Since 1997 Design-based Learning (DBL) has become the educational concept at Eindhoven University of Technology (TU/e). There was a need at that time to develop a common view for innovation in the educational system. DBL has been modelled to serve the purposes of scientific technical education with an underlying emphasis in ‘design’ (Wijnen, 2000). The rationale behind this approach was to provide the programs with a more competence-based orientation and to educate students to meet the requirements of technical systems. The profile of DBL was thus described in terms of features (i.e. Professionalization, Activation, Co- operation, Creativity, Integration, Multidisciplinary). DBL was not implemented following a uniform curriculum model, rather it was implemented according to the needs and ideas in every specific department. For Mechanical Engineering, the DBL working methodology to solve problems is based on Problem-based Learning (PBL), whereas the method to design a product departs from on project process orientation.

Mathematical modelling in Dutch textbooks : is it genuine mathematical modelling?

In this chapter, we analyse the two most frequently used Dutch mathematics textbooks for upper secondary schools in order to determine to what extent the tasks in these textbooks meet the criteria we have set for genuine mathematical modelling: does a modelling task have a modelling purpose, and do the students have to perform characteristic modelling activities? The criterion of having a modelling purpose stems from a modelling course in tertiary education by the last two authors. For the characteristic modelling activities, we used the research of the first two authors. Only a very small percentage of the analysed tasks meets the criteria. So, there is hardly any genuine mathematical modelling in the two textbooks, although it is explicitly mentioned in the formal curriculum.

Competencies in Higher Education: Experience with the Academic Competences and Quality Assurance (ACQA) Framework

The ACQA framework has been developed at the Eindhoven University of Technology (TU/e) as an alternative to the European Dublin Descriptors. Its goals were a characterisation of academic education, a detailed description of competencies, adding design competencies, and a sensibility for differences between disciplines.