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In a former, mainly quantitative, 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. The answering level generally increased between successive year groups of Bachelor students as well as within year groups during the year, mainly from the second to the third level. The reliability of the instrument appeared to be good, but the validity remained unclear. In this current study, more qualitative methods are used to investigate the validity; the results indicate that the validity is good too. The study uses a theoretical perspective from Mathematics Education research and points at the fruitfulness of combining quantitative methods with qualitative methods.

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.

In a former, mainly quantitative, 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. The answering level generally increased between successive year groups of Bachelor students as well as within year groups during the year, mainly from the second to the third level. The reliability of the instrument appeared to be good, but the validity remained unclear. In this current study, more qualitative methods are used to investigate the validity; the results indicate that the validity is good too. The study uses a theoretical perspective from Mathematics Education research and points at the fruitfulness of combining quantitative methods with qualitative methods.