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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