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TannazJavaheri,SarahSkipwith,KyaraMarkle

Research

Multiplication AnarticlebySpeiser,et.al.,2012,explainswhypaper-and-pencilmultiplicationisdifficultforsomanyindividuals.Theyexplainthatashumanswehavelimitedworkingmemoryandattentivefocuscapacity.Byitsverynature,workingmemoryisopentodistractionandhenceiseasilydisrupted.Themoreyouneedtoholdconcurrentlyinworkingmemory,themoredifficultyourtaskbecomes.Asuggestiongiveninthearticleistousemultiplestrategiesthatengagevariousareasofthebrain(i.e.kinestheticactivitiesactivatethemotorareasofthebrain).

Array Anarrayisanarrangementofrowsorcolumnsthatisusedasatooltodisplaymultiplication&division.Thistoolcouldbeusedforlearningorteachingtheseskills.Understandingstructuresisa“bigidea”inlearningmathematics.Abigideaforteachingmultiplicationisthroughthecommutativeproperty,whichallowschildrentoseeandexplorethepropertiesofmultiplication“inatwo-dimensionalarraydrawnongraphpaper”.Usingarraysarebeneficialtotheunderstandingofmultiplicationasstudents“createspatialstructuresforsetsofobjectsthroughthementalactionstheyperformonobjects”(Fosnot&Dolk,2001).

Hands-On Activities to Teach Multiplication Multiplicationisadifficultareaofmathematicsforchildrentounderstand.Itoftencausesnegativeattitudestowardsmathandaffectsone’sabilitytosolvemathproblems.Engagingmathhasbeenusedtoreachstudentswithvariouslearningneeds,ensureunderstandingandsuccessinmathematics.Ouraimistodemonstratehands-onteachingstrategiesthatcanbeusedtoteachstudentsmultiplicationinameaningfulway.

TheNationalAssessmentofEducationalProgress(2013)conductedastudyon14-year-oldstudentsingeneraleducation.Theresultsshowedthatonly50%ofthestudentsweremasteringmultiplicationskills.Withhalfofthestudentsstrugglinginmultiplication,animportantquestiontoaskishowdowerecognizethesestrugglingstudentsandhowdowe

supportthem?

CONTEXT:Ouractivitiesuseavarietyofarraystoteachmultiplication.Usingarrayspromotestudents’useofspatialreasoningastheyvisuallyapplymultiplicationtospatialstructures.Anarrayallowsforstudentstovisuallyseeandmanipulatetheareathatmultiplicationequationscreate.Byexaminingasetareaonanarray,studentscanalsovisuallyseethedifferentpartsthatmakeupawhole.

ACTVITIES:1) CUT AND PASTE MULTIPLICATION

Studentsplaythisgameindividuallyorinpairs.Studentsaregiventwodice,graphpaper,andalargepieceofcolouredpaperonwhichto‘paste’theiranswers.First,rollthedicetogetamultiplicationquestion(i.e.,6X6)andusethisequationtodrawonpapertoshowthatitisequaltoanarray.Anoptiontomakethismorechallengingistogivestudentsa

deckofcardsinsteadofdicetoworkwithlargernumbers.Studentscutouttheiroriginalarray.Theycanthenexplorewhatmakesuptheirmultiplicationquestionbycuttingtheirarrayintosmallerarrays(i.e.,3X6+3X6=6X6).Students‘paste’theircutarraysontoapieceofpapertoshowthatitisequaltotheoriginalequation.Therearedifferentwaysforstudentstocuttheiroriginalarray-encouragestudentstofindasmanywaystoshowtheoriginalarrayaspossible.

Material Options ● MultipleSizedGridPaper● Dice● MathlinkCubes● Lego● ConstructionPaper● Pencils● Markers● DryEraseMarkers● BaseTenBlocks● MuffinTray● Dominoes● Stickers● Scissors● Glue● BingoDabbers● Deckofcards

How to Support Our Students

Strugglingstudentsmaydemonstratelackofengagement,negativeattitudestowardsmultiplication,asenseofdiscouragementwhenengagedinmultiplication,andavoidanceofmathalltogether.Strugglesinmathandmultiplicationcanalsoleadtomathanxiety.Mathanxietyisacommon,yetaveryrealconcernandshouldnotbeignored.Whenstudentsdevelopmathanxiety,itcantransferintotheiradultlife,asBeilockandMaloney(2015)explain,“manypeoplealsoexperienceanxietyevenwhenengaginginmundaneeverydaymathtaskslikecalculatingatipatarestaurantordecidingwhetherornottheyreceivedtheproperchangeatthegrocerystore[...]infact,forsomepeople,theirlevelsofmathanxietyaresohighthattheybecomenervousevensimplyreadingaloudmathematicalequations.”

2) BATTLE OF ARRAYS

3) LEGO CONNECTION

MODIFICATIONS A.MuffinTrayUsingamuffintray(3by4)servesasamorebasicwaytovisualizearrays.Studentscanusevariousobjectstofillinthemuffintraytocreateanarray.Studentsmaywork1on1withateacher.Forexample,ateachermightask“Whatis2x2?”,andastudentcanuseobjectsofchoicetofillinthemuffintrayinordertodemonstratethatmultiplicationproblem.B.UsingStickersStudentscanrollasetofdiceandusestickerstofillinanarrayofthegiven2numbersonasheetofgridpaper.Providingmultipletypesofstickersaddschoiceandexcitementforstudents.C.MathlinkCubes/BingoDabbersStudentscanrollasetofdiceanduseMathlinkcubestophysicallyholdandfeeltheamountofareabeingcoveredorbingodabberstofillinanarrayofthegiven2numbersonasheetoflargegridpaper.Studentscanworkindividuallyorinpairs.Ifinpairs,twodifferentcolouredbingodabberswillberequired.

Studentsplayinpairs.Theyaregivena“BattleofArrays”GameBoardandasetofdice.Player1rollsthediceandusesamarkertocolourin/drawthearrayofthegiventwonumbers,

thenwritestheanswerofthemultiplicationproblem.Player2thenrollsthediceandrepeatstheabovestepsusingadifferentcolouredmarker.Ifaplayercan’tfindanarray,theymisstheirturn.Thewinnerisdeterminedbytheplayerwhohascolouredinthemostsquareswhentimeisuporthegridiscomplete.

Thisactivityallowsstudentstohaveavisualmodelandhasmultiplevariationstomeetarangeoflearners.Studentscanfocusonusingsmallerpiecesandfocusonarraysupto6x6.PlacethearraysontheLegosheet,usingLegocubesandlabelthemultiplicationequationit

replicates.StudentscanalsomakelargearrayswithmultipleLegopiecesandshowtheirabilitytosolvemulti-digitmultiplicationproblemsbygroupingintosmallerarrays.Itisimportanttoletstudentsplay,aswellasencouragingthelabellingandexplainingoftheircreationsinthisactivity.