QuantitativeReasoningand/or
QuantitativeLiteracyCSUStanislausQuantitativeReasoningWorkingGroup
SanJoseMeetingApril22,2016
http://csustan.csustan.edu/qr
Weare:
Dr.TomCarter,Chair/CoordinatorComputerScience/CognitiveStudies
Dr.MelanieMartinComputerScience(+Mathematics)
Dr.IanLittlewoodPhysics
OurDefinition,ExpandedDefinition,
andRubrics
ofQuantitativeReasoning
AGeneralMissionStatement/Definition
QuantitativeLiteracy(QL)– alsoknownasQuantitativeReasoning(QR)– isa“quantitativehabitofmind”,proficiency,andcomfortindealingwithandrationallyprocessingnumericaldata.IndividualswithstrongQLskillspossesstheabilitytoanalyzequantitativeproblemsineverydaylifesituationsusinglogicalreasoningsteps.Theyareabletoreadandunderstandnumericaldata.Theycancreatevalidargumentsbasedonquantitativeevidenceandknowhowtointerprettheirconclusions.Theyarecapableofclearlycommunicatingtheiranalysesandargumentsinavarietyofformats(includingwords,tables,graphs,mathematicalequationsandmodels,asappropriate).
Expandeddefinition:
TheformaldefinitionofQuantitativeLiteracyimpliescompetencyindifferentfieldsofbasicmathematics,andtheirapplicationtodiverseproblemsinthesciences,businessandadministration,politics,economics,andineverydaylife.Mostimportantly,QLrequiresanunderstandingofthemathematicsthatisdeeperthanmerememorizationof,andfacilitywith,calculationprocedures.PossessionofstrongQLskillsrequirescompetencyincriticalareas:
1. Approximation/estimation– Theabilitytodoeffectiveapproximationandestimation.
2. Mathematicalmodels– Theabilitytounderstandtheassumptionsbehindmathematicalmodels,andtheimplicationsthatthoseassumptionshaveforthevalidityandscopeofconclusionsthataredrawn.
3. Tablesandgraphs– Theabilitytorepresentandunderstanddataingraphicalformsandothervisualrepresentations.
4. Algebra– Theabilitytounderstandandmanipulatealgebraicequations,includingtheabilitytodrawconclusionsfromfunctionaldependencies.Competencyinthisareathusgoesbeyondtheabilitytosubstituteforknownvariablesandtoperformtherequisitearithmetic.
5. Geometry– Theabilitytothinkandvisualizeinhigherdimensions,includinganunderstandingofthedependenciesofgeometricproperties,suchasvolume,onthedimensionsoftheshapes.Theabilitytoexpresspropertiesintermsofangles.
6. Statistics– Theabilitytodrawappropriateconclusionsfromstatisticaldata,includinganunderstandingofstatisticaldistributionsandpropertiessuchasaverage,median,andstandarddeviation.Theabilitytoincorporateuncertaintiesinthedatawhendrawingconclusions.
Assessment of Overall Quantitative Literacy (1)
Topic Proficient Adequate Deficient
Logical Quantitative Reasoning and Analysis
Can understand problems and develop their own innovative logical quantitative analyses
Can follow and reproduce logical quantitative analyses
Analyses are based principally on random thoughts and guesswork
Assessment of Overall Quantitative Literacy (2)
Topic Proficient Adequate Deficient
Validity, applicability, and limitations of quantitative arguments
Adept at developing valid quantitative arguments and under-standing their assumptions, applicability, and limitations
Can apply learned arguments to similar problems, but also tries to apply them to problems which are beyond the scope of the argument / analysis
Tries to solve all problems using the same strategies without adaptation.
Assessment of Specific Literacies
1. Approximation / Estimation
Proficient Adequate Deficient
Can effectively perform meaningful and novel estimates and approximations.
Can incorporate estimated data to estimate expected results.
Over reliance on calculators. Views all answers as precise. Unable to distinguish between accuracy and precision.
CurricularModules:
Wearedevelopingvariouscurricularmodulesinavarietyofdisciplinesforintegrationintodiverseupperdivisioncourses,includingbothmajorcoursesandupperdivisionGeneralEducationcourses.
Includedherearebriefoverviewsofseveralexamples.Additionalmaterialisavailablehere:
http://csustan.csustan.edu/qr
ExampleCurricularModules
• Water• SpanishLiteratureclass• SociologyApproach
• Estimation• Birthrate• Radioactivetoxicity
• UniversalPre-School
WaterCSUStanislausQuantitativeReasoningwithWater
MelanieMartin,SandraGarcia-Sanborn,Jey StrangfeldComputerScience,ModernLanguages,Sociology
ThismoduleisdesignedforaSpanishLiteratureClass
Water-- AStory• ReadandanalyzeCostaRicanwriterCarmenNaranjo'sshortstory"Yvendimos lalluvia,”publishedin1989.Englishtitle:"Andwesoldtherain."
• Thestorysatirizesthecomplexityandconsequencesoftheeconomicdependencyofdevelopingcountries.
• Thecoreoftheproblemisthattheyhavealreadyexportedalltheirprimaryresources:coffee,rice,sugarcane,vegetables,wood,etc.,andthecountryanditspeoplearestillbroke.
ASolution
• Amiddle-easternSultanhearsofthelandwhererainaboundsandaplanishatchedtosellthewatertotheSultanfor10dollarspercubiccentimeter.
• Theconsequencesareeconomicallyandenvironmentallydevastatingforthisdevelopingcountryanditspeople,astheylosetheirmainnaturalresources(duetotheseveredrought).
• Howcanweunderstand10dollarspercubiccentimeterasapriceforwater?
Water– aSociologyFocus
• WaterFootprintAssessment• PersonalWaterFootprintCalculator• http://waterfootprint.org/en/resources/interactive-tools/personal-water-footprint-calculator/
• FootprintCalculator– thewaterfootprintcalculatorinitsmostsimplisticandbasicformasksrespondentstoanswerthefollowingquestions
• Countryofresidence• Gender(closed-ended,male/female)• Individualportionoffamilyincome(open-ended,indollars)• Vegetarianormeatconsumer(closed-ended,vegetarian,average,andhighmeatconsumption.“Average”and“High”aresubjective)
Pre-Assessment
• Understandingtheimpactofclassandwealthonwateruse.• Testing:Rubric3:UnderstandingTablesandGraphs(Questions1-5)
Rubric1:Estimation(Questions4-5)Rubric4:Algebraic/SymbolicApproaches(Question3)
• Thepie-chartsbelowindicatewaterusagebycountryincomelevelandsectorusage.Comparewateruseinformationinthethreecharts.Whatiswaterusedforprimarilyintermsofworldglobalconsumption,consumptioninlowandmiddleincomecountries,andconsumptioninhighincomecountries?
Estimation
ThismoduleisbeingusedinupperdivisionGeneralEducation,pairedcoursesbetweenEnglishandPhysics.
Introduction
• ThisexercisewasmeanttodevelopaclassestimateoftheamountofradioactivematerialwhichwasgiventoAlexanderLitvinenko,aRussiandissidentlivinginexileinLondon.Alltherequiredphysicshasbeencoveredalreadyinclass,afterwhichtherearetworemainingproblems
• Thereareanumberofstepsinvolved,andfornon-sciencemajorstonavigatetheirwaythroughthemisaskingalot.
• Althoughsomequantitiesareknown(principallyfromthepropertiesoftheradioactiveisotope)othersarenotandreasonableassumptionshavetobemade.
• Westartwithanunrelatedexampletointroducetheideaofestimationbeforetacklingtheproblemathand.
Figure 1b: Assignment of variables. Known variables are in red, assumed variables in blue, and calculated variables in green.
ShouldtheStateassureuniversalpre-schoolopportunitiesforall
children?AQuantitativeReasoningApproach
MelanieMartin
SteppingBack
• Whyareweaskingthis?• Isthereaproblem?• Ifthereisaproblemwhatisthescale?• Whatistheinterestofthestateinthis?• Howwouldwemakeadecision?
• Money• Cheaperthanprisonlater
• Educationaloutcomes• Morelikelytofinishhighschool,college
WhatDataDoINeed?
• Whatisthecurrentsituation:• whendokidsstartschoolinCA,• isTransitionalKindergartenuniversallyavailable,• whatpreschoolprogramsareavailable• Areavailableprogramseffective?
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FIN