Quantitative Reasoningor

Quantitative Literacy

Quantitative Reasoning Working Group

Fall, 20151

Our general topics:

Intro / Participants. 3

A General Mission Statement / Definition. 4

Rubrics. 12

References. 21

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Intro / Participants ←

tcarter@csustan.edu, Computer Science

and the rest of the Quantitative Reasoning core team:

Chris Nagel <CNagel@csustan.edu>, PhilosophyMelanie Martin <mmartin@csustan.edu>, Computer ScienceJungHa An <jan@csustan.edu>, MathematicsIan Littlewood <ilittlewood@csustan.edu>, PhysicsKoni Stone <kkstone@me.com>, ChemistryAugustine Avwunudiogba <aavwunudiogba@csustan.edu>, Geography

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A General Mission Statement /Definition ←

Quantitative Literacy(QL) – also known as QuantitativeReasoning (QR) – is a “quantitative habit of mind”,proficiency, and comfort in dealing with and rationallyprocessing numerical data. Individuals with strong QLskills possess the ability to analyze quantitative problemsin everyday life situations using logical reasoning steps.They are able to read and understand numerical data.They can create valid arguments based on quantitativeevidence and know how to interpret their conclusions.They are capable of clearly communicating their analysesand arguments in a variety of formats (including words,tables, graphs, mathematical equations and models, asappropriate).

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Expanded definition:

The formal definition of Quantitative Literacyimplies competency in different fields of basicmathematics, and their application to diverseproblems in the sciences, business andadministration, politics, economics, and ineveryday life. Most importantly, QL requires anunderstanding of the mathematics that is deeperthan mere memorization of, and facility with,calculation procedures. Possession of strong QLskills requires competency in critical areas:

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1. Approximation / estimation –The ability to do effectiveapproximation and estimation.

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2.Mathematical models – Theability to understand theassumptions behindmathematical models, and theimplications that thoseassumptions have for thevalidity and scope ofconclusions that are drawn.

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3.Tables and graphs – The abilityto represent and understanddata in graphical forms andother visual representations.

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4. Algebra – The ability tounderstand and manipulatealgebraic equations, includingthe ability to draw conclusionsfrom functional dependencies.Competency in this area thusgoes beyond the ability tosubstitute for known variablesand to perform the requisitearithmetic.

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5. Geometry – The ability tothink and visualize in higherdimensions, including anunderstanding of thedependencies of geometricproperties, such as volume, onthe dimensions of the shapes.The ability to expressproperties in terms of angles.

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6. Statistics – The ability to drawappropriate conclusions fromstatistical data, including anunderstanding of statisticaldistributions and propertiessuch as average, median, andstandard deviation. The abilityto incorporate uncertainties inthe data when drawingconclusions.

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Rubrics ←

We have developed some rubrics for various aspects ofQuantitative Reasoning:

Assessment of Overall Quantitative Literacy (1)Topic Proficient Adequate DeficientLogicalQuantitativeReasoningand Analysis

Canunderstandproblems anddevelop theirowninnovativelogicalquantitativeanalyses

Can followandreproducelogicalquantitativeanalyses

Analyses arebasedprincipally onrandomthoughts andguesswork

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Assessment of Overall Quantitative Literacy (2)Topic Proficient Adequate DeficientValidity,applicability,andlimitations ofquantitativearguments

Adept atdevelopingvalidquantitativeargumentsand under-standingtheirassumptions,applicability,andlimitations

Can applylearnedarguments tosimilarproblems,but also triesto applythem toproblemswhich arebeyond thescope of theargument /analysis

Tries tosolve allproblemsusing thesamestrategieswithoutadaptation.

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Assessment of Specific Literacies

1. Approximation / Estimation

Proficient Adequate DeficientCan effectivelyperformmeaningful andnovel estimatesandapproximations.

Can incorporateestimated data toestimate expectedresults.

Over reliance oncalculators. Viewsall answers asprecise. Unable todistinguishbetween accuracyand precision.

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2. Mathematical / Quantitative Models

Proficient Adequate DeficientCan analyze a realworld examplesufficiently toconceptualize asimulation of thesystem, which iscomplex enoughto give meaningfulresults, but simpleenough to beunderstandable.

Can simplifycomplex modelsto obtainapproximateresults andunderstand thelimitationsimposed by thatapproximation.

Can recognizeand appreciatemeaningful use ofmodels tounderstand theworld at large.

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3. Tables and Graphs

Proficient Adequate DeficientCan understanddata presented intabular orgraphical form,and recognizetrends in data.Understands thevalidity ofextrapolation.Can developsketch graphs.

Can extractrelevant datafrom tables orgraphs, andinterpolate, butwithout ability tosee the overallpicture.Recognizeimportance ofscales, labels, anderror bars.

Can retrieve datafrom tables. Failsto recognizeimportance ofscales, labels, anderror bars.

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4. Algebraic / Symbolic Approaches

Proficient Adequate DeficientUnderstandsfunctionalrelationships, canmanipulatesymbols, and candraw conclusionsfrom each. Caneffectively solvenovel wordproblems.

Can reliablymanipulatealgebraic /symbolicexpressions. Canhandle more thanone equation at atime. Can identifyand apply similarmethods tocorrespondingword problems.

Can only “plugand chug”. Makesfrequent mistakeswhenmanipulatingequations.Cannot do wordproblems.

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5. Geometry

Proficient Adequate DeficientCan visualize inthree dimensions.Can scale shapes.Effective atapplyinggeometricmethods tospecific problems.

Can visualizeabove twodimensions onlyfor simple shapes.Unable to scaleshapes.Competent atusing angularmeasurements inmultipledimensions.

Confusion aboutdifferencesbetween volumeand area.Difficulty withangularmeasurements.

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6. Statistics and ProbabilityProficient Adequate DeficientCan interpret datain other(“non-normal”)distributions.Understands thevalidity andlimitations ofsampling methodsincluding thechance of falsepositives.Familiarity withprobabilisticreasoning.

Can interpret datain a normaldistribution,including conceptssuch as mean,mode, median,and standarddeviation.Understands basicideas of samplingmethods and erroranalysis.

Understandssimple average,but does notdistinguish mean,mode, median. Isunfamiliar withstandarddeviation. Noclearunderstanding ofsampling methodsand error analysis.

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http://csustan.csustan.edu/˜ tom/

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References

[1] AACUQuantitative Reasoninghttps://www.aacu.org/peerreview/2014/summer

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