Student responses as a basis for whole class discussions in technology-rich environment
Full text
(2) . . )DE45>DB5C@?>C5C1C121C9C6?BG8?<53<1CC49C3ECC9?>C9>D538>?<?7I B9385>F9B?>=5>DC .ARIA'AHLGRENAND.ATS#RUNSTRnM ,ARLSTAD6NIVERSITY %EPARTMENTOF.ATHEMATICSAND$OMPUTER4CIENCE 4WEDEN MARIAFAHLGREN!KAUSE -?@JG8G<II<GFIKJ8JKL;PF==FLILGG<IJ<:FE;8IPJ:?FFCK<8:?<IJiLJ<F=FEE<:K<; C8JJIFFD-<:?EFCF>PKFJ<C<:KJKL;<EKI<JGFEJ<JKF:FDGLK<I98J<;8:K@M@K@<J8E;KF LJ<K?<J<I<JGFEJ<JKFC8LE:?JL::<JJ@M<JK8><JF=8GC8EE<;N?FC<:C8JJ;@J:LJJ@FE CK?FL>? K?< GI<G8I8K@FE =FI K?< :C8JJ ;@J:LJJ@FE N8J HL@K< JL::<JJ=LC @K N8J 8 :?8CC<E><=FIK?<K<8:?<IJKF:FE;L:KK?<N?FC<:C8JJ;@J:LJJ@FEG8IK@:LC8ICP@EGFJ@E> JG<:@=@:HL<JK@FEJ98J<;FE8GGIFGI@8K<JKL;<EKI<JGFEJ<J $<PNFI;J :FEE<:K<; :C8JJIFFD K<:?EFCF>P D8K?<D8K@:J <;L:8K@FE N?FC<:C8JJ ;@J:LJJ@FE *N A PREVIOUS STUDY 'AHLGREN #RUNSTRnM WE EXAMINED STUDENTS WRITTEN EXPLANATIONS OF AN OBSERVATION MADE IN A DYNAMIC MATHEMATICS SOFTWARE %.4 ENVIRONMENT 8E FOUND THAT FEW STUDENTS OFFERED A COMPLETE MATHEMATICAL EXPLANATION)OWEVER MOSTOFTHEMPROVIDEDELEMENTSOFEXPLANATION MANYOFWHICH THATCOULDBEUSEFULASSTARTINGPOINTSFORAWHOLECLASSDISCUSSION5HISHIGHLIGHTEDA NEED TO PROVIDE SUPPORT FOR TEACHERS IN SURVEYING STUDENTS COMPUTERBASED WORK PREFERABLY IN REAL TIME TO INFORM SUCH A DISCUSSION 'OR EXAMPLE THE PARTICIPATING TEACHERSREQUESTEDTECHNOLOGICALSUPPORTTOMONITORALLTHESTUDENTSWORKANDTOEASILY CHOOSEDIFFERENTSTUDENTSOLUTIONSFOR WHOLECLASSDISCUSSION/OWADAYS THEREISA TYPEOFTECHNOLOGYAVAILABLETHATCANSUPPORTTEACHERSTOACHIEVETHISWHICHWEREFER TOASFEE<:K<;C8JJIFFD-<:?EFCF>P $$5 5HISLEDUSTOCONDUCTACASESTUDYINA4WEDISHUPPERSECONDARYSCHOOL WORKINGWITH FOUR TEACHERS AND THEIR CLASSES 5HE OVERARCHING AIM WAS TO IDENTIFY CRITICAL ASPECTS WHENUSING$$5TOPREPAREANDCONDUCTAWHOLECLASSDISCUSSIONBASEDONSTUDENTS RESPONSES TO COMPUTERBASED ACTIVITIES " TEACHING UNIT CONSISTING OF THREE STAGES @EKIF;L:K@FE G8@INFIB ANDN?FC<:C8JJ;@J:LJJ@FEWASDESIGNEDANDTRIALLEDWITH THE FOUR CLASSES *N AN EARLIER PAPER WE HAVE PROVIDED A DETAILED DESCRIPTION OF THE DESIGNOFTHETEACHINGUNIT 'AHLGREN#RUNSTRnM *NANOTHERPAPERWEHAVE REPORTEDONTHETEACHERSUTILIZATIONOFTHE$$5DURINGTHEPAIRWORKSTAGE 'AHLGREN #RUNSTRnM 5HEFOCUSINTHISPAPERISONTHELASTSTAGEOFTHETEACHINGUNIT THE WHOLECLASS DISCUSSION 5HE RESEARCH QUESTION IS 8HAT ARE THE CHALLENGES FOR TEACHERSWHENUSING$$5TOSELECTSTUDENTRESPONSES ANDUSETHESERESPONSESTOLAUNCH SUCCESSIVESTAGESOFAPLANNEDWHOLECLASSDISCUSSION ,$!!(((*(($#($#()*#)'(%$#(( 5HEIMPORTANCEOFFOLLOWINGUPSTUDENTSPREVIOUSWORKINPAIRSORSMALLGROUPSAND USINGITASABASISFORAWHOLECLASSDISCUSSIONISWELLESTABLISHEDINTHEMATHEMATICS .+ ""!&*$/+#0%"+,& +*#"."* "
(3)
(4) . . .
(5) EDUCATION RESEARCH LITERATURE EG 'RANKE ,AZEMI #ATTEY 4TEIN &NGLE 4MITH )UGHES "TTHESAMETIME THISLITERATUREHIGHLIGHTSTHECHALLENGEFOR TEACHERS TO ORCHESTRATE STUDENT ACTIVE CLASSROOM DIALOGUES 3UTHVEN )OFMANN 4TEINETAL 5OADDRESSTHIS 4TEINETALDEVELOPEDAMODELCONSISTINGOF FIVEPRACTICESTOSUPPORTTEACHERSINTHEIRPLANNINGANDIMPLEMENTATIONOFWHOLECLASS DISCUSSION5HEFIRSTPRACTICE "NTICIPATINGLIKELYSTUDENTRESPONSES| P RELATES TO THE PLANNING OF THE LESSON 5HE SECOND THIRD AND FOURTH PRACTICES MONITORING SELECTINGANDSEQUENCINGSTUDENTRESPONSES ALLRELATETOTHESTAGEOFTHELESSONWHERE STUDENTS ARE WORKING ON ACTIVITIES 'INALLY THE FIFTH PRACTICE CONCERNS THE COLLECTIVE STAGEOFTHELESSONWHEREDIFFERENTSTUDENTRESPONSESAREDISPLAYEDANDDISCUSSEDINTHE WHOLE CLASS "LTHOUGH THE MODEL IS PRIMARILY INTENDED TO SERVE AS A ROAD MAP FOR TEACHERS IT PROVIDES A THEORETICAL FRAME WHICH RESEARCHERS CAN USE |AS A WAY OF CONCEPTUALIZINGINVESTIGATIONSOFCLASSROOMDISCOURSE 4TEINETAL P AS WELL 'OR EXAMPLE $USI .ORSELLI AND 4ABENA USED THIS MODEL WHEN INVESTIGATINGHOW$$5COULDBEUSEDTOFACILITATEWHOLECLASSACTIVITIES ,IERANETAL DEMONSTRATETHECHALLENGEFORTEACHERSTOORCHESTRATEFOLLOWUP DISCUSSIONS WHICH TAKE STUDENTS COMPUTERBASED WORK INTO ACCOUNT *N THEIR STUDY ONLYONEOFTHE THREE PARTICIPATINGTEACHERSREALLYINQUIREDINTOSTUDENTSTHINKINGAND UTILIZED IT AS A POINT OF DEPARTURE FOR A WHOLECLASS DISCUSSION ALTHOUGH SUCH DISCUSSIONSWEREANEXPECTEDPARTOFTHERESEARCHERDESIGNEDLESSONS)OWEVER THIS WASNOTMADEEXPLICITINTHEACCOMPANIEDTEACHERGUIDANCESINCEITDIDNOTSPECIFYHOW TOPERFORMTHEDISCUSSION ALTHOUGHITINCLUDEDSUGGESTIONSFORMATHEMATICALCONTENT TO DISCUSS 4IMILARLY 3UTHVEN AND )OFMANN IN A DESIGN STUDY IDENTIFIED SITUATIONSWHEREDISAPPOINTINGCLASSROOMMATHEMATICALDISCUSSIONAROSEFROMTEACHERS NOTCAPITALISINGONPROMISINGSTUDENTCONTRIBUTIONS5OADDRESSTHIS THEYSUGGEST THERE IS A NEED TO SENSITISE TEACHERS TYPICALLY THROUGH MAKING THE POTENTIAL OF SUCH CONTRIBUTIONSMOREEXPLICITINTHETEACHERGUIDANCE ")$ 5HEFIELDWORKFORTHISSTUDYWASCONDUCTEDINSPRINGWITHFOURUPPERSECONDARY SCHOOLTEACHERSANDTHEIRCLASSESUNDERTAKINGTHESTAGETEACHINGUNITALREADYREFERRED TO *N UNDERTAKING THE UNIT TWO TYPES OF TECHNOLOGY WERE USED A DYNAMIC MATHEMATICS SOFTWARE %.4 IN THIS CASE <F <9I8 AND A SPECIFIC $$5 <JDFJ C8JJIFFD :K@M@K@<J %URING THE PAIRWORK STAGE THE STUDENTS USED TWO COMPUTERS ONEWITH <F <9I8ANDONEWITHANEWORKSHEETIN<JDFJ*NCONTRASTTOTHE%.4 THE$$5WASANOVELTEACHINGRESOURCEFORTHEPARTICIPATINGTEACHERS 8HEN PLANNING THE TEACHING UNIT THEN WE GAVE PARTICULAR ATTENTION TO PROVIDING TEACHERSWITHGUIDANCEONMAKINGUSEOFTHE$$5TOEXAMINESTUDENTSWORKDURING THECENTRALPAIRWORKSTAGEOFTHELESSON ANDTOPREPAREEXAMPLESFROMTHISWORKFOR USE IN THE CONCLUDING WHOLECLASS DISCUSSION STAGE 5HIS GUIDANCE WAS INFORMED PRIMARILYBYTHE4TEINETALMODEL WITHTHENECESSARYMATHEMATICALCONCEPTUALDETAIL DERIVEDTHROUGHANALYSISOFSTUDENTRESPONSES GATHEREDFROMEIGHTCLASSESINAPREVIOUS . .+ ""!&*$/+#0%"+,& +*#"."* "
(6)
(7) . .
(8) . . STUDY 'AHLGREN #RUNSTRnM . TO THE EXPLANATION TASK FEATURED IN THE LESSON 5ASKCIN'IGURE 5HISANALYSISPROVIDEDINFORMATIONABOUTANSWERSLIKELYTOBE PRODUCEDBYSTUDENTSDURINGTHEPAIRWORKSTAGE IERELATINGTOTHEFIRSTPRACTICEINTHE 4TEINETAL MODEL}"NTICIPATINGLIKELYSTUDENTRESPONSES. 2UADRATICFUNCTIONSCANALWAYSBEWRITTENINTHEFORM. = + + WHEREAND. AREREALNUMBERSAND ≠ '/,-#!-2+!!#'!-",%#+#'0"-02-"/%.( %-+,-"!+)",+##'2(.+ (0'0(+, "/%.( -"(',-'-' (.'#'-"((+#'-,2,-&(0 #/&-"&-#%1)%'-#('0"2-"/%.( ' (.'#'-"#,02. 97EB5 *8569BCDD1C;C9>3<E49>71B5AE5CD6?B1>5H@<1>1D9?>*1C; 3. %ETAILEDSTEPBYSTEPGUIDANCE BASEDONTHE4TEINETALMODEL ANDEXPLOITING PARTICULAR FUNCTIONALITIES OF $$5 WAS DEVELOPED AND DISCUSSED WITH THE TEACHERS %URINGTHEPAIRWORKSTAGE TEACHERSAREENCOURAGEDTOUSETWODIFFERENT$$5VIEWSTO MONITOR THE STUDENTS WORK *N THE ,LDD8IP VIEW THE TEACHER CAN SURVEY ALL THE STUDENTS PROGRESSION ACROSS THE WHOLE ACTIVITY AND IN THE ,G<:@=@: @K<D VIEW THE TEACHERCANMONITORALLSTUDENTSANSWERSTOAPARTICULARTASK RELATINGTOTHESECOND PRACTICEINTHE4TEINETALMODEL}.ONITORINGSTUDENTRESPONSES *NTHELATTERVIEW THETEACHERALSOCANSELECTAPPROPRIATESTUDENTRESPONSESTODISPLAYANDUSEASABASIS FORTHEWHOLECLASSDISCUSSION RELATINGTOTHETHIRDPRACTICEINTHE4TEINETALMODEL} 4ELECTING STUDENT RESPONSES *N THE VIEW THAT WE DENOTE )I<J<EK8K@FE GI<G8I8K@FE VIEW THETEACHERSCANSEQUENCETHESELECTEDSTUDENTRESPONSES RELATINGTOTHEFOURTH PRACTICE IN THE 4TEIN ET AL MODEL } 4EQUENCING STUDENT RESPONSES 5O SUPPORT THE SELECTIONANDSEQUENCING THEGUIDANCEINCLUDEDRESPONSECATEGORIESTOSEARCHFORAS WELLASASUGGESTEDSEQUENCINGOFTHERESPONSES SEE'IGURE '-# 2',%-('(+-0())+()+#-,-.'-+,)(',, +(&-"# +'--!(+#, )-#'!-"',0+-(,$#('%2#'#-#'!-"-#-#,0"+-"!+)" ! +(/##'!! !3# #-#'-+,-,-"&1#,- 4(++ ++#'!-((+ (&)+#'!0#-"-",-'+ !3(++,)(',-(4 '#-#'!-"-#$(+-"-# $ . 97EB5
(9) H35B@D6B?=D85D51385B7E941>359<<ECDB1D9>7D85B5C@?>C531D57?B95C. .OREOVER THEGUIDANCEINCLUDESAPROBINGQUESTIONTOPOSEINRELATIONTOEACHOFTHE DIFFERENT RESPONSE CATEGORIES SEE 'IGURE DURING THE WHOLECLASS DISCUSSION 5HE DETAILED THINKING BEHIND THE RECOMMENDED SEQUENCING AND THE CORRESPONDING QUESTIONSISREPORTEDIN'AHLGRENAND#RUNSTRnM BUTTHEGISTSHOULDBECLEAR FROMINSPECTIONOFTHETWO5ABLES"TAPLANNINGMEETING THEGUIDANCEWASDISCUSSED ANDTHERESEARCHERSANDTHETEACHERSAGREEDTHATITWASAPPROPRIATE .+ ""!&*$/+#0%"+,& +*#"."* "
(10)
(11) . .
(12) .
(13) ! ! !!!$ #0"-#,-"#,-#'-#('-0' ,+#)-#('''1)%'-#('#'&-"&-#, % " %! !"!!
(14)
(15) !!%! !% %% %%# "!%! !!"! & ! !!! ! ! !&% $& ",#,.,,#(',,"(.%%-(%,,!+&'-('0"-(',-#-.-,'))+()+- 1)%'-#('#'-"#,)+-#.%+,,$. 97EB5 H35B@D6B?=D85D51385B7E941>35C8?G9>7D85AE5CD9?>CCE775CD54. )$!!)$###!.(( 8E SOUGHT THEN TO EXAMINE HOW TEACHERS MADE USE OF $$5 IN PREPARING FOR AND IMPLEMENTING THE WHOLECLASSDISCUSSION STAGE OF THE TEACHING UNIT 5HE MAIN DATA CONSISTOFSCREENRECORDINGSOFEACHTEACHERSCOMPUTERASWELLASAUDIORECORDINGSAND FIELD NOTES FROM THE WHOLECLASSDISCUSSION *N ADDITION A JOINT MEETING WITH THE TEACHERS AFTERWARDS WAS AUDIO RECORDED 5HE FOCUS IN THIS PAPER IS ON THE STUDENT RESPONSES SELECTED AND ON TEACHERS UTILIZATION OF THESE DURING THE WHOLECLASS DISCUSSION GUIDEDBYTHEQUESTIONSSUGGESTEDINTHETEACHERSUPPORTMATERIALS "LLSTUDENTRESPONSESWERECATEGORIZEDBASEDONTHEANTICIPATEDCATEGORIESIN'IGURE 5HISANALYSISPROVIDEDINFORMATIONABOUTTHEOCCURRENCEOFSTUDENTRESPONSESINEACH CLASSASWELLASRESPONSESSELECTEDBYTHETEACHERS5HISENABLEDUSTOASCERTAINWHETHER EACHTEACHERMANAGEDTOSELECTRESPONSESFROMALLOFTHECATEGORIESAVAILABLEINTHEIR CLASS4CREENRECORDINGSOFTHE)I<J<EK8K@FEGI<G8I8K@FEVIEWPROVIDEDINFORMATION ABOUTTHESEQUENCING OFTHESELECTEDRESPONSES MADEBYTHETEACHERSINPREPARATION FORTHEWHOLECLASSDISCUSSION /EXT THE AUDIO RECORDINGS WERE TRANSCRIBED AND SCREEN SHOTS FROM THE SCREEN RECORDINGSWEREINSERTEDTOINDICATEWHICHRESPONSETHETEACHERDISPLAYEDWHENPOSING DIFFERENTQUESTIONS5HESETRANSCRIPTSWEREANALYSEDTOINDICATETHENUMBEROFQUESTIONS POSEDBYEACHTEACHERINRELATIONTODIFFERENTRESPONSECATEGORIES8EALSOCOMPARED THESEQUESTIONSWITHTHESUGGESTEDONES CATEGORIZINGTHETEACHERSACTIONAS4UGGESTED QUESTION OREQUIVALENT 4OMEOTHERFORMOFQUESTION OR/OQUESTION '(*!)( 5HIS SECTION STARTS BY PRESENTING THE FINDINGS RELATED TO THE TEACHERS PREPARATION IN TERMSOFSELECTIONANDSEQUENCINGOFSTUDENTRESPONSES5HENTHEFINDINGSCONCERNING THEIRCONDUCTOFTHEWHOLECLASSDISCUSSIONSISREPORTED %D7B3D3F;A@8ADI:A>75>3EE6;E5GEE;A@ 5HE RESPONSES MAKING UP OUR CATEGORY SYSTEM ARE IDEALIZED IN THE SENSE THAT EACH APPEALSTOASINGLEDISTINCTIVEIDEA)OWEVER THEEMPIRICALRESPONSESTHATWERECEIVED FROM STUDENTS COULD MAKE REFERENCE TO MORE THAN ONE OF THESES IDEALIZED RESPONSES ANDORTOFURTHERIDEASABSENTFROMTHECATEGORYSYSTEM$ONSEQUENTLY THESEEMPIRICAL RESPONSESWEREMAINLYOFTHREETYPES'IRST THEREWERETHOSETHAT INOURINTERPRETATION . .+ ""!&*$/+#0%"+,& +*#"."* "
(16)
(17) . .
(18) . . REFER ONLY TO A SINGLE CATEGORY 4ECOND SOME REFER TO MORE THAN ONE CATEGORY OR COMBINEONECATEGORYWITHOTHERIRRELEVANTINFORMATION'INALLY THEREWERERESPONSES THATDIDNOTRELATEATALLTOTHEANTICIPATEDANSWERCATEGORIES CATEGORIZEDAS0THER 5HESERESPONSESWEREIRRELEVANT EG#ECAUSETHE:VARIABLEISTHESLOPEINTHISCASE ORNOTINFORMATIVEENOUGH EGP: "LTHOUGH THE TEACHERS FOUND THE SELECTION PROCESS CHALLENGING THEY ALL MANAGED TO SELECTRESPONSESFROMALLCATEGORIESAVAILABLE INTHEIRCLASS 5HEREWERENOCATEGORY B ANSWERSAVAILABLEINANYOFTHECLASSES ANDNOCATEGORY E ANSWERIN5SCLASS "SINDICATEDIN5ABLE SOMEOFTHESELECTEDRESPONSESDIDNOTONLYCONSISTOFONE CATEGORYORWERECATEGORIZEDAS0THER"SWILLBEDEMONSTRATEDLATER THISCAUSED TROUBLEINTHESUBSEQUENTSTAGEOFTHELESSON 5ABLESHOWSTHESEQUENCINGMADEBYTHETEACHERS5HELETTERSWITHINBRACKETSINDICATE OURCATEGORIZATIONOFTHEDIFFERENTSTUDENTRESPONSES*NCASESWHENASTUDENTRESPONSE INCLUDESMORETHANONECATEGORY ORFURTHERIRRELEVANTINFORMATION BOTHCATEGORIESARE INDICATEDWITHINTHEBRACKETS'OREXAMPLE IN5SFIRSTPRESENTATIONVIEW THEREARE TWOSTUDENTRESPONSES ONECATEGORIZEDASBOTH C AND A ANDTHEOTHERAS A ONLY 5ABLEINDICATESTHATTHETEACHERSMOREORLESSFOLLOWEDTHESUGGESTEDSEQUENCING AND THATTHREETEACHERSUTILIZEDTHEOPPORTUNITYTODISPLAYMORETHANONERESPONSEONTHE SAMEPRESENTATIONVIEW . . . . . . . . . . . -"+. . . . . . #++. . . . . . . #++,#' .
(19) . . #++,#' . . . . . . -"+. . *12<5 *85C5AE5>39>7?649665B5>DCDE45>DB5C@?>C5C9>D856?EB3<1CC5C. :3>>7@97E;@>3G@5:;@9F:7EF397EA8F:7B>3@@76I:A>75>3EE6;E5GEE;A@ 5HETIMESDEVOTEDFORTHEWHOLECLASSDISCUSSIONWEREMIN 5 MIN 5 MIN 5 ANDMIN 5 5HEPRESENTATIONOFTHERESULTSINTHISSECTIONISORGANIZED ACCORDINGTOTWOIDENTIFIEDCRITICALASPECTS?8CC<E><@ELJ@E>K?<JL>><JK<;HL<JK@FEJ AND?8CC<E><J;L<KFJKL;<EKI<JGFEJ<=<8KLI<J ?8CC<E><@ELJ@E>K?<JL>><JK<;HL<JK@FEJ 5ABLE SHOWS THE TYPE OF QUESTION POSED BY THE TEACHERS IN RELATION TO RESPONSE CATEGORIES A C AND D *NCASESWHERESEVERALQUESTIONSWEREPOSED THENUMBEROF QUESTIONSISINDICATEDWITHINBRACKETS .+ ""!&*$/+#0%"+,& +*#"."* "
(20)
(21) . . .
(22) . " "
(23) " . .!!,-*.,-#('. (&(-"+ (+&( . (+*.#/%'-. *.,-#('. . . . . . . . . . . . . . (*.,-#('. *12<5
(24) *85>E=25B1>4DI@5C?6AE5CD9?>@?C542ID85D51385BC. 0NEOFTHETEACHERS 5 USEDTHEQUESTIONSUGGESTEDFORCATEGORY A WHILETWOOFTHE TEACHERSPOSEDQUESTIONSWITHOUTREFERRINGTOTHEDISTINCTIONBETWEENADESCRIPTIONAND ANEXPLANATION*NSTEAD 5FOCUSEDONASSESSINGTHEQUALITYOFTHEEXPLANATION 8HAT DOYOUTHINKABOUTTHATEXPLANATION WHILE5JUSTASKEDWHETHERTHERESPONSECOULD BEREGARDEDASANEXPLANATION5MADEAPOINTABOUTTHEDIFFERENCESBETWEENWHAT YOU CAN SEE IN THE GRAPH IE A DESCRIPTION AND AN EXPLANATION ALTHOUGH WITHOUT POSINGANYQUESTION 2UESTIONSRELATEDTOCATEGORY C RESPONSESWEREPOSEDSEVERALTIMESINTHREEOFTHE CLASSES 'OR EXAMPLE 5 POSED QUESTIONS IN RELATION TO THREE DIFFERENT STUDENT RESPONSES )OWEVER THE QUESTION CLOSEST TO THE SUGGESTED ONE 8HAT DO THESE TWO HAVEINCOMMON WASPOSEDWHENPOINTINGTOTHETWOFORMULAS WRITTEN ONTHEBOARD PBO
(25) DANDP8O
(26) 9O
(27) : IENOTBASEDONASTUDENTRESPONSE5HISWASALSOOBSERVED IN5SCLASS ALTHOUGHATTHEENDOFTHECLASSDISCUSSION0NEOFTHETEACHERS 5 USED THE QUESTION SUGGESTED FOR CATEGORY C HOWEVER THE TEACHER ADDED SOME FURTHER QUESTIONSTHATMIGHTHAVEBEENCONFUSINGFORTHESTUDENTS.OSTOFTHEQUESTIONSPOSED ONTHISCATEGORYAREVAGUEANDOFAMOREGENERALCHARACTER *N RELATION TO CATEGORY D ONLY ONE TEACHER 5 POSED A QUESTION *S THIS A MATHEMATICALEXPLANATION 5HEREASONWHY5DIDNOTPOSEANYQUESTIONMIGHTBE THATASTUDENTPROVIDEDASATISFACTORYEXPLANATIONWITHOUTANYREQUESTFROMTHETEACHER ?8CC<E><J;L<KFJKL;<EKI<JGFEJ<=<8KLI<J 4TUDENT RESPONSES THAT INCLUDE ONE CATEGORY PLUS EITHER ONE MORE CATEGORY OR SOME IRRELEVANT INFORMATION CAUSED TROUBLE DURING THIS STAGE OF THE LESSON 5WO OF THE TEACHERS 5AND5 DISPLAYEDRESPONSESINCLUDINGMORETHANONECATEGORY#ELOWARE DESCRIPTIONSOFTHESEINSTANCES 6NFORTUNATELY 5INITIALLYMISSEDTOUTILIZETHE1RESENTATIONVIEWFORDISPLAYINGTHE SELECTED ANDORDERED RESPONSES*NSTEAD THETEACHERUTILIZEDTHE,G<:@=@:@K<DVIEW ANDDISPLAYEDTHEFIRSTANSWERINTHISVIEW WHICHHAPPENEDTOBEONEOFTHEANSWERS IN15HETEACHERREADALOUDTHERESPONSECATEGORIZEDAS C
(28) A <:8LJ<K?<M8CL<F=:@JDN?<I<K?<C@E<@EK<IJ<:KJK?<P8O@JPBODD: 5HEN THETEACHERASKED$OMPARINGDAND: ISTHEREANYONEWHOCANEXPLAINTHIS THE THINKINGBEHINDIT 4INCENOBODYRESPONDEDTOTHISQUESTION THETEACHERSHIFTEDTHE . .+ ""!&*$/+#0%"+,& +*#"."* "
(29)
(30) . .
(31) . . FOCUSTOWARDSTHEPARTOFTHERESPONSETHATBELONGSTOCATEGORY A ANDASKED8HAT DO YOU THINK ABOUT THAT EXPLANATION *N THIS WAY THE TEACHER DID NOT FOLLOW THE PLANNED ANDSUGGESTED SEQUENCING PROBABLYBECAUSETHEDISPLAYEDRESPONSEINCLUDE TWORESPONSECATEGORIES 8HEN DISPLAYING THE RESPONSE CATEGORIZED AS C
(32) E 5 DIRECTED THE FOCUS TO THE CATEGORY C PARTOFTHERESPONSE DESPITETHATCATEGORY C ALREADYHADBEENDISPLAYED AND DISCUSSED 4HE ASKED #UT HOW DO WE THEN SEE THAT C IS M 0NE STUDENT ANSWEREDBYPROVIDINGAPROPERCATEGORY E ANSWER IEFOCUSINGONTHEOTHERPARTOF THE RESPONSE 5HIS ILLUSTRATES HOW AN ANSWER THAT INCLUDES TWO RESPONSE CATEGORIES MIGHT INFLUENCE THE DISCUSSION IN TWO WAYS 'IRST THE SAME KIND OF RESPONSE WAS DISCUSSEDSEVERALTIMES ANDSECOND THEREWASAMISMATCHBETWEENTHEQUESTIONPOSED BYTHETEACHERANDTHESTUDENTRESPONSE 5OSUMMARIZE THEFINDINGSINDICATETHATTHETEACHERSQUITESUCCESSFULLYFOLLOWEDTHE SUGGESTED SELECTION AND SEQUENCING )OWEVER CHALLENGES DURING THE CONDUCT OF THE WHOLECLASS DISCUSSION APPEARED WHEN STUDENT RESPONSES INCLUDING MORE THAN ONE CATEGORY WERE DISPLAYED .OREOVER IT WAS CHALLENGING OVERALL FOR THE TEACHERS TO FOLLOWTHEGUIDANCEINTERMSOFTHESUGGESTEDQUESTIONS (*(($# 4INCETHISISACASESTUDY THEINTENTIONISNOTTOPROVIDEGENERALIZABLERESULTS BUTTO IDENTIFYSOMECHALLENGESAPPEARINGWHENTEACHERSUTILIZE$$5TOORCHESTRATEAWHOLE CLASSDISCUSSIONBASEDONSTUDENTSCOMPUTERBASEDWORK*NTHISWAY THEFINDINGSCAN PROVIDESOMEGUIDANCEFORFUTUREPRACTICEANDRESEARCH "LTHOUGH THE TEACHERS FOUND THE $$5 USEFUL THE FINDINGS INDICATE THAT IT WAS A CHALLENGEFORTHEMTOFOLLOWTHEAGREEDTEACHERGUIDANCE1ARTICULARLY THESUGGESTED QUESTIONTOPOSEINRELATIONTODIFFERENTTYPESOFSTUDENTRESPONSEWEREUSEDTOASMALL EXTENT ANDWHENUSED THEYMOSTOFTENWEREPOSEDINAQUITEDIFFERENTWAY0FCOURSE THERE COULD BE SEVERAL REASONS FOR THIS NOT LEAST THE TEACHERS OWN BELIEFS AND KNOWLEDGEASWELLASTHECLASSROOMNORMS ,IERANETAL )OWEVER ONEREASON PROBABLYWASTHENEEDFORTEACHERSTOMAKEINMOMENTDECISIONSINTHECLASSROOM0NE WAYTOFACILITATEFORTHETEACHERSTOFOLLOWTHETEACHERGUIDANCEWOULDBETOEMBEDTHE PLANNEDQUESTIONSINTOTHEPRESENTATIONVIEWTOGETHERWITHTHESTUDENTRESPONSES5HIS COULDALSOADDRESSTHECHALLENGEFORTEACHERSTOBASETHEDISCUSSIONONPROPERSTUDENT RESPONSES ACHALLENGEALSOOBSERVEDBY3UTHVENAND)OFMANN *TWASALSOACHALLENGEFORTHETEACHERSTOFOLLOWTHETEACHERGUIDANCE INCASESWHEN THEY SELECTED RESPONSES INCLUDING MORE THAN ONE CATEGORY 5WO PROBLEMS WERE OBSERVED DURING THE WHOLECLASS DISCUSSIONS 'IRST THE PLANNED SEQUENCING BECAME DISTURBED ANDSECONDITBECAMEUNCLEARWHATPARTOFTHERESPONSETHATWASDISCUSSED 0NEWAYTODEALWITHTHISWOULDBETOSELECTONLYCLEANRESPONSES IFPOSSIBLE5HIS RAISESTHEQUESTIONWHETHERTECHNOLOGYCANSUPPORTTEACHERSWITHTHECHALLENGINGTASK. .+ ""!&*$/+#0%"+,& +*#"."* "
(33)
(34) . . .
(35) OF CATEGORISING STUDENT RESPONSES ON THE SPOT 5HIS IS AN IMPORTANT ISSUE FOR FUTURE RESEARCH *NTHISSTUDY TEACHERSWERESUPPOSEDTOIMPLEMENTANAGREEDLESSONDESIGNBASEDONA SYSTEMATICANALYSIS DONEBYTHERESEARCHERS *NREFLECTION THESTUDYILLUSTRATESTHAT THIS TYPE OF IMPLEMENTATION IS NOT STRAIGHTFORWARD 4OME REASONS FOR THIS AND WHAT COULDBEDONETOSUPPORTTEACHERSHAVEBEENDISCUSSED ''#( $USI " .ORSELLI ' 4ABENA $ 1ROMOTING FORMATIVE ASSESSMENT IN A CONNECTED CLASSROOM ENVIRONMENT %ESIGN AND IMPLEMENTATION OF DIGITAL RESOURCES3& DOIS 'AHLGREN . #RUNSTRnM . )OW THE WORD MATHEMATICALINFLUENCES STUDENTS RESPONSES TO EXPLANATION TASKS IN A DYNAMIC MATHEMATICS SOFTWARE ENVIRONMENT*N)(8EIGAND "$LARK8ILSON "%ONEVSKA5ODOROVA / 'AGGIANO / (RzNByK + 5RGALOV` &DS )IF:<<;@E>J F= K?< K? +& -FG@: FE=<I<E:< &
(36) PP %ENMARK 6NIVERSITY OF $OPENHAGEN 'AHLGREN . #RUNSTRnM . 0RCHESTRATING WHOLECLASS DISCUSSIONS IN MATHEMATICSUSINGCONNECTEDCLASSROOMTECHNOLOGY*N##ARZEL 3#EBERNIK -(nBEL )3UCHNIEWICZ '4CHACHT %5HURM &DS )IF:<<;@E>JF=K?<
(37) K? "EK<IE8K@FE8C FE=<I<E:< FE -<:?EFCF>P @E &8K?<D8K@:J -<8:?@E> "-&-
(38) PP &SSEN (ERMANY 'AHLGREN . #RUNSTRnM . FEE<:K<;C8JJIFFD-<:?EFCF>PKFDFE@KFI J<C<:K8E;J<HL<E:<JKL;<EKI<JGFEJ<J1APERPRESENTEDATTHETWELFTHRESEARCH SEMINAROFTHE4WEDISH4OCIETYFOR3ESEARCHIN.ATHEMATICS&DUCATION 7bXJn 4WEDEN 'RANKE .- ,AZEMI & #ATTEY % .ATHEMATICSTEACHINGANDCLASSROOM PRACTICE *N ' , -ESTER &D ,<:FE; ?8E;9FFB F= I<J<8I:? FE D8K?<D8K@:J K<8:?@E>8E;C<8IE@E> 7OL PP $HARLOTTE /$*NFORMATION"GE 1UBLISHING ,IERAN $ 5ANGUAY % 4OLARES " 3ESEARCHERDESIGNEDRESOURCESANDTHEIR ADAPTATIONWITHINCLASSROOMTEACHINGPRACTICE4HAPINGBOTHTHEIMPLICITANDTHE EXPLICIT *N ( (UEUDET # 1EPIN - 5ROUCHE &DS IFD -<OK KF %@M<; +<JFLI:<J PP /EW:ORK /:4PRINGER 3UTHVEN , )OFMANN 3 $HANCE BY DESIGN DEVISING AN INTRODUCTORY PROBABILITY MODULE FOR IMPLEMENTATION AT SCALE IN &NGLISH EARLYSECONDARY EDUCATION3& DOIS 4TEIN . , &NGLE 3 " 4MITH . 4 )UGHES & , 0RCHESTRATING PRODUCTIVEMATHEMATICALDISCUSSIONS'IVEPRACTICESFORHELPINGTEACHERSMOVE BEYOND SHOW AND TELL &8K?<D8K@:8C -?@EB@E> 8E; %<8IE@E>
(39) DOI. . .+ ""!&*$/+#0%"+,& +*#"."* "
(40)
(41) . .
(42)
Related documents
The exploration will explore different connections between translations and fictions, modes and technologies for their fabrication and their relationships to history,
Qua in re, quod eft omnium primum, Pra/ens &C Imperfettum, quod Medium föret, nihil moramur: ipfi eniui utrique Formam patere Pasfivam, nemo negat: quibus. vero neque Aétiva
Detta öppnade upp för nya idéer och jag kom fram till att ett väskformat skulle vara smidigt då de är gjorda för att kunna bäras med till olika platser.. Därför gjordes lite
Building on a theoretical framework based on Coale’s contraception paradigm, this MA thesis explores how armed conflict affects the propensity to use modern contraceptive in Colombia
För barnen är det ingen tvekan i det långa loppet är det en resurs, det är självklart, att växa upp och sedan ha två språk, som de kan använda när de växer upp det kan inte
The rule book figures as a key device in care choice reform, and provides a way into studying how values are enacted in the reform process. This thesis claims that the
n Vassilios Kapaklis, Senior Lecturer at the Department of Physics and Astronomy, Hans Lennernäs, Professor at the Department of Pharmacy, In- gela Nilsson, Professor at the
Mathcoach (www.mattecoach.se) and Swedishcoach (www.svenskacoach.se) offers K-12 students help with their homework in Swedish for immigrants and mathematics online.. The coaches