Table Of ContentUndergraduate Topics in Computer Science
Edwin F. Meyer III
Nickolas Falkner · Raja Sooriamurthi
Zbigniew Michalewicz
Guide to Teaching
Puzzle-based
Learning
Undergraduate Topics in Computer Science
Undergraduate Topics in Computer Science (UTiCS) delivers high-quality instructional content for
undergraduatesstudyinginallareasofcomputingandinformationscience.Fromcorefoundationaland
theoreticalmaterialtofinal-yeartopicsandapplications,UTiCSbookstakeafresh,concise,andmodern
approachandareidealforself-studyorforaone-ortwo-semestercourse.Thetextsareallauthoredby
established experts in their fields, reviewed by an international advisory board, and contain numerous
examplesandproblems.Manyincludefullyworkedsolutions.
Forfurthervolumes:
http://www.springer.com/series/7592
Edwin F. Meyer III (cid:129) Nickolas Falkner (cid:129)
Raja Sooriamurthi (cid:129) Zbigniew Michalewicz
Guide to Teaching
Puzzle-based Learning
EdwinF.MeyerIII NickolasFalkner
BaldwinWallaceUniversity UniversityofAdelaide
Berea,Ohio,USA SouthAustralia,Australia
RajaSooriamurthi ZbigniewMichalewicz
CarnegieMellonUniversity UniversityofAdelaide
Pittsburgh,Pennsylvania,USA SouthAustralia,Australia
SeriesEditor
IanMackie
AdvisoryBoard
SamsonAbramsky,UniversityofOxford,Oxford,UK
KarinBreitman,PontificalCatholicUniversityofRiodeJaneiro,RiodeJaneiro,Brazil
ChrisHankin,ImperialCollegeLondon,London,UK
DexterKozen,CornellUniversity,Ithaca,USA
AndrewPitts,UniversityofCambridge,Cambridge,UK
HanneRiisNielson,TechnicalUniversityofDenmark,KongensLyngby,Denmark
StevenSkiena,StonyBrookUniversity,StonyBrook,USA
IainStewart,UniversityofDurham,Durham,UK
ISSN1863-7310 ISSN2197-1781(electronic)
UndergraduateTopicsinComputerScience
ISBN978-1-4471-6475-3 ISBN978-1-4471-6476-0(eBook)
DOI10.1007/978-1-4471-6476-0
SpringerLondonHeidelbergNewYorkDordrecht
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To my Parents: Both PhDs who raised six
children, each of whom has earned a PhD.
Thanks for continually holding us to such
high standards.
E. F. M.
To my wife, Katrina, and my friend, Marita,
bothofwhombelievedthattherewasmoreto
me.
N. F.
To my sons, Anand and Santosh, who are
each other’s puzzle and solution.
R. S.
To my friend, Paweł Kerntopf, who, during
my high-school years, introduced me to the
world of mathematical puzzles.
Z. M.
ThiSisaFMBlankPage
Introduction to Teaching Puzzle-based
Learning: What Is It and What Is This Book
About?
Nowmorethanever,aneducationthatemphasizesgeneral
problemsolvingskillswillbeimportant.–BillGates
Whatismissinginmostcurricula–fromelementaryschoolallthewaythroughto
university education – is coursework focused on the development of problem-
solving skills. Most students never learn how to think about solving problems.
Usuallytheyarejusttrainedtoapplyparticularformulaetoaproblemandmostof
theireffortisrelatedto“calculatingtheanswer.”
Students are not prepared for framing and solving problemsthat are given ina
descriptive form: they have serious difficulties in extracting relevant information,
eliminatingnoise (that is always present indescriptive-type problems), building a
model ofthe problem,andreasoning aboutthesolution.Further, throughouttheir
education,theyareconstrained toconcentrateonspecific questionsatthe backof
chapters.
So,withoutmuchthinking,theyapplythematerialfromeachchaptertosolvea
fewproblemsgivenattheendofeachchapter(whyelsewouldaproblembeatthe
end of the chapter?). One of our favourite examples to illustrate this point is a
puzzleonbreakingachocolatebar:
Arectangularchocolatebarconsistsofm(cid:1)nsmallrectanglesandyouwishtobreakitinto
itsconstituentparts.Ateachstep,youcanonlypickuponepieceandbreakitalonganyof
itsverticalorhorizontallines.Howshouldyoubreakthechocolatebarusingtheminimum
numberofsteps(breaks)?
If you do not know the answer, which textbook would you search to discover the
solution? Textbooks on optimization? Simulation? Strategies? Games? Other
textbooks? Or it might be that someone wrote a book on chocolates where in
Chapter 7 there is a full discussion on efficient breaking strategies of a chocolate
bar?Veryunlikely.Thesameappliestosolvingmanyreal-worldproblems:which
textbook should you search to find an approach that would lead to the solution?
Some individuals (including the authors of this book), when interviewing job
candidates, would ask them to solve problems during the interview. When a
candidate responds, “I didn’t have that in school,” they would reply, “Yeah, I
knowyoudidn’t;that’swhyI’maskingit.”
vii
viii IntroductiontoTeachingPuzzle-basedLearning:WhatIsItandWhatIsThisBookAbout?
In the introduction of Heard on the Street, Quantitative Questions from Wall
StreetJobInterviews,1theauthorwrites:“Thisbookbridgestheconsiderablegap
between the typical education and the knowledge required to successfully answer
job interview questions. The considerable gap arises because interviewers must
separate the wolves from the sheep. The sheep are confined by the boundaries of
their education. The wolves are not. Of course, most interviewers are wolves.
Unfortunately, most interviewees are sheep. The ‘butchering’ that can take place
intheseinterviewsishorrific.”
Clearly, it is not surprising that most students are ill prepared for framing and
addressing real-world problems. When they finally enter the real world, they sud-
denly find that problems do not come with associated formulas, instructions, or
textbooks. Although many educators are interested in teaching “thinking skills”
rather than “teaching information and content,” the fact remains that young people
often have serious difficulties in independent thinking (or problem-solving skills)
regardless of the nature of a problem. As Alex Fisher wrote in his book, Critical
Thinking2: “... 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
teachingthecontentwhichbelongstotheirspecialsubject.Increasingly,educators
havecometodoubttheeffectivenessofteaching‘thinkingskills’inthisway,because
most students simply do not pick up the thinking skills in question.” The curricular
approach of emphasizing “remembering” over “reasoning” has dominated the edu-
cationalarena–whetherinhistory,physics,geography,oranyothersubject–almost
ensuringthatstudentsneverlearnhowtothinkaboutsolvingproblemsingeneral.
Overthepastfewdecades,variouspeopleandorganizationshaveattemptedto
addressthiseducationalgapbyteaching“thinkingskills”basedonsomestructure
(e.g. critical thinking, constructive thinking, creative thinking, parallel thinking,
verticalthinking,lateralthinking,confrontationalandadversarialthinking).How-
ever, all these approaches are characterized by a departure from mathematics as
theyconcentratemoreon“talkingaboutproblems”ratherthan“solvingproblems.”
Itisourviewthatthelackofproblem-solvingskillsingeneralistheconsequenceof
adecreasinglevelofmathematicalsophisticationinmodernsocieties.
Itseems thatadifferentapproach isneeded.Manyindividualsandeducational
organizationshaverecognizedthisneedsometimeago.Manyinstructorshavebeen
introducing puzzles and various problem-solving activities in more or less formal
way over the last twenty years. For example, in How to Solve It: Modern
Heuristics3 the authors introduced a variety of puzzles to support a course on
modernheuristicmethods.A.LevitinandM.Levitinhavebeenbasingtheircourses
onpuzzles.4TimBellfromUniversityofCanterbury(NewZealand)incorporated
1CrackTF(2008)Heardonthestreet,quantitativequestionsfromWallStreetjobinterviews,11th
edn.Typesetbytheauthor,USA.
2FisherA(2001)Criticalthinking:anintroduction.CambridgeUniversityPress,Cambridge.
3MichalewiczZ,FogelDB(2000)Howtosolveit:modernheuristics.Springer,Berlin/NewYork.
4LevitinA,LevitinM(2011)Algorithmicpuzzles.OxfordUniversityPress,Oxford/NewYork.
IntroductiontoTeachingPuzzle-basedLearning:WhatIsItandWhatIsThisBookAbout? ix
puzzlesintotheirComputerSciencecurriculum.HisCSUnplugged5isacollection
offreelearningactivitiesthatteachComputerSciencethroughengaginggamesand
puzzles.Puzzle-basedproblemsolvinghasbeenofferedasafor-creditcoursesince
2002attheBaldwinWallaceUniversity(Ohio,USA)–andnowtherearetwosuch
problem-solving courses that Ed Meyer teaches in the graduate business program
(not to mention his teaching of problem solving during the summer at Gedanken
Institute for problem solving for many years now). His Naked Physics6 contains
64problems(fromphysicsandmathematics)todevelopstudents’problem-solving
skills.AtCarnegieMellonUniversity,Puzzle-basedLearninghasbeenofferedasa
very popular freshmen seminar since 2009. Abbreviated versions of this course
have been offered to range of audiences from middle school, to high-school
outreach programs, to graduate school, to managers and engineers in industry
workshops,andtoretiredprofessionalsincontinuingeducationprograms.
Clearly,manyindividualsallovertheworldexperimentedwithsuchapproaches
over many years; however, the term Puzzle-based Learning emerged just a few
yearsago.7Asitwasthecasewithallearlierattempts,itfocusesongettingstudents
to think about framing and solving unstructured problems (those that are not
encountered at the end of some textbook chapter). The idea is to increase the
student’smathematical awareness andproblem-solvingskillsby solvingavariety
ofpuzzlesandreflectingontheirsolutionprocesses.
SowhatisPuzzle-basedLearning?
Puzzle-based Learning is a foundational approach to develop thinking skills,
mental stamina and perseverance at solving problems. We focus on unstructured,
generallycontext-free(i.e.,doesnotrequiredomainknowledge)andalmostalways
entertainingproblems,betterknownaspuzzles.
Overtheyears,researchershavedevelopedsetsofrulesforsolvingpuzzlesand
problemsanditislefttothereadertoidentifyonethatworksforhisorherteaching
situation. However, there are a couple of places to start looking. Gyorgy Po´lya8
presentedfourfundamentalstepstoproblemsolving:
1. Understandingtheproblem(Recognizingwhatisaskedfor)
2. Devisingaplan(Respondingtowhatisaskedfor)
3. Carryingouttheplan(Developingtheresultoftheresponse)
4. Lookingback(Checkingwhatdoestheresulttellme)
andalsoprovideda(large)listofdifferentproblemsolvingapproaches(heuristics)
that would give the puzzler a starting point or a way to rearrange the problem to
5Seecsunplugged.org.
6MeyerEF(2011)Nakedphysics.GedankenPublishing.
7MichalewiczZ,MichalewiczM(2008)Puzzle-basedlearning:anintroductiontocriticalthink-
ing,mathematics,andproblemsolving.HybridPublishers,Melbourne.
8GyorgyPo´lyawasborninBudapeston13December1887.FormostofhiscareerintheUnited
States,hewasaprofessorofmathematicsatStanfordUniversity.Heworkedonagreatvarietyof
mathematicaltopics,includingseries,numbertheory,combinatorics,andprobability.Inhislater
days,GyorgyPo´lyaspentconsiderableeffortontryingtocharacterizethegeneralmethodsthat
peopleusetosolveproblems,andtodescribehowproblemsolvingshouldbetaughtandlearned.
