asking questions that encourage inquiry-based …asking questions that encourage inquiry-based...
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ASKINGQUESTIONSTHATENCOURAGEINQUIRY-BASEDLEARNING
Howdoweaskquestionstodevelopscientificthinkingandreasoning?
IntroductionThisunitcontainsaselectionofprofessionalactivitiesthataredesignedtohelpteacherstoreflecton:
• characteristicsoftheirquestioningthatencouragestudentstoreflect,thinkandreason;• waysinwhichteachersmightencouragestudentstoprovideextended,thoughtfulanswers,
withoutbeingafraidofmakingmistakes;• thevalueofshowingstudentswhatreasoningmeansby'thinkingaloud'.
Theactivitiesdescribedbelowaregivenhereasa'menu'ofsuggestionstohelptheproviderselectandplan.Theyarepresentedinalogicalorder,buildingupknowledgeandexpertise.Anyplannedprofessionaldevelopmentprogramshouldofferopportunitiesforteacherstotrynewpedagogiesintheclassroomandthenreportbackandreflectontheirexperiences.Activity4isthereforeessentialintheprogram.
ActivitiesActivityA: Reflectingonthequestionsweask..................................................................................2 ActivityB: Whatkindsofquestionspromoteinquiry?......................................................................4 ActivityC: Observingalesson............................................................................................................6 ActivityD: Planalesson,teachitandreflectontheoutcomes.........................................................8 ActivityE: Solveaproblem,"thinkingaloud"..................................................................................10 Acknowledgement:ThismaterialisadaptedforPRIMASfrom:Swan,M;Pead,D(2008).Professionaldevelopmentresources.BowlandMathsKeyStage3,BowlandCharitableTrust.AvailableonlineintheUKat:http://www.bowlandmaths.org.ukItisusedherebykindpermissionoftheBowlandCharitableTrust.
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ACTIVITYA:REFLECTONTHEQUESTIONSWEASK
Timeneeded:15minutes.
Giveteacherstimetodiscussthefollowingquestionsinpairsorsmallgroups.Askthemtorecordtheircollectiveideasonacopyofthehandout.Thenholdaplenarydiscussiontocollectandshareideas.Asteacherssuggestdifferentpurposes,askthemtogiveparticularexamples.Teachersaskmanydifferenttypesofquestionsandtheyservemanydifferentpurposes.
• Whatdifferenttypesofquestionsarethere?• Whatdifferentfunctionsdothesequestionsserve?• Whichtypesofquestionsdoyouusemostfrequently?• Whatcommonmistakesdoyoutendtomakewhenaskingquestions?
Whataretheireffects?
Weaskquestionsformanypossiblereasons,includingthefollowingeight:• tointerest,engageandchallenge;• toassesspriorknowledgeandunderstanding;• tostimulaterecall,inordertocreatenewunderstandingandmeaning;• tofocusthinkingonthemostimportantconceptsandissues;• tohelpstudentsextendtheirthinkingfromthefactualtotheanalytical;• topromotereasoning,problemsolving,evaluationandtheformationofhypotheses;• topromotestudents’thinkingaboutthewaytheyhavelearned;• tohelpstudentstoseeconnections.Thefollowingisalistofsomeofthemorecommonmistakesthatteachersmake:• Askingtoomanytrivialorirrelevantquestions.• Askingaquestionandansweringityourself.• Simplifyingthequestionwhenstudentsdon'timmediatelyrespond.• Askingquestionsofonlythemostableorlikeablestudents.• Askingseveralquestionsatonce.• Askingonlyclosedquestionsthatallowoneright/wrongpossibleanswer.• Asking'guesswhatisinmyhead'questions,whereyouknowtheansweryouwanttohearand
youignoreorrejectanswersthataredifferent.• Judgingeverystudentresponsewith'welldone','nearlythere''notquite'.'Welldone'can
discouragealternativeideasbeingoffered.• Notgivingstudentstimetothinkordiscussbeforeresponding.• Ignoringincorrectanswersandmovingon.
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Handout1. Thinkingaboutwhyweaskquestions
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ACTIVITYB: WHATKINDSOFQUESTIONSPROMOTEINQUIRY?
Timeneeded:20minutes.
Giveteacherstimetodiscussthefollowingissues.AskthemtorecordtheircollectiveideasonacopyofHandout2shown.
• Whattypesofquestionspromoteinquiry-basedlearning?• Givesomeexamplesthatyouhaverecentlyused.• Handout3describessomecharacteristicsofeffectivequestioning.
Reflectontheimplicationsoftheseideasforyourownpractice.
AfterwardsgivethemcopiesofHandout3.Thiscontainsasummaryofsomeresearchfindingsintoquestioning.Thisshowsthateffectivequestioningdisplaysthefivecharacteristics:• Theteacherplansquestionsthatencouragethinkingandreasoning.• Everyoneisincluded.• Studentsaregiventimetothink.• Theteacheravoidsjudgingstudents'responses.• Students'responsesarefollowedupinwaysthatencouragedeeperthinking.
Inviteteacherstodiscusstheresearchfindingsinsmallgroups.
• Whichoftheseprinciplesdoyouusuallyimplementinyourownteaching?• Whichprinciplesdoyoufinditmostdifficulttoimplement?Whyisthis?
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Handout2. Whatkindsofquestionspromoteinquiry-basedlearning?
Handout3. Fiveprinciplesforeffectivequestioning
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ACTIVITYC: OBSERVEANDANALYSEALESSON
Timeneeded:30minutes.
WorkontheproblemshownonHandout4.
• Comparethetwosolutions.Whichdoyouconsiderbetterandwhy?NowwatchwatchthevideoclipofGwen'slessonandconsiderthefollowingquestions:
• WhichofthefollowingprinciplescanyouseeGwenusinginherlesson?Giveexamples.o Planquestionsthatencouragethinkingandreasoning.o Askquestionsinwaysthatincludeeveryone.o Givestudentstimetothink.o Avoidjudgingstudents'responses.o Followupstudents'responsesinwaysthatencouragedeeperthinking.
• Whatdoyouthinkstudentslearnedfromthelesson
• Planquestionsthatencouragethinkingandreasoning.
Gwenhascarefullyplannedthelessonsothatthefocusisnotonanswersbutonreasoning.Shebeginsthelessonbyemphasisingthatlessonwillbefocusedonthequalityofstudents'thinking,reasoningandexplainingandonlisteningtoeachother.Thismessageisreinforcedthroughoutbyherinteractionswithstudents:"Doyouwanttoexplaintomewhythatisfair?";"Howareyouthinkingofthejourney?canyouexplaintome...";"Howareyougoingtoworkout....";"Whatelseistherethatmighthelpyou?That'sallI'mgoingtosay.Keepthinking."
• Askquestionsinwaysthatincludeeveryone.Gwenhasintroduceda'nohandsup'rule,sothatshecanchoosewhowillrespondtoherquestionsandsothatstudentscontinuetothinkwhileresponsesaremade.Shetriestoencouragearangeofresponsesandasksstudentstocommentoneachothers'responses.
• Givestudentstimetothink.Gwengivesstudentstimetothinkindividuallybeforediscussing,sothattheyallhavesomethingtoshare.
• Avoidjudgingstudents'responses.Gwencollectsthestudents'initialideasandwritestheseontheboard.Sheasksfollow-upquestionsforclarification("Justexplainalittlebitmoreaboutthat.")andthanksthemfortheircontributions,butdoesnotjudgeresponseswith'Welldone",or"That'snotquiteright."
• Followupstudents'responsesinwaysthatencouragedeeperthinking.Forexample,Gweninvitesstudentstoelaborate:"Canyoujustsaythatagain?";asksstudentstothinkaloud:"CanyouexplainyourthinkingAlex?";cuesalternativeresponses:"Bethany,whatdoyouthinkisbestoutofHannah'ssuggestions?";"Girls,canyouseehowthatmighthelpyou?...Howmightthathelpyou?".
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Handout4. Observingalesson
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ACTIVITYD:PLANALESSON,TEACHITANDREFLECTONTHEOUTCOMES
Timeneeded:
• 15minutesdiscussionbeforethelesson• 1hourforthelesson• 15minutesafterthelesson
Chooseaproblemtotrywithyourclass.UsethepromptsonHandout5toplanalessonthatwillpromotethinkingandreasoning.
• Howwillyouorganisetheclassroomandtheresources?• Howwillyouintroducethequestioningsession?• Whichgroundruleswillyouestablish?• Whatwillbeyourfirstquestion?• Howwillyougivetimeforstudentstothinkbeforeresponding?• Willyouneedtointerveneatsomepointtorefocusordiscussdifferentstrategiesthey
areusing?• Whatquestionswillyouuseinplenarydiscussionsduringortowardstheendofthe
lesson?
Becauseteacherswillbefocusingonthequestionsthattheyuseandthewaythatthestudentsanswerthosequestionswesuggestthattheyaudio-recordsomewholeclassquestioninglessonfordiscussioninActivity5.Asamplelessonplanusingthe"SharingPetrolCosts"problemisshownonHandout6.Thismaybeusedasamodelforteacherstofollow.Afteryouhavetriedoutyourlessonwithyourownstudents,discussthefollowingissues:
• Whichquestionsappearedtopromotethemostthoughtfulandreasonedresponsesfromstudents?Whywasthis?
• Whichquestionsdidn'tworksowell?Whywasthis?• Whichofthefollowingfourprinciplesdidyouuse?Giveexamples.
o Planquestionsthatencouragethinkingandreasoning.o Askquestionsinwaysthatincludeeveryone.o Givestudentstimetothink.o Avoidjudgingstudents'responses.o Followupstudents'responsesinwaysthatencouragedeeperthinking.
• Whatwillyoudodifferentlynexttime?
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Handout5. Planningforeffectivequestioning
Handout6. Alessonplanonsharingpetrolcosts
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ACTIVITYE: SOLVEAPROBLEM,"THINKINGALOUD"
Timeneeded:20minutes.
Teachersusuallypresentscienceandmathematicsasthoughtheyareasetoftidyresultsandprocedures.Studentsoftendon'trecognisetheinvisible,messyprocessesthatgooninsidetheheadsofscientists.Onereasonwhysomestudentsarereluctanttopersististhattheydonotrecognisethatitisperfectlynaturaltogetstuck,makemistakes,backtrackandlookforalternativestrategies.Itisthereforehelpfulforateachertomodeltheseprocessesbytacklingaproblemfromstarttofinish,thinkingaloudandinvolvingtheclassbycarefulquestioning.Intheprofessionaldevelopmentsession,itisusefulforteacherstothinkthroughthisprocessbytacklingaproblemtogether,'thinkingaloud'.Tryworkingoutananswertothefollowingproblem,thinkingaloudasyoudoso:
Abouthowmanydentistsarethereinyourcountry?Afterwardsthinkwhatitwouldfeellike,doingthiswithaclass,notknowingtheanswerbeforehand.
Ifyouareworkingwithagroupofteachers,asktwovolunteerstotackletheproblempublicly,thinkingaloudatthefrontoftheroom.Theotherteachersshouldtaketheroleofthepupilsandtrytoassistwhenaskedtodoso.Afterwards,discussotherpossiblestrategiesthatmighthelpstudentsrealisethementalprocessesthatscientistsandmatehmaticiansuseeveryday.Thesemayinclude,forexample:
• Makingavideoofyourselfandsomecolleaguessolvingaproblem,whilethinkingaloudanddiscussingthiswithyourclass.Wehaveincludedonesuchvideoontheresource.
• Studentswatchingorreadingbiographiesofmathematiciansandscientistsastheytellabouttheirstrugglesandbreakthroughs.Seeforexample,AndrewWiles'storyonYoutube:http://video.google.com/videoplay?docid=8269328330690408516
• Afterworkingonaproblem,readingsolutionattemptsthathavebeenproducedbyotherstudentsthatrevealerrorsandthemultipletrialsanddeadendsthathavebeenencountered.Askthestudentstoworktogethertofind,correctandcommentonthe‘errorsinreasoning’.Theyshouldalsocommentonwherethereasoningwasgoodsothattheymayusetheseideasagain.
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SUGGESTEDFURTHERREADING
EffectivecollectionofquestionsformathematicalthinkingBills,C.,Bills,L.,WatsonA.,J.Mason(2004),Thinkers,AssociationofTeachersofMathematics,Derby.www.atm.org.ukMoreeffectivequestionsforpromotingmathematicalthinkingBills,L.Latham,P.andWilliams,H.(2002)‘Encouragingalllearnerstothink’MathematicsTeaching,181,pp14-16http://www.atm.org.uk/mt/archive/mt181files/ATM-MT181-14-16.pdfQuestioningtoenableeffectivelearningandassessmentforlearningLee,C.(2006)LanguageforLearningMathematics–assessmentforlearninginpractice.OpenUniversityPress.Questioninginthemathematicsclassroom,whatreallyhappensandwhatcouldhappen?Martin,N.(2003),‘Questioningstyles’,MathematicsTeaching,184,pp18-19http://www.atm.org.uk/mt/archive/mt184files/ATM-MT184-18-19-mo.pdfIsquestioningreallyimportant?Smith,J.(1986),‘QuestioningQuestioning’,MathematicsTeaching,115,p47.ThequestionsthatmakepupilsthinkmathematicallyWatson,A.andMason,J.(1998)QuestionsandPromptsforMathematicalThinking,AssociationofTeachersofMathematicsDerby,www.atm.org.uk