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THE CARNEGIE FOUNDATION

for the ADVANCEMENT of TEACHING

StatwayStatisticsandMathematicsStudentLearningGoalsandOutcomes

PhilosophicalDesign,Content,andInstructionalParadigmStatwayisaone‐yearexperienceofcollege‐levelstatisticsmeldedwithnecessarymathematicstopics.Thepathwayisdesignedfornon‐STEMstudentswhodesireacollege‐levelstatisticscourseandplaceintoBeginningAlgebra(orhigher).ThestatisticsoutcomesinStatwayareasrigorousasthoseinafirstcourseofcollege‐levelstatistics.Thestatisticscontentistransferrable,college‐levelcontentthatmeetstherequirementsofvariousacademicprogramsandcareers.Thus,studentswhosuccessfullycompletethesequencereceivecreditforacollege‐levelstatisticscourse.ThemathematicscontentinStatwayisbasedonthemathematicsneededforstatisticsandthemathematicsstudentsneedbroadlyforsuccessintheiracademicprogramsandtobeproductivecitizens.Theessentialmathematicsconceptsareintroducedinthecontextofstatistics,orotherappropriatecontexts,andintegratedthroughout.Thefundamentalmathematicalconceptsarepresentedwithinstatisticalsituationsthatadultstudentscanrelatetoandareexperiencedthroughvariousinstructionalapproaches.Asaresult,studentsseemathematicsasatooltounderstandandusestatisticsinavarietyofreal‐world,quantitativescenariosasopposedtomathematicsbeingasetofnumerousanddiscreteproceduresandtasksthatneedmemorizing.Thegoalisforstudentstobeabletoapplymathematicsandstatisticstoinvestigate,explain,andsolveproblemsthatarerealworldbased.

SomealgebraicskillsandconceptsgenerallythoughttobeprerequisitetoCollegeAlgebraorothercollege‐levelmathematicscoursesarenotincludedintheStatwayexperience.ThisdoesnotmeanthatthemathematicalpreparationinStatwayisnotthoroughorrigorous.Rather,Statwaypromotesdeeplearningofconceptsthatallowsstudentstoselectandintegrateappropriatemathematicalandstatisticalapproachestosolvenonroutineproblems.IfastudentchoosestopursueaSTEMcourseorprogram,someadditionalmathematicsconceptsmayneedtobedevelopedafterStatwaythroughafollow‐upbridgecourse.WithinStatway,themathematicsexperienceandthemethodsemployedbyfacultyengagestudentsinmathematicsandstatisticalsituationsthatmotivatelearning.Criticalknowledgeandconceptsareassessedattheentrypointofeachmajortopic,andstudentsareprovidedwiththemeanstoremediatetargetedprerequisitematerial,asneeded.TheoverarchinggoaloftheStatwayexperienceisthatstudentswillbemoresuccessfulinmathematics,willbemotivatedtostudymoremathematics,willdevelopbetterproblem‐solvingskills,andwillbemoreconfidentandcompetentinquantitativesituations.

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StatisticsStudentLearningGoalsandOutcomesforStatwayConsistentwiththeAmericanStatisticalAssociation’sGuidelinesforAssessmentandInstructioninStatisticsEducation,theStatwaylearningoutcomescenteraroundprovidingstudentswithafirmconceptualunderstandingthatallowsthemtousestatisticaltoolsintelligentlyandtobesophisticatedconsumersofinformationfromstudieswhoseconclusionsarebasedondata.StudentscompletingtheStatwaycoursewillunderstandthatdataanalysisisaprocessthatbeginswiththeformulationofaquestionthatcanbeaddressedwithappropriatedata,followedbythedevelopmentofathoughtfulplanforidentifyingandcollectingthenecessarydata.Studentswillknowhowdatacanbedisplayedandsummarizedininformativeways,andtheywillunderstandhowthedatacanbeusedtodrawconclusionsinthepresenceofuncertainty.Thefollowinggoalsandlearningoutcomeshavebeenchosentoenablestudentstoachievethisoverarchingvisionofwhatitmeanstobestatisticallyliterate.GoalS.1:Studentswillunderstandthedataanalysisprocessandthecharacteristicsofwell‐designedstatisticalstudies.LearningOutcomesforGoalS.1Studentsshouldbeableto:

• S.1.1Developaplanforastatisticalstudy.a. Givenareal‐worldproblem,formulateaquestionthatcanbeaddressedby

data.b. Identifyappropriatedatathatcanbeusedtoaddressthequestion.c. Selectanappropriatedatacollectionstrategytoaddressaquestionofinterest.

• S.1.2Knowthetypeandscopeofconclusionsthatcanbedrawnfromdifferenttypesofstatisticalstudies(e.g.,surveys,otherobservationalstudies,experiments).

• S.1.3Knowthecharacteristicsofgoodsamplingplans(e.g.,representativeoflargerpopulation,minimizesourcesofbiasandvariability),well‐designedexperiments(e.g.,randomassignment,replication,control,blocking),andwell‐designedobservationalstudies(e.g.,recognizingpotentialsourcesofbias).

• S.1.4Criticallyevaluateallaspectsofastudy.GoalS.2:Studentswilldemonstratetheuseofdistributionalthinkingtoreasonaboutthedatainordertodescribeandsummarizedistributionsofdata,identifytrendsandpatterns,judgethefitofamodeltoadistribution,anddescribesimilaritiesanddifferencesincomparingdistributions.

Distributionalthinkinginvolvestheabilitytoconsideracollectionofindividualobservationsasanentity(insteadoffocusingonindividualobservations)andtoconsidercharacteristicsofthedistributiontoreasonaboutthedata.

LearningOutcomesforGoalS.2Studentsshouldbeableto:

• S.2.1Givenadatasetofaparticulartype(i.e.,numerical,categorical,bivariatenumerical,bivariatecategorical,ortimeseries).

a. Displaythedatausingappropriategraphicaldisplays.

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b. Summarizethedatausingappropriatenumericalsummaries.c. Describethedatadistributionincontext.d. Viewingdataasamodelpluserror,assesstheappropriatenessofpotential

models(e.g.,normaldistributionasamodelfornumericaldata,theleastsquaresregressionlineasafittobivariatenumericaldata,independenceasamodelforbivariatecategoricaldata,linearorexponentialgrowthasamodelfortimeseriesdata).

• S.2.2Recognizedifferentrepresentationsofthesamedatadistribution(e.g.,dotplot,boxplot,histogram)andunderstandhownumericalsummariesarerelatedtocharacteristicsofthedatadistribution(e.g.,extremeleftskewtendstohavemean<median;theeffectofoutliersandinfluentialobservations).

• S.2.3Makemeaningfulandappropriatecomparisonsofdistributionsofdatacollectedfromtwoormoredifferentgroups.

GoalS.3:Studentswilldemonstrateanabilitytouseappropriatestatisticalevidencetoreasonaboutpopulationcharacteristicsandaboutexperimentaltreatmenteffects.LearningOutcomesforGoalS.3Studentsshouldbeableto:

• S.3.1Demonstrateabasicunderstandingofprobability.a. Interpretaprobability.b. Estimateprobabilities(includingconditionalprobabilities)empiricallyandusing

simulation.c. Understandhowaprobabilitydistributionmodelsthebehaviorofavariable.d. Understandhowsamplingdistributionsmodelthebehaviorofasamplestatistic

(e.g.,asamplemeanorsampleproportion).• S.3.2Understandhowsamplingdistributionsandprobabilitysupportdrawing

conclusionsbasedondataandassessingtheassociatedrisks.• S.3.3Understandthelogicandreasoningusedtointerpretresultsfromdifferenttypes

ofstatisticalstudies,includingsurveys,otherobservationalstudies,andexperiments.• S.3.4Determinewhatstatisticalmethodsareappropriateinagivensituationbasedon

thegoaloftheanalysisandthedataavailable,andknowandassesstheconditionsrequiredforappropriateuseofagivenstatisticalmethod.

• S.3.5Criticallyevaluatewhetherconclusionsbasedondataarereasonable.• S.3.6Computeconfidenceintervalestimatesandinterpretconfidenceintervals,

confidencelevel,andmarginoferrorincontext.• S.3.7Inagivencontext,determineappropriatenullandalternativehypothesesand

understandwhatconclusionsreasonablyfollowfromadecisiontorejectthenullhypothesisandfromadecisionnottorejectthenullhypothesis.

• S.3.8Understandtheconceptofstatisticalsignificance,includingsignificancelevelsandP‐values.

• S.3.9Carryouthypothesisteststoreachaconclusionandcommunicatetheconclusionincontext.

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MathematicsStudentLearningGoalsandOutcomesforStatwayTobestservethediverseaudience,themathematicscomponentofStatwayfocusesinstructionandassessmentonkeyconceptsthatsupportstatisticalthinkinganddataanalysis.BroadObjectives• Studentswillbeabletoeffectivelyusethelanguageofmathematicstocommunicateideas.• Studentswillbeproficientinproceduralfluency,conceptualunderstanding,strategic

competence,adaptivereasoning,andproductivedisposition.• Studentswillbeengagedinquantitativeproblemsandinvestigationswheretheydiscover

ideasandgaininsightsthatdevelopquestioningandsolution‐buildingskills.• Studentswillusementalstrategiesandtechnologyaccuratelyandappropriately.M.1.NumeracyGoal:Studentswilldevelopandapplytheconceptsofnumeracytoinvestigateanddescribequantitativerelationshipsandsolveproblemsinavarietyofcontexts.LearningOutcomesforGoalM.1Studentswilldeepentheirabilitytoreasonandusenumbersandbeableto:

• M.1.1 Demonstratenumbersense.• M.1.2 Displayproficiencyinmakingcalculationswithrationalnumbers;knowhowand

whentoestimateresultsandroundresults.• M.1.3 Createmultiplerepresentationsofrationalnumbersandbeabletorecognize

whichrepresentationismostusefulforaddressingaproblemortoconveyquantitativeinformation.

M.2.ProportionalReasoningGoal:Studentswillrepresentproportionalrelationshipsandsolveproblemsthatrequireanunderstandingofratios,rates,proportions,andscaling.LearningOutcomesforGoalM.2Studentswillbeableto:

• M.2.1 Compareproportionalrelationshipsthatmayberepresentedindifferentwaysandunderstandtheroleandfunctionofkintherelationshipy=kx.

• M.2.2 Distinguishbetweenabsolutedifferenceandrelativedifference,andusepercentagestodescribechangesinaquantityortheerrorofanestimategiventheexactvalueofthequantity.

• M.2.3 Applyquantitativereasoningstrategiestoproportionalrelationshipsinreal‐worldproblemsusingunitseffectivelyandprecisely.

M.3.AlgebraicReasoningGoal:Studentswillreasonusingthelanguageandstructureofalgebratoinvestigate,represent,andsolveproblems.LearningOutcomesforGoalM.3Studentswillbeableto:

• M.3.1 Usevariables,evaluateexpressions,andsolveforunknownquantitiesandforquantitiesthatmayvary.

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• M.3.2 Representreal‐worldandquantitativerelationshipswithequations,inequalities,expressions,tables,verbaldescriptions,symbols,andgraphs.

• M.3.3 Solveequationsandinequalitiesandexplainhowresultsrelatetotheoriginalcontext.

M.4.FunctionsandModelingGoal:Studentswillunderstandfunctionsasawayofmodelingacorrespondencebetweentwovariables.Studentswillbeabletorepresentfunctionsinvariousways:verbally,algebraically,andgraphically.Statwayfocusesonlinearandexponentialfunctions.LearningOutcomesforGoalM.4Studentswillbeableto:

• M.4.1 Representafunctionalgebraicallyandbeabletocomputevaluesofafunction.• M.4.2 Describeafunctionverbally,algebraically,graphically,andinatableofvalues,

andmakeconnectionsamongrepresentations.• M.4.3 Makeconjecturesaboutthebehaviorofafunctiongivenseveralvaluesofthe

functionandagivencontext.• M.4.4 Modelsituationswithlinear,quadratic,andexponentialfunctions,inequalities

andequations.• M.4.5 Beabletoinvestigategraphicallyandnumerically(withtechnology)theeffectof

changingaparameterwithinamodel.

Forlinearfunctions• M.4.6 Studentswillbeableto:

a. Uselinearfunctionstomodelsituationsinvolvingconstantratesofchange.b. Describetheconstantofproportionality,slope,astherateofchangeofthe

functionusingappropriateunits.c. Giventhegraph,anequation,ortwoormorepointsonaline,determineand

interprettheintercept(s)andslope.d. Givenasetofpointsthatexhibitalineartrend,determinethelineofbestfit.e. Computeandinterprettheerrorsordeviationfromalineofbestfitthatisused

tomodeladatasetwithalineartrend.

Forexponentialfunctions• M4.7 Studentswillbeableto:

a. Identifyandquantifyexponentialgrowthordecayinformulas,graphs,tables,andapplications.

b. Characterizeanddescribeexponentialmodelsandcomparethemtoothermodels.

c. Useexponentialfunctionstorepresentrelationshipsbetweenvariablesininvolvingexponentialgrowthanddecay.

d. Describetransformationsofthegraphsofexponentialfunctions.