Developing Mathematical Proficiency - Handouts Page 1 March 2017 Release
Developing Mathematical Proficiency The potential of different types of tasks for student learning
Handouts
Contents
Handout1:TheFiveStrandsofMathematicalProficiency.............................................................2Handout2:TaskA...........................................................................................................................3Handout3:TaskB...........................................................................................................................4Handout4:TaskC...........................................................................................................................5Handout5:TaskD...........................................................................................................................6Handout6:Reflection.....................................................................................................................7
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Developing Mathematical Proficiency - Handouts Page 2 March 2017 Release
Handout 1: The Five Strands of Mathematical Proficiency
ConceptualUnderstanding
Thecomprehensionofmathematicalconcepts,operations,andrelations.
• Enablesstudentstoconnectideastowhattheyalreadyknow
• Supportsretentionandpreventscommonerrors
ProceduralFluency
Skillincarryingoutproceduresflexibly,accurately,efficiently,andappropriately.
• Learningprocedurescanstrengthenanddevelopmathematicalunderstanding,whileunderstandingmakesiteasiertolearnskills
StrategicCompetence
Theabilitytoformulate,represent,andsolvemathematicalproblems.
Tocomeupwithanswertoaproblem,studentsmust:• followasolutionmethodandadaptasnecessary• understandthequantitiesintheproblemand
theirrelationships• representtherelationshipsmathematically• havethemathematicalskillsrequiredtosolve
themathematicalproblem
AdaptiveReasoning
Thecapacityforlogicalthought,reflection,explanation,andjustification.
Asstudentsreasonaboutaproblemtheycan:• buildtheirunderstanding• carryouttheneededcomputations• applytheirknowledge• explaintheirreasoningtoothers
ProductiveDisposition
Thehabitualinclinationtoseemathematicsassensible,useful,andworthwhile,coupledwithabeliefindiligenceandone’sownefficacy.
Requiresfrequentopportunitiesto:• makesenseofmathematics• recognizethebenefitsofperseverance• experiencetherewardsofsensemakingin
mathematics
Adaptedfrom:https://mathequality.wordpress.com/2012/06/25/nrcs-five-strands-of-mathematical-proficiency/
© 2017 Math Assessment Resource Service, University of Nottingham – Published under Creative Commons BY-NC-SA
Developing Mathematical Proficiency - Handouts Page 3 March 2017 Release
Handout 2: Task A
Percent Change Game
Usethese12numberstofillinthegapsbelow.
10,20,25,35,40,50,60,70,75,80,90,100
$____increasedby____%=$____
$____increasedby____%=$____
$____decreasedby____%=$____
$____decreasedby____%=$____Youscoreapointforeachnumberusedonlyonce–andinacorrectexpression.Trytogetthehighestscoreyoucan.(Maximumscore:12points)
Adaptedfromhttp://www.foster77.co.uk/Percentage%20Change%20TASK%20SHEET.pdf
© 2017 Math Assessment Resource Service, University of Nottingham – Published under Creative Commons BY-NC-SA
Developing Mathematical Proficiency - Handouts Page 4 March 2017 Release
Handout 3: Task B
Describing and Defining a Square Whichpairsofstatementsdefineasquare?Whichdonot?
Alessoncalled‘DescribingandDefiningQuadrilaterals’basedonthistask,canbefoundontheMathematicsAssessmentProjectwebsite(http://map.mathshell.org/)
Fourequalsides
Twopairsofparallelsides
Twoequaldiagonals
Rotationalsymmetryoforder4
Fourrightangles
Fourlinesofsymmetry
Diagonalsmeetatrightangles
© 2017 Math Assessment Resource Service, University of Nottingham – Published under Creative Commons BY-NC-SA
Developing Mathematical Proficiency - Handouts Page 5 March 2017 Release
Handout 4: Task C
Always, Sometimes or Never True?
Hereisacollectionofmathematicalstatementsorconjectures:
Considereachstatementinturnanddecidewhetheritisalways,sometimesornevertrue.
• Ifitisalwaystrue,showsomeexamples,andthentrytoprovideanexplanationastowhyitisalwaystrue.
• Ifitisnevertrue,explainwhy.• Ifitissometimestrue,giveexamplesanddefinepreciselywhenitistrueand
whenitisnottrue.
© 2017 Math Assessment Resource Service, University of Nottingham – Published under Creative Commons BY-NC-SA
Developing Mathematical Proficiency - Handouts Page 6 March 2017 Release
Handout 5: Task D
Schoolteachers and Dentists
Thereareabout320millionpeopleintheUS.• Abouthowmanyschoolteachersarethere?
Estimatesomeotherfactsandcheckthemout.
Adaptedfromhttp://www.bowlandmaths.org.uk/pd/pd_01.html
• Abouthowmanydentistsarethere?
© 2017 Math Assessment Resource Service, University of Nottingham – Published under Creative Commons BY-NC-SA
Developing Mathematical Proficiency - Handouts Page 7 March 2017 Release
Handout 6: Reflection
Thinkabouttasksthatarealreadyinuse(eitherbyyouorwellknowntasks)andcategorisethemunderthefivestrandsofmathematicalproficiency:
DescriptionofTask ConceptualUnderstanding
ProceduralFluency
StrategicCompetence
AdaptiveReasoning
ProductiveDisposition
Whichofthefivestrandsofmathematicalproficiencydostudentscurrentlyhavethemostopportunitytodevelopinyourclassroom?
Describehowyouplantoincludeabalanceofthemathematicalproficiencystrandsinyourcurriculumoverthecomingweeks.
