Standard for Mathatics Quia.ppt

domainiii mathematicscompetency016 mathematicsinstruction theteacherunderstandshowchildrenlearnmathematicalskillsandusesthisknowledgetoplan organize andimplementinstructionandassesslearning principlesofmathematics thenctmidentifiedsixprinciplesforschoolmathematics equity curriculum teaching learning assessmentandtechnology 2000 1 equity excellenceinmathematicseducationrequiresequity highexpectationsandstrongsupportforallstudents 2 curriculum acurriculummustbecoherent focusedonimportantmathematics andwellarticulatedacrossgrades 3 teaching effectivemathematicsteachingrequiresunderstandingofwhatstudentsknowandneedtolearn andthenchallengingandsupportingthemtolearnitwell 4 learning studentsmustlearnmathematicswithunderstanding activelybuildingnewknowledgefromexperienceandpreviousknowledge 5 assessment assessmentshouldsupportthelearn ofimportantmathematicsconcepts andfurnishusefulinformationtobothteachersandstudents 6 technology technologyisessentialinteachingandlearningmathematicsitinfluencestheteachingofmathematicsandenhancesstudent slearning principlesofmathematics usevariousmaterialstoteachskillsandconcepts usedifferentinstructionaltechniques havestudentsexplainskillsandconcepts allowstudentstoseetheirprogress e g recordsofperformance teachthelanguageofmathematics e g wordwalls flashcards etc useavarietyofcuestocheckforunderstanding e g thumbsup colorcodedcards happyfacecards etc includeconcrete representational andabstractactivities avoidoverrelianceonworkbooksfordictatingcurriculumandprovidingpracticeopportunities principlesofmathematics cont useinstructionalapproachesthatwillensurecomprehensionandmasteryofskillsandconcepts suchascooperativelearning graphicorganizers useofmanipulatives etc avoidexcessivepaper and pencildrillthatservesmerelyasbusyworkratherthanasameaningfulpracticeexperience linknewinstructionalknowledgetopresentknowledge showstudents andhavestudentsexplain howmathematicsispartofdailyliving teachmathematicalskillsandconceptswithinaproblem solvingcontext remember welearn 10 ofwhatweread20 ofwhatwehear30 ofwhatwesee50 ofwhatwebothhearandsee70 ofwhatwediscusswithothers80 ofwhatweexperiencepersonally95 ofwhatweteachtosomeoneelsewilliamglasser howdochildrenlearnmathematics researchindicatesthatchildrenmustdevelophigherlevelthinkingabilitiesinordertointerpretcertainmathematicalconcepts becausethedevelopmentofsomeoftheseabilitiesissonatural teachersoftenfailtoconsiderthatchildrenincertainstagesofdevelopmentmaynothaveacquiredthem tobeaneffectiveteacheryoumustknowwhenchildrencanbeintroducedtoagivenconceptandatwhatlevelofabstractiontheycandealwiththeconcept basicallytherearethreelevelsatwhichconceptscanberepresented concrete pictorial andsymbolic levelsofmathdevelopment concretelevel aconceptcanberepresentedbytheappropriatemanipulationofobjects example placingthreebeansintoeachoffourmargarinetubsandfindingthetotalnumberofbeansillustratesthat4x3 12 pictoriallevel aconceptcanberepresentedbyappropriatepictures example apictureoffourgroupsofthreetoillustrate4x3 12 symboliclevel aconceptcanberepresentedbysymbols example 4x3 12 standardformathematics thestandardsformathematicsaredividedintotwosections contentandprocess contentstandardsprocessstandards standardformathematicscontentstandards 1 numberandoperations thesecomponentsincludetheconceptofnumber andfraction andbasiccomputation 2 algebra thiscomponentincludeselementaryalgebraicreasoninginvolvingingpatternsandsetsofnumbers3 geometry thisencompassesthestudyofgeometricshapesandspatialreasoning 4 measurement thiscomponentincludestheunitsofmeasurements standardandmetric andtheprocessformeasurementingeneral 5 dataanalysisandprobability thesetwocomponentscoverthecollection analysis anddisplayofmathematicsinformation standardformathematicscontentstandards numberandoperations pre k 1stgrade draw read andwritevaluesto99 countobjectsbygroupingtens compareandordernumbersto99usingmodels pictures identifycoinsandvalue pennies nickelsanddimes 2ndgrade draw read andwritevaluesto999 compareandordernumbersto999 countvaluesofallcoins recognizefractionsusingmodels skipcount recognizeoddandevennumbers 3rdgrade draw read andwritevaluesto99 999 compareandordernumbersto99 999 showbillsandcoinstoequalagivennumber 4thgrade read write anddetermineplacevalueofnumbersuptoonemillion drawpicturesofnumberstomillions draw read andwritevaluestohundredths compareandorderdecimalsusingmodelstohundredths roundnumberstotenandhundred comparefractionsusingpicturesandpatterns standardformathematicscontentstandards numbersandoperations con t additionandsubtraction pre k 1stgrade useobjectstoactoutandsubtractionstories additionandsubtractiontoten actoutoruseobjectstodescribeadditionorsubtractionsituationsincluding comparing missingparts howmanyleft representadditionandsubtractionsituationswithanumbersentence 2ndgrade estimatesumsanddifferencesto99 selectcorrectoperationandsolvereallifeproblemsinvolvingadditionandsubtraction useadditiontosolveproblemsto999 additionandsubtractionwithmoney centsto99 dollarsto999 usesubtractiontosolveproblemswithminuendsthrough99 basicfactrecalladditionandsubtractionto18 3 5secondsaveragerecallperfact 3rdgrade estimatesumsanddifferencesto9 999 useadditiontosolveproblemswithnumbersthrough9 9994thgrade useadditionandsubtractionofdecimalstosolveproblems tenthsandhundredths standardformathematicscontentstandards numbersandoperations con t multiplicationanddivision pre k 1stgrade useamultiplicationordivisionnumbersentencetodescribeamodeledsituation drawapictureforagivenmultiplicationordivisionwordproblem 2ndgrade useamultiplicationordivisionnumbersentencetodescribeamodeledsituation drawapictureforagivenmultiplicationordivisionwordproblem 3rdgrade multiplynumberwithfactorsthrough10 selectcorrectoperationtosolvereal lifeproblemsinvolvingmultiplicationanddivision 4thgrade estimateproductsof2digitby2digitfactors usemultiplicationanddivisiontosolveproblems multiplication3digitby2digit divisiononedigitquotientswithandwithoutremainders basicfactrecall multiplicationanddivision 3to5secondaveragerecallperfact standardformathematicscontentstandards algebra pre k 1stgrade identifyandextendpatternusingobjects demonstratetherelationbetweenadditionandsubtraction 2ndgrade identifyandextendpattern determinemissingelements writenumberfamiliesforadditionandsubtraction useoperationproperties additionandsubtractionwithzero addendsordersdoesnotmatter commutativeproperty 3rdgrade findtherelationshipofnumberpairs function andextendthepattern writenumberfamiliesformultiplicationanddivision 4thgrade useoperationproperties multiplicationanddivisionbyone multiplicationcommutativeanddistributive usepatternstosolveproblems standardformathematicscontentstandards geometry pre k 1stgrade constructsquares rectangles trianglesongeoboardsandwithpatternblocks locateinteriorandexteriorpoints locations onplanefigures 2ndgrade identifyandsortrealobjectsbyshape cube cone sphere cylinder constructcongruentshapesonageoboardandondotpaper 3rdgrade classify sort polygons identifyfigureshavingsymmetry identifylineofsymmetry identifyafigurecongruenttoasamplefigure 4thgrade listcharacteristicsofpolygons quadrilaterals parallelograms rectangle rhombus square trapezoid pentagons hexagons octagons classify3dimensionfiguresandfaces cube sphere cone cylinder prisms pyramids standardformathematicscontentstandards measurement pre k 1stgrade comparelengthandweight readacalendar telltimetohourandhalf hour 2ndgrade estimateandmeasure customaryinches feet yards pounds metriccentimeters meters kilograms telltimeto5minutes 3rdgrade estimateandmeasure customaryinches feet yards miles kilometers ounces pounds metriccentimeters meters grams kilograms temperature4thgrade findareasofrectangles findperimeters estimateandmeasurecapacity customarycup pint quart gallon metricmilliliter liter solveproblemsinvolvingelapsetime standardformathematicscontentstandards dataanalysisandprobability pre k 1stgrade makerealgraphs identifyeventsthataresuretohappen surenottohappen orunsureofoutcome 2ndgrade makeandinterpretpicturegraphsandbargraphs interpretandusecharts 3rdgrade makepictureandbargraphswhereeachcellrepresentmultipleunits usebargraphstosolveapplicationandnonroutineproblems 4thgrade listpossibleoutcomesinagivensituation interpretlinegraphs plotpointsinacoordinateplane collectrecordandorganizedataintotables charts bargraphsandlinegraphs standardformathematicsprocessstandards 1 problemsolving inthiscomponentstudentsareguidedtoformulateandsolvemathematicsproblemsthatcanbeusedinreallifesituations 2 reasoningandproof thesetwocomponentsallowstudentopportunitiestoexamineproblems findsolutions andjustifythemusinglogicalandmathematicsprinciples 3 communication thiscomponentteacheschildrentousepreciseandappropriatemathematicsvocabularytoexplainprocessesandoutcomes 4 connections thiscomponentemphasizestheimportanceofmathematicsandtheconnectiontoothercontentareasandlifeingeneral 5 representations thiscomponentteacheshowmathematicsinformationcanbepresentedinvariousways numbers letters tablesgraphsandsoon standardformathematicsprocessstandards problemsolving pre k 1stgrade actoutanddrawpicturestorepresentadditionandsubtractionincluding howmanyleft missingparts comparing 2ndgrade drawapictures usepatterns actoutanddrawpicturestorepresent wordproblems multiplicationanddivision non routineproblems 3rdgrade usestrategies makeanorganizedlist makeatable writeanumbersentencetodescribewordproblemsinvolvingadditionandsubtraction andmultiplicationanddivision 4thgrade solvewordproblemswithextrainformationanddeterminingmissinginformation solveproblemsworkingbackwards standardformathematicsprocessstandards problemsolving con t ingradesk 4 thestudyofmathematicsshouldemphasizeproblemsolvingsothatstudentscan useproblemsolvingapproachestoinvestigateandunderstandmathematicalcontent formulateproblemsfromeverydaymathematicalsituations developandapplystrategiestosolveawidevarietyofproblems verifyandinterpretresultswithrespecttotheoriginalproblem acquireconfidenceinusingmathematicalmeaningfully standardformathematicsprocessstandards problemsolving con t themathematicsteacherunderstandsandusesnumbers numbersystemsandtheirstructure operationsandalgorithms quantitativereasoning amtechnologyappropriatetoteachthestatewidecurriculum texasessentialknowledgeandskills teks inordertopreparestudentstousemathematics standardformathematicsprocessstandards reasoningandproof ingradesk 4 thestudyofmathematicsshouldemphasizereasoningsothatstudentscan drawlogicalconclusionsaboutmathematics usemodels knownfacts properties andrelationshipstoexplaintheirthinking justifytheiranswersandsolutionprocesses usepatternsandrelationshipstoanalyzemathematicalsituations believethatmathematicalmakesense standardformathematicsprocessstandards communication foronestepproblems studentscanbeaskedthefollowingquestionsasawaytodiscusstheirwork whatareyoutryingtofind whichdatainthestorywereneededtofindthesolution werethereunnecessarydata whatactioninthestorysuggestedtheoperationyouusedtofindtheanswer canyougivetheanswerinacompletesentence haveyoucheckedyourworkandyouranswer standardformathematicsprocessstandards connections studentsshouldlearnhowmathisconnectedtotheothercontentareas suchas languagearts science socialstudies health physicaleducation art music etc forexample iftheyarestudying temperaturechanges theyshouldknownumbers algebraiccomputations basicoperations etc toreadthethermometerandusethisinformationingraphs standardformathematicsprocessstandards representations studentsshouldlearnthedifferentwaystorepresentthenumericalinformationtheygatheredfromaproblembyusingalgorithms numbers tables charts graphs etc thetexasessentialknowledgeandskills teks thetexasessentialknowledgeandskills teks requiresawell balancedcurriculumbeginninginkindergartenandcontinuingthroughgrade12 tea 2006 itincorporatestheprinciplesandstandardsofthenctmandintroducestheseinasequentialmannerthatreflectsthecognitivedevelopmentofchildren childreninkindergartenbeginexploringnumberconceptsusingconcreteobjectsandmasteringone to onecorrespondence infirstandsecondgradestheycontinueexploringnumberconceptsandbeginstudyingbasiccomputationsskills inthirdthroughfifthgradestheycontinueexpandingnumberconceptstoincludemultiplication divisionfractions decimalrepresentations geometricprinciplesandalgebraicreasoning mathematicscurriculumfork 4 kindergartenwhole numberconceptsandusing patternsandsortingtoexplorenumbers dataandshapesfirstaddingandsubtractingwholenumbersandorganizingandanalyzingdatasecondcomparingandorderingwholenumbers applyingadditionalandsubtraction andusingmeasurementprocessesthirdmultiplyinganddividingwholenumbersconnectingfractionsymbolstofractionalquantitiesandstandardizinglanguageandproceduresingeometryandmeasurementfourthcomparingandorderingfractionsanddecimals applyingmultiplicationmiddivisionanddevelopingideasrelatedtocongruenceandsymmetry cognitivedevelopmentandmathematics thecognitivedevelopmentofchildreninpre kindergarten pre k throughgrade4representsaspecialchallengewhenattemptingtolearnthesymbolicandabstractrepresentationsusedinmathematics piagetclassifiedstudentsinpre kthroughgrade4intotwobroadstages preoperational 2 7years andconcreteoperational 2 11years citedinsperrysmith 2001 childreninthepreoperationalstageofcognitivedevelopment 2 7years pre kthroughgrade2 experienceproblemswithatleasttwoperceptualconcepts centrationandconservation sperrysmith 2001 cognitivedevelopmentandmathematics centrationfourandfive year oldchildrenfocusattentionononecharacteristicofanobjectandignoretheothers theymightnoticethattheobjectsareround butfailtonoticethattheyhavedifferentcolorsandtexture childrenatthisageplaywithblocksinaverysimplisticandsystematicway linearfashion theydonotbecomemorecreativebecausetheyareemphasizingonefeatureattime basedoncognitivedevelopment childrenatthisagegenerallyexperienceproblemsdevelopingandrecognizingpatternsinmathematics cognitivedevelopmentandmathematics conservationfourandfive years oldsmightnotunderstandthatchangesintheappearancedonotnecessarilychangecharacteristicsoftheobject conservation thislimitationcanaffectchildren sabilitytomeasurevolumeandtounderstandthevalueofmoney thatis childrenmightgetconfusedwhenliquidismovedbetweencontainersofdifferentshapesorwhentrying todeterminethevalueofaquarterversusfivenickels theseperceptuallimitationscanaffectchildren sabilitytounderstandmeasurementandthevalueofmoney cognitivedevelopmentandmathematics duringtheconcreteoperationalstageofcognitivedevelopmentsecondtoseventhgradeschildrenexperiencerapidgrowthincognitivedevelopment thisstageischaracterizedbytheabilitytothinklogicallyaboutconcreteobjectsorrelationships someof theaccomplishmentsofstudentsatthisstageareasfollows canformconclusionsbasedoilreasonratherthanperceptioncanarrangeobjectsbasedoilcharacteristics classification canorganizeobjectsbasedoilmultiplecriteria orderingorseriation callunderstandthatchangesiiiappearancedonotnecessarilyaffectthesubstance conservation canconceptualizewhatwouldhavehappenedifanactionisreversed reversibility cognitivedevelopmentandmathematics despitethecognitivegrowthofthisstageteachershavetostructurelessonstoprovidestudentswithaconcretefoundationtosupporttheirthinking forexample ateachercanintroducetheconceptofgraphingbyaskingstudentstofollowthegrowthofaplantforaperiodoftimeanddocumentthegrowthusingaiinegraphortocomparehowoneplantgrowsversusanotherplantusingabargraph teachersshouldalsobreakdownataskintomanageablecomponentswiththeuseofgraphicorganizers charts diagrams webs timelines etc piaget slevelsofcognitivedevelopment childrenevolvethroughspecificstagesinwhichcognitivestructuresbecomeprogressivelymorecomplex cognitivedevelopmentreferstothechangesthatoccurinanindividual scognitivestructures abilities andprocesses cognitivedevelopmentisthetransformationofthechild sundifferentiated unspecializedcognitiveabilitiesintotheadult sconceptualcompetenceandproblem solvingskill piagetbelievedchildren sschemes orlogicalmentalstructures changewithageandareinitiallyaction based sensorimotor andlatermovetoamental operational level piaget slevelsofcognitivedevelopment sensorimotorstage 0 2years intelligencedevelopsthroughsensoryexperiencesandmovement duringthesensorimotorstage infantsandtoddlers think withtheireyes ears hands andothersensorimotorequipment piagetsaidthatachild scognitivesystemislimitedtomotorreflexesatbirth butthechildbuildsonthesereflexestodevelopmoresophisticatedprocedures theylearntogeneralizetheiractivitiestoawiderrangeofsituationsandcoordinatethemintoincreasinglylengthychainsofbehavior learninginvolvespullingpushing turning twisting rolling poking andinteractingwithmanydifferentpropertiesofobjects piaget slevelsofcognitivedevelopment preoperationalstage 2 6 7years intelligenceincludestheuseofsymbolssuchaspicturesandwordstorepresentideasandobjects atthisage accordingtopiaget childrenacquirerepresentationalskillsintheareaofmentalimagery andespeciallylanguage theyareveryself oriented andhaveanegocentricview thatis preoperationalchildrencanusetheserepresentationalskillsonlytoviewtheworldfromtheirownperspective learninginvolvesdiscoveringdistinctpropertiesandfunctionsofobjectsastheycompare sort stack roll distinguishtrianglesfromsquares andbegintouseabstractionstocommunicate piaget slevelsofcognitivedevelopment concreteoperationalstage 6 7 11 12years cognitivedevelopmentincludeslogicbutrequiresphysicalexamplestowhichthelogiccanbeapplied theyrequireexperienceswithtouching smelling seeing hearing andperforming theymustusehands ontoolstoinvestigate asopposedtopreoperationalchildren childrenintheconcreteoperationsstageareabletotakeintoaccountanotherperson spointofviewandconsidermorethanoneperspectivesimultaneously withtheirthoughtprocessbeingmorelogical flexible andorganizedthaninearlychildhood piaget slevelsofcognitivedevelopment concreteoperationalstage cont childrencanalsorepresenttransformationsaswellasstaticsituations althoughtheycanunderstandconcreteproblems piagetwouldarguethattheycannotyetcontemplateorsolveabstractprob