Universiteit Leiden

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PhD project

Indefinite integration through recognition based heuristic search

Towards a framework that integrates content-based and process-based accounts of mathematical thinking

2016 - 2021
Stefan Pouwelse
Ministry of Education, Culture and Science under the Dudoc programme


  • S.R. Pouwelse MSc - PhD candidate
  • prof.dr.ir. F.J.J.M. Janssen - supervisor
  • prof.dr. S.J. Edixhoven - co-supervisor
  • drs. P.M.G.M. Kop

In this research project, a framework will be developed for the problem solving process of indefinite integration involving levels of recognition and heuristics. It will be used to identify student difficulties and support calculous teaching.

Research question

Can the problem solving process for indefinite integration be described in terms of recognition based heuristic search, and can this be used to identify student difficulties and support  teaching?

The importance of understanding and developing mathematical thinking is widely recognized. Two approaches can be distinguished. According to the content-oriented approach, mathematical thinking is mainly dependent on available types of knowledge and the organization of this knowledge. According to the process-oriented approach, mathematical thinking is mainly dependent on available generic mathematical thinking activities such as representation, abstraction, etcetera activities.

We are trying to develop an approach in which content and processes are integrated and connected to a particular domain. We found points of departure for this in recent theory on expertise in which differences in problem solving are explained as interaction between two processes: recognition and heuristic search. The available knowledge enables a problem solver to recognize a problem at a certain level. With complete recognition, the solution is immediately known. If the recognition is less complete, heuristics can be used to search for possible solutions. The level of recognition determines the search space within which a search can be made.

Kop has already successfully applied this model for mathematics education to understand and develop expertise in the field of graphing formulas. In this study, this model is further elaborated and applied for indefinite integration at University level.

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