A number of universities are introducing courses, modules, or freshman seminars that relate to the puzzle-based learning paradigm. The purpose of such units is to attract, motivate and retain engineering/computer science students, and to increase their mathematical awareness and their problem-solving skills. This is essential in developing students as general problem-solvers, rather than training students to limit their thinking to the problems that are immediately pertinent to the specific area that they are studying. The business world has already recognised that problem-solving skills are valuable and some major companies actively recruit good puzzle-solvers. We introduce and define our puzzle-based learning approach, provide an example of the syllabus and course material and provide evidence of two current implementations, including early student feedback. IntroductionA recent article describes a puzzle-based freshman seminar introduced at the University of California, Santa Barbara, to motivate and retain computer engineering students (Parhami, 2009). The author argues that attracting students to computer science and engineering programs represents only one aspect of a broader problem of the shortage of a skilled information technology workforce, and that recruitment efforts must be augmented with additional strategies for retaining and motivating students -strategies that are missing in curricula recommendations of the IEEE Computer Society and the ACM.The problem may be even broader. Today's marketplace needs graduates capable of solving real problems of innovation and a changing environment -we need more skilled graduates. What is missing in most engineering/computer science curricula is coursework focused on the development of problem-solving skills. Most engineering students never learn how to think about solving problems in general -throughout their education, they are constrained to concentrate on textbook questions at the back of each chapter, solved using material discussed earlier in the chapter. This constrained form of "problem solving," is not sufficient preparation for addressing real-world problems. On entering the real world, students find that problems do not come with instructions or guidebooks. One of our favourite examples to illustrate this point is a puzzle on breaking a chocolate bar: If you do not know the answer, which textbook would you search to discover the solution? The same applies to solving many real world problems: which textbook should you search to find a solution, if that is the solution strategy that you've learned?Students often have difficulties in independent thinking or problem-solving skills regardless of the nature of a problem. At the same time, educators are interested in teaching "thinking skills" rather than "teaching information and content." The latter approach has dominated in the past. As Alex Fisher wrote in his book (Fisher, 2001) The puzzle-based learning approachThe puzzle-based learning approach aims at encouraging engineering/computer scien...

Recursion is a very powerful and useful problem solving strategy. But, along with pointers and dynamic data structures, many beginning programmers consider recursion to be a difficult concept to master. This paper reports on a study of upper-divisiun undergraduate students on their difficulty in comprehending the ideas behind recursion. Three issues emerged as the points of difficulty for the students: (1) insufficient exposure to declarative thinking in a programming context (2) inadequate appreciation of the concept of functional abstraction (3) lack of a proper methodology to express a recursive solution. The paper concludes with a discussion of our approach to teaching recursion, which addresses these issues. Classroom experience indicates this approach effectively aids students' comprehension of recursion.

Abstract. Much current CBR research focuses on how to compact, rene, and augment the contents of individual case bases, in order to distill needed information into a single concise and authoritative source. However, as deployed case-based reasoning systems become increasingly prevalent, opportunities will arise for supplementing local case bases on demand, by d r a wing on the case bases of other CBR systems addressing related tasks. Taking full advantage of these case bases will require multi-case-base reasoning: Reasoning not only about how to apply cases, but also about when and how to draw on particular case bases. This paper begins by considering tradeo s of attempting to merge individual case bases into a single source, versus retaining them individually, a n d argues that retaining multiple case bases can bene t both performance and maintenance. However, achieving the bene ts requires methods for case dispatching|deciding when to retrieve from external case bases, and which case bases to select|and for cross-case-base adaptation to revise suggested solutions from one context to apply in another. The paper presents initial experiments illustrating how these procedures may a e c t the bene ts of using multiple case bases, and closes by delineating key research issues for multi-case-base reasoning.

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Abstract. While computer science and engineering students are trained to recognise familiar problems with known solutions, they may not be sufficiently prepared to address novel real-world problems. A successful computer science graduate does far more than just program and we must train our students to reach the required levels of analytical and computational thinking, rather than hoping that it will just 'develop'. As a step in this direction, we have created and experimented with a new first-year level course, Puzzle-based Learning (PBL), that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is increase students' mathematical awareness and general problem solving skills by employing puzzles, which are educational, engaging, and thought provoking. We share our experiences in teaching such a course -apart from a brief discussion on our pedagogical objectives, we concentrate on discussing the presented material which covers (in two lectures) just one selected topic (pattern recognition). In this paper we present the ideas behind foundations for PBL and the material of the first of two lectures on pattern recognition, in which we address core concepts and provide students with sufficient exemplars to illustrate the main points.Key words and phrases: puzzle-based, computational thinking, problem-based. ZDM Subject Classification: A20, B50, B70, D40, D50. IntroductionStudents often have difficulties in independent thinking or problem-solving skills regardless of the nature of a problem. At the same time, educators are interested in teaching "thinking skills" rather than "teaching information and content." The latter approach has dominated in the past. As Fisher (2001) ". . . though many teachers would claim to teach their students 'how to think', most would say that they do this indirectly or implicitly in the course of teaching the content which belongs to their special subject. Increasingly, educators have come to doubt the effectiveness of teaching 'thinking skills' in this way, because most students simply do not pick up the thinking skills in question." Further, many analysts lament the decreasing mathematical skills of students. A recent Mathematics Working Party Final Report, issued by the University of Adelaide (June, 2008) includes statements such as "There is an urgent need to raise the profile and importance of mathematics among young people. . . " and "The declining participation in mathematics and related subjects is not limited to Australia. . . ".Over the past few decades, various people and organizations have attempted to address this educational gap by teaching "thinking skills" based on some structure (e.g. critical thinking, constructive thinking, creative thinking, parallel thinking, vertical thinking, lateral thinking, confrontational and adversarial thinking). However, all these approaches are characterized by a departure from mathematics as they concentrate more on "talking about problems" rather than "solving problems." It is our ...