No abstract

Inthis paper we d e s cribe a Curry-like t ype system for graphs and extend it w i th uniqueness information to indicate that certain objects are only `locally accessible'. The correctness o f t ype assignment guarantees that no external access o n s u c h a n object will take place in the future. We prove that types are preserved under reduction (for both type systems) for a large class o f rewrite systems. Adding uniqueness information provid e s a s olution to two p r oblems i n i mplementations of functional languages: e cient space management and interfacing with nonfunctional operations.

Science teachers' pedagogical content knowledge (PCK) has been researched in many studies, yet little empirical evidence has been found to determine how this knowledge actually informs teachers' actions in the classroom. To complement previous quantitative studies, there is a need for more qualitative studies to investigate the relationship between teacher knowledge (as formulated by the teacher) and classroom practice, especially in the context of an educational innovation. In this study we explored a possible way to investigate this relationship in an in-depth and systematic fashion. To this end, we conducted a case study with a chemistry teacher in the context of the implementation of a context-based science curriculum in The Netherlands. The teacher's PCK was captured using the Content Representation form by Loughran, Mulhall, and Berry. We used an observation table to monitor classroom interactions in such a way that the observations could be related to specific elements of teachers' PCK. Thus, we were able to give a detailed characterization of the correspondences and differences between the teacher's personal PCK and classroom practice. Such an elaborate description turned out to be a useful basis for discussing mechanisms explaining the relationship between teachers' knowledge and teachers' actions.

Recently, computational thinking has attracted much research attention, especially within primary and secondary education settings. However, incorporating computational thinking (CT) in mathematics or other disciplines is not a straightforward process and introduces many challenges concerning the way disciplines are organised and taught in school. The aim of this paper is to identify what characterises CT in mathematics education and which CT aspects can be addressed within mathematics education. First, we present a systematic literature review that identifies characteristics of computational thinking that have been explored in mathematics education research. Second, we present the results of a Delphi study conducted to capture the collective opinion of 25 experts in both the fields of mathematics education and computer science regarding the opportunities for addressing computational thinking in mathematics education. The results of the Delphi study, which corroborate the findings of the literature review, highlight three important aspects of computational thinking to be addressed in mathematics education: problem solving, cognitive processes, and transposition.

We present two type systems for term graph rewriting: conventional typing and (polymorphic) uniqueness typing. The latter is introduced as a natural extension of simple algebraic and higher-order uniqueness typing. The systems are given in natural deduction style using an inductive syntax of graph denotations with familiar constructs such as let and case.The conventional system resembles traditional Curry-style typing systems in functional programming languages. Uniqueness typing extends this with reference count information. In both type systems, typing is preserved during evaluation, and types can be determined effectively. Moreover, with respect to a graph rewriting semantics, both type systems turn out to be sound.

This exploratory study focuses on concepts and their assessment in K-9 computer science (CS) education. We analyzed concepts in local curriculum documents and guidelines, as well as interviewed K-9 teachers in two countries about their teaching and assessment practices. Moreover, we investigated the 'task based assessment' approach of the international Bebras contest by classifying the conceptual content and question structure of Bebras tasks spanning five years. Our results show a variety in breadth and focus in curriculum documents, with the notion of algorithm as a significant common concept. Teachers' practice appears to vary, depending on their respective backgrounds. Informal assessment practices are predominant, especially in the case of younger students. In the Bebras tasks, algorithms and data representation were found to be the main concept categories. The question structure follows specific patterns, but the relative frequencies of the patterns employed in the tasks vary over the years. Our analysis methods appear to be interesting in themselves, and the results of our study give rise to suggestions for follow-up research.

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.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.