2010 DSI Instructional Innovation Award Competition FinalistToday's marketplace needs skilled graduates capable of solving real problems of innovation in a changing environment. PuzzleBased Learning (PBL) is a new and emerging model of teaching critical thinking and problemsolving. We have run courses and workshops on PBL in the United States, Australia, and the MiddleEast (Qatar and Abu Dhabi) in a range of formats. Preliminary assessment indicates that the PBL approach is assisting students by providing a framework to explore critical thinking, as well as being fun and engaging. In addition to our home institutions, several universities worldwide have introduced courses on PBL based on our curriculum or have introduced PBL themes in existing courses. Companies and organizations are also finding PBL as an effective way of exposing their executives (managers and engineers) to an innovative approach towards honing their problemsolving skills. In this paper we discuss our experience of the past three years and outline PBL's effectiveness with our preliminary evaluations. PuzzleBased Learning: An Introduction to Critical Thinking and Problem Solvingby Zbigniew Michalewicz and Nickolas Falkner, University of Adelaide; and Raja Sooriamurthi, Carnegie Mellon University While students are trained to recognize familiar problems with known solutions, they may not be sufficiently prepared to address novel realworld problems. What is missing in many of the curricula that we have examined is coursework focused on the development of general problemsolving skills. Further, courses that introduce elements of problemsolving skills often do so at the third or fourth level of the programs after students have already faced the majority of their inacademy intellectual challenges. While some courses with a design content emphasis may meet this requirement, many students do not learn how to think about solving problems in general. Throughout their education they are often constrained to concentrate on textbook questions at the end of each chapter, solved using material discussed earlier in the chapter. This constrained form of "problem solving" is not sufficient preparation for addressing realworld problems—on entering the real world, students find that problems do not come with instructions or guidebooks. As a step towards addressing this situation, we have created and experimented with a new approach, PuzzleBased Learning, that is aimed at getting students to think about how to frame and solve unstructured problems. The pedagogical goal is to increase students' analytical awareness and general problemsolving skills by employing puzzles, which are educational, engaging, and thought provoking. What is PuzzleBased Learning?Consider the following puzzles:
What is common to all of the above? Apart from being fun to ponder, solutions to these puzzles exemplify several problemsolving heuristics. What general problemsolving strategies can we learn from the way we solve these puzzles? As entertaining and engaging puzzles inherently are, they are just a means to our pedagogical end of fostering general domainindependent reasoning and critical thinking skills that can lay a foundation for problem solving in future course work. Pedagogical InnovationsThe puzzlebased learning approach aims to encourage students to think about how to frame and solve problems that are not encountered at the end of some textbook chapter. Our goal is to motivate students, and also to increase their mathematical awareness and problemsolving skills by discussing a variety of puzzles and their solution strategies. In this course we concentrate on educational puzzles that support problemsolving skills and creative thinking. These educational puzzles satisfy most of the following criteria:
Many realworld problems can be perceived as largescale puzzles. As William Poundstone discusses in his exposition of the famous Microsoft / Silicon Valley interview puzzles (Poundstone, 2000), companies perceive a strong connection between the ability to solve puzzles and the ability to solve industry/business problems. Puzzlebased Learning vs. Problembased Learning vs. Projectbased Learning Puzzlebased Learning vs. Problembased Learning vs. Projectbased LearningThe ultimate goal of puzzlebased learning is to lay a foundation for students to be effective problem solvers in the real world. At the highest level, problem solving in the real world calls into play three categories of skills: dealing with the vagaries of uncertain and changing conditions; harnessing domain specific knowledge and methods; and critical thinking and applying general problemsolving strategies. These three skill categories are captured in the three forms of learning depicted in Figure 1. Figure 1. A continuum of learning and skills needed for problem solving in the real world.
There are a few different versions of the puzzlebased learning course being taught currently. The course can be offered as a fullsemester (three units) elective course (typically three contact hours per week, split into lectures and tutorials), a fullsemester (three units) freshman seminar (three contact hours per week), one unit freshman seminar, and one unit core module as part of some other course. One of the important points about puzzlebased learning courses is that the course is not about presenting and discussing a variety of puzzles but rather about presenting, discussing, and understanding problemsolving principles and some mathematical principles in the context of puzzles that serve as entertaining illustrations of the presented concepts. Also, the process of understanding problemsolving principles leads students through a variety of topics, exposing them to many important concepts at early stages of their college education. Despite a variety of possible offerings of puzzlebased learning, the structure of the course is very much the same. The topics listed below correspond to a 12week semester regardless whether each topic is allocated one hour or three hours.
Each topic is illustrated by a variety of puzzles presented in an interactive manner. The course introduces a few simple problemsolving rules that we refer to in every class. Every week students are presented with homework assignments: one or more puzzles on the topic covered in the class. The following week, at the beginning of a class, the solutions are presented and discussed. The University of Adelaide Experience. The initial implementation of puzzlebased learning was a oneunit course set up as a component of a threeunit firstyear course. A threeunit firstyear course for students planning to major in computer science was launched simultaneously in 2009 and made available to all nonengineering students in the University. We refer to the oneunit offering as PBLE (PBL for engineers) and the threeunit offering as PBL Main. The courses cover the same material, at different levels of depth. Lectures in PBL follow a set pattern. The first lecture of the week presents the solution to the previous homework, identifies the key points for this week's lectures, and then builds on the topic area. The lecture concludes with the next assignment. PBL Main has a second lecture that develops the themes of the week's topic. Lecture materials are developed in parallel, with the single PBLE lecture derived from a revision and abridgement of the two PBL Main lectures for that topic to maintain currency between the two courses. Tutorials are offered for PBL Main and allow students to take part in collaborative problemsolving exercises, with a tutor to provide assistance and guidance. Tutorial groups are up to 25 students, with subgroup formation of five to eight students for problem solving. During these sessions, we introduce fundamental mathematical concepts that are useful in the later course, including counting and the bases of probability, including factorials, combinations, and permutations. The Carnegie Mellon University Experience. Puzzlebased learning was offered as a threecredit freshman seminar in Spring 2009 and 2010. Given the seminar nature of the spring course, enrollment was capped at 15 but it was encouraging to see that the wait list was longer than the class enrollment. The class had an interdisciplinary mix of students majoring in Information Systems, Computer Science, Psychology, Statistics, Cognitive Science, Economics, and Physics. The class met twice a week for 80 minutes. Given the smaller size of the class we were able to experiment with several alternative themes. For example, after the introductory classes, each session started with a puzzleoftheday. One student would present a puzzle of their choice. The class as a whole would try to solve the puzzle with hints and guidance provided by the puzzle poser. Student chosen puzzles ranged across the gamut of logic puzzles to diagrammatic reasoning to physical puzzles. Students had to submit a onepage writeup of their puzzle, solution, and most importantly, their reflection on the puzzle: what did they find interesting in the puzzle, variations, how does the solution tie into the general class discussions, etc. During our discussion of scientific induction and mathematical induction, given the smaller size of the class, we played Robert Abbott's inductive game of Eleusis that models the process of scientific method. To introduce students to some of the problemsolving thoughts of leaders in the field we watched a few videos. These included Polya's "Let us teach guessing" wherein Polya beautifully illustrates several problemsolving heuristics (Polya, 1945) (that are embraced by puzzlebased learning) in the process of deriving a solution to the fiveplane problem; an interview with Nobelprizewinning economist Herb Simon on being a researcher, with advice to undergraduates; Nobelprizewinning physicist Richard Feynman on problem solving and induction. We also visited a local Super Computing Center open house to get a glimpse of problem solving in the real world. To emphasize the link between the thought processes involved in solving puzzles and addressing open realworld problems, we examined a few case studies including the recently cracked Netflix Prize (www.netflixprize.com) and the classic work of Mosteller in resolving the authorship of some of the disputed Federalist papers. EvaluationEarly student response shows that students enjoy the course material and that it does develop their thinking skills. The first implementation of PBL as a threeunit course has shown a consistent development of student puzzlesolving skills, culminating in excellent examination performance that outstripped our initial expectations. Figures 2a and 2b show the overall improvement of the students during the semester as we provided personalized feedback as well as overall assignment solutions. Figure 2a. Student results for assignments over the semester.
Figure 2b. Averaged student results for assignments over the semester.
Following are some sample quotes from our students in their endofterm evaluations (reproduced verbatim): "I think the topic is very interesting. I enjoy coming to class because it is very handson and allows me to use critical thinking." "This course seems to be expanding my mind by giving me new ways to interpret and solve problems that I would be completely lost on." "I like that the course opens my eyes to independent critical thinking and learning new ways to approach problems." "The way you are taught a new way about attempting problems, helps in all courses, not just this one." Effectiveness and TransferabilityPuzzlebased learning originated with the goal of enhancing the general problemsolving and criticalthinking skills of freshmen college students. This student demographic group continues to be our primary focus, and we have personally offered such semesterlong courses in the United States, Australia, and Qatar. Our curriculum is supported by a 328page textbook (Michalewicz, 2008) that details our approach. Sample syllabi, slides, assignments, exams, simulation software are all available off of our website (www.puzzlebasedlearning.edu.au) dedicated to puzzlebased learning. This educational material has been (or is in the process of being) translated to French, Polish, Japanese, and Hebrew to be offered to local communities. Currently, approximately 20 universities worldwide are in the process of offering PBLthemed courses. In addition, since our original conception, PBL has transferred both downwards, upwards, and outwards from the college freshman curriculum. Two high schools are currently experimenting with PBL courses for their students. A graduate version of PBL targeting Information Systems majors was designed and delivered in the summer of 2010. We have offered several workshops on PBL at conferences to other faculty to introduce them to our approach. We have also delivered training workshops to government and industry employees. Apart from a full puzzlebasedlearningthemed course, portions of these ideas have also been blended into courses on intelligent systems, decision support, system development, and highschool outreach efforts to highlight various problemsolving strategies. ConclusionsPuzzlebased learning is a pedagogical experiment in progress. The goal is to foster general domain independent reasoning and critical thinking skills that can lay a foundation for problemsolving in future course work (as depicted in Figure 1). As fun as puzzles inherently are, they are just a means to this pedagogical end. Our preliminary experience in different instantiations of the course and educational contexts has been encouraging and well received as we continue to explore this approach. We are in the process of collecting relevant data to demonstrate the benefit of our approach. Early results (Falkner, 2009) indicate that students perceive an improvement in their thinking and general problemsolving skills. ReferencesBlumenfeld, P. C., Soloway, E., Marx, R. W., Krajcik, J. S., Guzdial, M., & Palincsar, A. (1991). Motivating projectbased learning: Sustaining the doing, supporting the learning. Educational Psychologist, 26(3 & 4), 369398. Bransford, J. D., Sherwood, R. S., Vye, N. J., & Rieser, J. (1986). Teaching thinking and problem solving: Research foundations. American Psychologist, 41, 10781089. Falkner, N., Sooriamurthi, R., & Michalewicz, Z. (2010). Puzzlebased learning for engineering and computer science. IEEE Computer, 43(4), April, 2028. Falkner, N. J. G., Sooriamurthi, R., & Michalewicz, Z. (2009). Puzzlebased learning: The first experiences. Proceedings of the Twentieth Annual Conference of the Australasian Association for Engineering Education (AaeE 2009), Adelaide, Australia, December 69. Michalewicz, Z., & Michalewicz, M. (2008). Puzzlebased learning: Introduction to critical thinking, mathematics, and problem solving. Melbourne: Hybrid Publishers. Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton: Princeton University Press. Poundstone, W. (2000). How would you move Mount Fuji?: Microsoft's cult of the puzzleHow the world's smartest companies select the most creative thinkers. Little Brown and Company.

