Erik Barendsen

Autarkic Computations in Formal Proofs

Formal proofs in mathematics and computer science are being studied because these objects can be verified by a very simple computer program. An important open problem is whether these formal proofs can be generated with an effort not much greater than writing a mathematical paper in, say, LATEX. Modern systems for proof development make the formalization of reasoning relatively easy. However, formalizing computations in such a manner that the results can be used in formal proofs is not immediate. In this paper we show how to obtain formal proofs of statements such as Prime(61) in the context of Peano arithmetic or (x+1)(x+1)=x2+2x+1 in the context of rings. We hope that the method will help bridge the gap between the efficient systems of computer algebra and the reliable systems of proof development.

Conventional and Uniqueness Typing in Graph Rewrite Systems

In this paper we describe a Curry-like type system for graphs and extend it with uniqueness information to indicate that certain objects are only ‘locally accessible’. The correctness of type assignment guarantees that no external access on such an object will take place in the future. We prove that types are preserved under reduction (for both type systems) for a large class of rewrite systems. Adding uniqueness information provides a solution to two problems in implementations of functional languages: efficient space behaviour and interfacing with non-functional operations.

Uniqueness Type Inference

We extend the Uniqueness Type System with uniqueness polymorphism. Using a notion of ‘principal uniqueness variants’ the type system is shown to be effective in the sense that a uniqueness variant of a given conventional type can be determined automatically. The presented algorithm serves as a basis for type checking in the language Clean. We illustrate the system by some concrete examples.

Cognitive Mechanisms of Conceptual Modelling

Conceptual modelling involves many higher order cognitive processes, such as relational reasoning and abstraction, which are based on integration and maintenance of information. Evidence from cognitive psychology suggests that these processes are subject to individual differences which cannot be explained by training and experience alone. In this review, we study how the cognitive processes that enable modelling interact to produce modelling behaviour, and where in this process we can find individual differences that may explain some of the variation in performance seen in actual modelling settings. We discuss interaction between working memory, executive control and attention as they facilitate relational reasoning and abstraction, which we consider to be key cognitive processes in modelling. Eventually, a thorough understanding of modelling cognition can help us to provide better cognitive support for modellers.

Abstract Reasoning in Collaborative Modeling

This paper reports on a case study of abstract reasoning in a real collaborative modeling setting. The study was conducted according to the behavioral observation principles of human ethology. Our findings indicate a relation between an individuals executive functioning and his ability to do abstract reasoning. Furthermore, we find individual differences in these abilities, and our results suggest that lack of certain skills pushes a session back to its initial phase until a shared conception of what is being modeled is achieved. These findings further our understanding of the process of collaborative modeling, how the qualities and behaviors of an individual modeler influence the interactive modeling process and its final outcomes.

Towards an empirically validated model for assessment of code quality

We present a pilot study into developing a model of feedback on code quality in introductory programming courses. To devise such a model, we analyzed professional standards of code quality embedded in three popular software engineering handbooks and found 401 suggestions that we categorized into twenty topics. We recorded three instructors who performed a think-aloud judgment of student-submitted programs, and we interviewed them on the topics from the books, leading to 178 statements about code quality. The statements from the instructor interviews allowed us to generate a set of topics relevant to their practice of giving feedback, which we used to create criteria for the model. We used the instructor statements as well as the book suggestions to distinguish three levels of achievement for each criterion. This resulted in a total of 9 criteria for code quality. The interviews with the instructors generated a view of code quality that is very comparable to what was found in the handbooks, while the handbooks provide detailed suggestions that make our results richer than previously published grading schemes. As such, this process leads to an overview of code quality criteria and levels that can be very useful for constructing a standards-based rubric for introductory programming courses.

Computational thinking skills in Dutch secondary education

Computational Thinking is regarded as a necessary analytical skill for young people in the present day information society. We report on an ongoing design research project on Computational Thinking (CT) skills in Dutch secondary computer science (CS) education. The first phase of the project investigates the occurrence and nature of typical CT aspects in existing CS teaching materials, teachers pedagogical content knowledge and policy documents. In the poster we focus on the overall research design and on the method and preliminary results of the first phase.

Designing a rubric for feedback on code quality in programming courses

We investigate how to create a rubric that can be used to give feedback on code quality to students in introductory programming courses. Based on an existing model of code quality and a set of preliminary design rules, we constructed a rubric and put it through several design iterations. Each iteration focused on different aspects of the rubric, and solutions to various programming assignments were used to evaluate. The rubric appears to be complete for the assignments it was tested on. We articulate additional design aspects that can be used when drafting new feedback rubrics for programming courses.

Extending Graph Rewriting with Copying

The notion of term graph rewrite system (TGRS) is extended with a lazy copying mechanism. By analyzing this mechanism, a confluence result is obtained for these so-called copy term graph rewrite systems (C-TGRS). Some ideas on the use of lazy copying in practice are presented.

Typifying Informatics Teachers’ PCK of Designing Digital Artefacts in Dutch Upper Secondary Education

This paper reports on the results of the first phase of an ongoing research project in design-oriented education in informatics in Dutch upper secondary education. Our study focused on eliciting and categorizing the pedagogical content knowledge (PCK) with respect to design of digital artefacts of the informatics teachers participating in the research project. Our results suggest that teachers’ PCK on design can be typified in terms of two aspects, namely (i) teachers’ knowledge about objectives and goals of designing digital artefacts by students, and (ii) teachers’ knowledge about ways to assess students’ understanding and performance. As to (i), we distinguish an orientation towards more conceptual objectives, and one towards more practical objectives. Also with respect to (ii), we found two types of teachers’ knowledge, one focused on process-based assessment and another on product-based assessment.