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Guide to Teaching Puzzle-based Learning

verfasst von: Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

Verlag: Springer London

Buchreihe : Undergraduate Topics in Computer Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book provides insights drawn from the authors’ extensive experience in teaching Puzzle-based Learning. Practical advice is provided for teachers and lecturers evaluating a range of different formats for varying class sizes. Features: suggests numerous entertaining puzzles designed to motivate students to think about framing and solving unstructured problems; discusses models for student engagement, setting up puzzle clubs, hosting a puzzle competition, and warm-up activities; presents an overview of effective teaching approaches used in Puzzle-based Learning, covering a variety of class activities, assignment settings and assessment strategies; examines the issues involved in framing a problem and reviews a range of problem-solving strategies; contains tips for teachers and notes on common student pitfalls throughout the text; provides a collection of puzzle sets for use during a Puzzle-based Learning event, including puzzles that require probabilistic reasoning, and logic and geometry puzzles.

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Inhaltsverzeichnis

Frontmatter

Motivation and Teaching

Frontmatter

1. Motivation

Abstract

Consider the following puzzles. Some of the solutions to these are discussed in detail in further chapters. For now, just ponder the puzzles themselves.

Given two eggs, for a 100-story building, what would be an optimal way to determine the highest floor, above which an egg would break if dropped?
Suppose you buy a shirt at a discount. Which is more beneficial to us: apply the discount first and then apply sales tax to the discounted amount or apply the sales tax first and then discount the taxed amount? What do stores do?
If you have a biased coin (say, comes up heads 70 % of the time and tails 30 %), is there a way to work out a fair, 50/50 toss?
A $10 gold coin is half the weight of a $20 gold coin. Which is worth more: a kilogram of $10 gold coins or half a kilogram of $20 gold coins?
A farmer sells 100 kg of mushrooms for $1 per kg. The mushrooms contain 99 % moisture. A buyer makes an offer to buy these mushrooms a week later for the same price. However, a week later, the mushrooms would have dried out to 98 % of moisture content. How much will the farmer lose if he accepts the offer?
If you heat a metal washer with a hole in the middle, what happens to the size of the hole?

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

2. Getting Started

Abstract

When we discuss with colleagues our motivation and experience in teaching Puzzle-based Learning, a question that quickly follows from those interested in exploring this paradigm further is: How can I do this in my university? Given our engagement with teaching Puzzle-based Learning in a range of settings and to a range of audiences, in this chapter we discuss how an instructor could start teaching Puzzle-based Learning and also how to initiate students to such course.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

3. Icebreakers

Abstract

The amount and type of teacher–student interaction in a Puzzle-based Learning course can vary widely based on the number of students in the course. In our experience, we have taught this course to as many as 300 and as few as 10. Irrespective of the size of the class, it is important that students are active rather than passive. The goal of the teacher should be to get students to use their System 2 thought process as much as possible. Students should treat the course as if it is a workout for their minds, as a mental gymnasium.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

4. Effective Teaching Approaches

Abstract

One of the challenges in implementing a Puzzle-based Learning approach is taking a love of puzzles, or a desire to make students think in a more open-ended fashion, and making it work in a classroom environment. Many courses reward students for sitting quietly and, when prompted, answering a set of well-defined questions with rehearsed answers built from what their teacher has said. When we describe an effective teaching approach to support Puzzle-based Learning, we are not just talking about buying a book or finding some problems, we are talking about a complete change in the way that many of us think about working with our students.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

Tools, Tips, and Strategies

Frontmatter

5. Understand the Problem

Abstract

In this chapter we look at one of the biggest stumbling blocks for students and teachers alike: working out what the problem actually is so that we can solve the right problem. When approaching puzzles, some people feel overwhelmed because they can’t even start on a path to a solution. We show you in this chapter that with some preparation and practice, most people will be able to make a good start on even the most (initially) overwhelming puzzles!

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

6. Reasoning: Logic and Reasoning Backwards

Abstract

Starting from the end of the problem and working backwards to the original condition is a problem-solving technique that should be part of any good problem-solver’s arsenal. This is a problem-solving technique that is well known and is used in many disciplines. It is also known as retrograde analysis, backward chaining, and backward induction. As Holmes noted, however, familiarity with the usual approach of trying to push forwards until we reach a stumbling block, often giving up, often prevents us from trying a more successful approach of starting from the end and working backwards!

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

7. Pattern Recognition

Abstract

Our ability to recognize patterns is very useful in solving a variety of problems. Once we identify the pattern, it might be easier to suggest a solution – whether this might be to predict the next (or missing) symbol, number, action, or event (in the same way that fraud detection systems try to discover patterns in historical data and then use these patterns to predict which new transactions might be fraudulent (for more information on how patterns can help us to detect fraud, look for Benford’s law, which uses an unexpectedly predictable distribution of numerical digits to detect possible fraud)).

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

8. Enumerate and Eliminate

Abstract

One of the most powerful (and popular) problem-solving techniques applicable to many problems is a technique that is based upon the enumeration of all possible solutions and the systematic elimination of solutions which are “wrong.” By repeating this process of elimination, we zoom in into the (usually relatively small) subset of possible solutions. This was one of the methods used frequently by Holmes, as seen in the opening quote!

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

9. Simplify!

Abstract

Much of being a good problem-solver is utilizing clever strategies to make the solution to the problem more accessible. One of the most useful of these strategies is to simplify the problem. There are a number of different simplifications that will lead to progress towards the solution. One of these is to simply restate or rephrase the problem in terms that are more understandable. In mathematics and computer science, you will use techniques described as divide-and-conquer, decrease-and-conquer, and transform-and-conquer, but we’re going to talk about them here under the general banner of “simplify.”

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

10. Perform a Gedanken: “What If?” and “So What?”

Abstract

A gedanken (from the German) is a thought experiment, a hypothesis that is evaluated in the mind. There can be many reasons to perform a gedanken. One is that the actual experiment is too difficult or even impossible to perform. Many great discoveries are made with or start from a gedanken. Albert Einstein wondered how a light beam would look if he could travel right beside it, and this led to the development of special relativity. In 300 B.C., Euclid proved that there was infinitude of primes just by thinking and wondering, which is perhaps the most impressive gedanken of all. Euclid simply wondered, “What if there was a highest prime number?”

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

11. Simulation and Optimization

Abstract

Many real-world problems are so complex that it is impossible to conduct a full theoretical analysis. In such cases, we can turn to simulation – we make experiments and carefully record the results. We have already suggested simulation when we discussed Problem 7.5, where different tennis players might have different probabilities of winning their games against different opponents, and we have to determine the probability of twins playing against each other in the tournament.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

Challenges

Frontmatter

12. Probabilistic Reasoning

Abstract

Probability theory is the branch of mathematics that deals with estimating or calculating the degrees of likelihood. If it is impossible that a particular event would happen, it is given a probability of zero. If it is certain that a particular event would happen, it is given a probability of one. The probabilities of other events (expressed as fractions or decimals) lie between zero and one.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

13. Logical Reasoning

Abstract

This chapter contains a set of problems that do not require any high-level mathematics or formal training in logic. They do not require any knowledge of vocabulary or culture. There are no “tricks.” The problems just require a focused mind that is able to ask the appropriate “What if” questions and then follow the line of reasoning to the only result that makes logical sense.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

14. Geometric Reasoning

Abstract

The word geometry comes from the ancient Greek geo, meaning earth, and metron, meaning measurement. So, geometry originally meant measuring the earth. Today geometry has expanded to include the study of two- and three-dimensional shapes as well as how multiple three-dimensional shapes are connected and how multiple two-dimensional shapes will tessellate. Tessellation is covering a surface with shapes so that there are no gaps or overlapping, usually where we only have one shape. A mosaic floor is an example of a tessellated surface. (If you’re interested in reading more about tessellations, you can look at the works of Roger Penrose.)

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

15. Grand Challenges

Abstract

Here is a collection of challenging problems that require multiple problem-solving strategies and a solid foundation in understanding and framing the problem. These can be used as grand challenges that advanced students work on outside of the classroom or as a “special bonus” if the class is doing well.

Edwin F. Meyer III, Nickolas Falkner, Raja Sooriamurthi, Zbigniew Michalewicz

Backmatter

Titel: Guide to Teaching Puzzle-based Learning
verfasst von: Edwin F. Meyer III
Nickolas Falkner
Raja Sooriamurthi
Zbigniew Michalewicz
Copyright-Jahr: 2014
Verlag: Springer London
Electronic ISBN: 978-1-4471-6476-0
Print ISBN: 978-1-4471-6475-3
DOI: https://doi.org/10.1007/978-1-4471-6476-0

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