Quantitative Reasoning and / or Quantitative Literacy€¦ · Quantitative Literacy(QL) –also...

QuantitativeReasoningand/or

QuantitativeLiteracyCSUStanislausQuantitativeReasoningWorkingGroup

SanJoseMeetingApril22,2016

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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:

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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