True/False
1.Itisestimatedthatbetween20and25percentofallelementarystudentsstrugglewithlearningmathematics.
a.True
b.False
2.Thecurrentemphasisinmathematicaleducationisnowonthedevelopmentofmathliteracyandconceptual
knowledge.
a.True
b.False
3.Moststudentswillneedconcreteexperiencesandatleastsomedirectinstructiontobuildastrongfoundationin
measurement.
a.True
b.False
4.Inmathematicalcommunication,astudentmustbeabletoconnectEnglishwordswithsymbolsinordertodevelop
mathliteracy.
a.True
b.False
5.Mathvocabularyshouldnotbedirectlytaught,butlearnedthroughauthenticproblemsolvinginvestigations.
a.True
b.False
6.​
Childrenfirstlearnhowtoordernumbersandusetheminoperationsandthenprogresstolearningthingslikehowto
matchobjects,recognizegroupsofobjects,andcount.
a.True
b.False
7.Manydiverselearnersneed“handson”mathsotheycansee,hold,andmoveobjectsinordertograspskillsand
concepts.
a.True
b.False
8.Unlikeothersubjectareas,astudent’scultureisirrelevantintheteachingofmathematics.
a.True
b.False
9.Studentswhostrugglewithmathematicscanincreasetheirabilitytoreasoninalgebrathroughtheuseofguided
practice,independentpractice,frequentreviews,andcorrective/positivefeedback.
a.True
b.False
10.Ascognitiveandmetacognitivechallengesincrease,theneedforconcreterepresentation,directinstruction,
scaffolding,andtaskanalysisconverselydecrease.
a.True
b.False
MultipleChoice
11.Inthe21stcenturytheleveloftechnicalandmathematicalskillsrequiredofeveryone,regardlessofwhetherornot
theygotocollege,has:​
a.​remainedthesame.
b.​increased.
c.​decreased.
d.​Diminished.
12.Theimpactoftechnologycanbefelt:​
a.​inschools.
b.​inthehomeatwork.
c.​inthecommunity.
d.​Allofthechoicesarecorrect.
13.Allofthefollowinghavecontributedtotheincreasedemphasisonmathematicseducation,EXCEPT:
a.​Goals2000:EducateAmericaActof1994.
b.​PrinciplesandStandardsforSchoolMathematics.
c.​ReauthorizationofIDEA,1997.
d.​CommonCoreStateStandards.
14.Thestandards-basedreformmovementinmathematicseducationhasmadeteachingstudents_____________a
priority.​
a.​tobecriticalthinkers
b.​proceduralknowledge
c.​rule-drivenknowledge
d.​tobeconcretethinkers
15.________________hasbecomethenumberonepriorityformathcurriculuminbothgeneralandspecialeducation.​
a.​Mathematicalcommunication
b.​Numbersandoperations
c.​Problem-solving.
d.​Computationfluency
16.Inordertobeagoodproblemsolver,studentsmustpossessallofthefollowingcharacteristics,EXCEPT:
a.​understandingthereisonlyonerightwaytoarriveatananswer.
b.confidence.​
c.​risk-taking.
d.​willingnesstolearnfrommistakes.
17.Goodproblemsolversmusthaveallofthefollowingcharacteristics,EXCEPT:
a.​anabilitytoreason.
b.​highlevelsofreadingfluency.
c.​ausefulinnerlanguage.
d.​anabilitytoevaluateandpredict.
18.Asstudentsgetolder,risk-takinginmathproblemsolvingtendsto:​
a.​increase.
b.​decrease.
c.​bethesameaswhentheywereyoung.
d.​changeforthebetter.
19.StudentswithADHDappeartohavethemostdifficultywithproblemsolvingandcalculationbecause:​
a.theyalsohavecognitivedeficits.​
b.​theycanonlylearninreallifesettings.
c.​theytendtofocusonlessrelevantstimuliandmissthe“bigpicture.”
d.​behavioralissuesimpedetheirlearningofmathconcepts.
20.Inordertofostergeneralizationofconceptsandskillapplication,itisbesttoteachmaththrough:​
a.skillstaughtinisolation.​
b.​intensivedirectinstruction.
c.​afocusonrelevantstimuliasopposedtothebigpicture.
d.​authentic,anchoredlearning.
21.Astudentwhounderstandsthatthewordaddisrepresentedbythesymbol+isdemonstratingabilityin:​
a.​visual-motorskills.
b.spatiallearning.​
c.​mathliteracy.
d.​computationfluency.
22.Studentswhohavedifficultyunderstandingthatthewordquartercanbeusedtodescribe15minutes,twenty-five
cents,orone-fourthofawholehaveaproblemwithlanguage____________.​
a.​phonology
b.alphabeticprinciple​
c.​semantics
d.​morphology
23.Thereisevidencetosupportallthefollowingstatementsregardingsecondlanguagelearnersandmathematics,
EXCEPT:
a.​SecondlanguagelearnerswhohavedevelopedbasicinterpersonalcommunicationskillsinEnglishwillalso
haveasufficientmathvocabulary.
b.​Englishlanguagelearnersneedexposureearlytomathvocabularyinordertoacceleratetheirmath
performance.
c.​Difficultieswithmathcanbeovercomeintimewhenanextraeffortismadetolearnthelanguageandrelated
mathskills.
d.​LowerperformancesonmathassessmentsbyEnglishlanguagelearnersrelatesmoretolackofexposureto
mathematicalwordsandphrasesthentolackofmathematicalskill.
24.Studentsneedtoseehowmathematicaloperationssuchasadding,subtracting,multiplying,anddividingareall
connectedsothatlaterontheywillbeableto:​
a.​passadditiontests.
b.​makereasonablepredicationsandestimates.
c.​earnreasonablegradesinmathclasses.
d.​improvetheirvisual-motorskills.
25.Computationalfluencyreferstotheabilityto:​
a.​useanumberline.
b.workfromrighttolefttosolvecolumn-formcalculations.​
c.​calculateaccuratelyandefficiently.
d.​lineupcomputationalproblemsinmath.
26.Successinalgebrarequiresstudentstobeabletodoallofthefollowing,EXCEPT:
a.understandpropertiesofnumbersandrecognizepatterns.
b.​identifysymbolsandunderstandtherelatedlanguage.
c.​usereasoningabilities.
d.​easilyseepicturesandshapes,orhavevisualspatial“intelligence.”
27.Allofthefollowingstatementsregardingalgebraaretrue,EXCEPT:
a.​algebraicthinkingcanbeseenonallgradelevelsaswemovetowardaproblemsolvingemphasisinmath.
b.​concretethinkersgenerallydopoorlyinalgebra,whilemoreabstractthinkersgenerallydowell.
c.​strongskillsinalgebraarenecessarytodevelophigherlevelcriticalmathskillsneededinmostworkplaces
today.
d.​usingalgebraicsymbols,graphs,equations,etc.,studentslearntorepresentandanalyzemathematicalsituations
andseerelationshipsbetweennumbers.
28.Allofthefollowinggroupofstudentsarelikelytoneedextrasupportsinunderstandinggeometry,EXCEPTstudents
whoare:
a.​spatially-challenged.
b.​physically-challenged.
c.​verbally-challenged.
d.​cognitivelychallenged.
29.Learningtotelltime,determiningtheoutsidetemperature,cooking,anddoinglaundryallrequirethemathematicalskill
of:
a.​algebra.
b.​geometry.
c.​measurement.
d.​computationfluency.
30.Studentswithlearningdisabilitiessometimeshavegreatdifficultymeasuring:​
a.​timeandlength.
b.lengthanddirection.​
c.​heightsanddirection.
d.​directionandtime.
31.Mathvocabularylike“certain”or“impossible”areassociatedwith:​
a.dataanalysisandprobability.​
b.​geometryanddataanalysis.
c.​probabilityandalgebra.
d.​dataanalysisandmeasurement.
32.Teachersneedtoshowstudentshowweusedataanalysisandprobabilityinoureverydaylivesso:​
a.​itdoesn’tseemsoconcrete.
b.theyknowweunderstandtheconcepts.​
c.​itdoesn’tseemsoabstract.
d.​theyareincompliancewithstandardsbasedreform.
33.Inordertodetermineastudent’sworkinglevelinmathematics,_____________shouldbeused.​
a.​informalassessments
b.​amixtureofassessmenttools
c.​resultsfromgroupadministeredachievementtests
d.​standardizedassessments
34.Whichtypeofformalassessmentfocusesmorespecificallyonmathskillareasandhelpstodeterminestrengthsand
needswithinthemathdomain?​
a.Achievementtests​
b.Interestinventories​
c.​Diagnostictests
d.​Erroranalyses
35.Informalmathassessmentscangiveusinsightstostudentlearningthatwecannotgetthroughanyothermeans.
WhichofthefollowingisNOTanexampleofaninformalassessment?​
a.​Criterion-referencedassessment
b.Curriculumbasedassessment​
c.​Portfolioassessment
d.​Erroranalysis
36.Allofthefollowingcanoccurwhenstudentshavemathanxiety,EXCEPT:
a.​initiallearningcanbeblocked.
b.​workingmemorycanbehindered.
c.demonstrationofskillsandconceptsonassessmentscanbehindered.​
d.longtermmemorycanbehindered.​
37.Researchhassuggestedthatallofthefollowingcanhelpreducemathanxiety,EXCEPT:
a.​providingpeermodelsandsocialsupport.
b.​assigningindividualseatwork.
c.​discussingincorrectanswers.
d.​eliminatingunnecessarycompetition.
38.WhilegradingJohn’sadditionandsubtractionhomeworkassignmentsandquizzes,theteachernoticesthatwhenever
Johnbeginswithanadditionproblem,hecontinuestoperformadditiononalloftheproblems,includingthosethatare
subtractionproblems.Likewise,ifthefirstquestionisasubtractionproblem,Johnperformssubtractiononallofthe
problems.Theteacherhasperformeda(n)__________ofJohn’swork.
a.​diagnosticassessment
b.criterionreferencedtest​
c.​erroranalysis
d.​mathinterview
39.Studiesongenderandmathhassuggestedallofthefollowing,EXCEPT:
a.​boysareinherentlymoreskilledinmaththangirls.
b.​boysprefertousespatialrepresentationsandmemorytosolvemathproblems.
c.​girlsprefermathstrategiespairedwithmanipulativestosolvemathproblems.
d.​teachersmayreinforcepositiveperformanceinmathwithattentionandpraisemoreoftenforboysthanfor
girls.
40.Whenstudentsfirstunderstandthatsymbols,suchaslettersinalgebra,canbeusedtostandforunknownnumbers,
theyhavemovedtowhichofthefollowinginstructionalstages?​
a.​Concrete
b.​Representational
c.​Abstract
d.​Manipulative
41.Allofthefollowinginstructionaltechniquescanhelpstudentsintheproblemsolvingprocess,EXCEPT:
a.​creatingastoryboard.
b.​creatingtimedcompetitions.
c.​usingmnemonicstrategies.
d.usingmultisensorymanipulatives.​
42.Astudyonearlymathskillsofchildrenconcludedallofthefollowing,EXCEPT:
a.​nosignificantdifferencewasfoundintheconventionalmathknowledgeoffour-year-oldchildrenaccordingto
theirsocioeconomicstatus.
b.​themore“teachertalk”aboutmathematicsthatoccursthegreatertheoverallachievementinmathbyall
students.
c.​earlydevelopmentinmathhaslongtermeffectsonmathachievement.
d.promoting“bestpractices”inmathinstructionatthepreschoollevelcansetthestageforfuturemathsuccess.
43.WhichofthefollowingisNOThelpfulinpromotingmathcommunicationintheclassroom?​
a.Makesuremathvocabularyisembeddedintothecontent,modeled,andusedfrequentlyaspartofevery
lesson
b.FordiversestudentsandEnglishlanguagelearners,avoidmathematicalvocabularyandteachusingsimpler
terms
c.Usecorrect,universalmathematicaltermswhenteaching,andputthemoncards,posters,orlabels
d.​Usevisualimagery,keywordmnemonics,andconnectionstopriorlearning
44.Allofthefollowingprogramsandtechniquescanhelpsupportstudentsastheylearnaboutnumbersandoperations,
EXCEPT:
a.completedmultisensory,TouchMathtoolssuchasbeans,foamdots,andpipecleanercirclesthatcanrepresent
therelationshipbetweennumbersandvalues.
b.​lefttorightsubtractionalgorithmstohelpstudentswhohavedifficultywithrighttoleftworkorwith
regrouping.
c.​lessonextensionswherestudentareexpectedtointuitivelybeabletotransferthebasicprinciplesinmathto
reallifeproblemsolving.
d.​thelatticemultiplicationmethodtobreakdownlargemultiplicationproblemsintosmall,manageablesteps.
45.WhichofthefollowingstatementsdoesNOTapplytobestpracticeinteachingalgebratodiverselearners?​
a.​Advanceorganizersintheformofquestions,promptsonacardorworksheet,etc.shouldbeused
b.​Explicitinstructionsinself-monitoring,suchasusing“thinkalouds”tomodelyourownthinkingprocess,help
studentsdevelopreasoningskills
c.​StrategiessuchastheSTARstrategyhelpstudentstovisualizehowtosolveanequation
d.​Assessmentofprerequisitemathematicalskillsisnotnecessarywhenplanningalgebrainstruction
46.Geometryconceptscanbecomemoremeaningfulfordiverselearnersthroughtheuseofallofthefollowing,
EXCEPT:
a.​concreterepresentationsofgeometricshapes.
b.​independentpracticeworksheetsandhomeworkassignmentstoassiststudentsinremediatingweakand
underdevelopedmathskills.
c.posters,models,andcomputerpresentationstorepresentgeometricskillsandconcepts.
d.​specializedcomputerprogramssuchasDynamicGeometrySoftware(DGS).
47.Concreteinstructionaltechniquesthatincludeusingrealclockstoteachtime-telling,realcoinstoteachmoneyskills,
constructinggridsthatstudentscanactuallywalkon,orconstructinga‘GallonMan’toteachunitsofcapacityare
usefulinteachingstudentsconceptsof:​
a.​algebra.
b.​problemsolving.
c.​measurement.
d.​geometry.
48.Allofthefollowingstatementsondataanalysisandprobabilityaretrue,EXCEPT:
a.​youngerstudentsenjoycollecting,organizing,analyzing,anddisplayingdatabutthesearenotageappropriate
activitiesforolderstudents.
b.datacollectioncaneasilyoccurinallareasofthecurriculum,thusreinforcingmathematicalconcepts.​
c.​graphingstudentpreferences,suchasfavoritemovies,music,etc.,canactivatetheaffectivedomain.
d.​probabilitylessonslendthemselvesquiteeasilytoemployingmultisensorylearning.
SubjectiveShortAnswer
49.Whichgroupofstudentstendstofindproblemsolvingmostchallenging?Providearationaleforyouranswer.
50.Explainhowteachingamathconcepttoanonverbalstudentcouldhelpateacherarriveatcreativewaystoteachthe
sameconcepttoallstudentsintheclassroom.Giveatleasttwoexamplestoillustrateyouranswer.
51.Whyisearlynumberlearningsocriticalforsubsequentsuccessinmath,andwhatbasicmathematicalconcepts
shouldchildrenlearnatthepreschoollevel?
52.Whatkindsofmathematicalskillsandconceptsdostudentsneedtohaveinordertosuccessfullyunderstand
measurement?
53.Whatkindsofinformationcanwegatheronastudent’smathematicalabilitiesfromformalassessments?
54.Explainwhatisinvolvedinprogressmonitoringandwhyitisacriticalcomponentofmathinstructionfordiverse
learners
55.Whatcanteachersdotohelptheirstudents’progressthroughthethreeinstructionalstagesinmathematicallearning
(e.g.,concrete,representational,andabstract)?
56.Howcanteacherssupportstudentswhomaystrugglewithproblem-solvingassignments?
Essay
57.Basedonlarge-scaleassessmentsmonitoredbytheNationalAssessmentofEducationalProgressintheUnited
Statesfrom2011to2013(NCES,2014),36%ofhighschoolseniorslackedabasicunderstandinginmath,andthereis
asizablegapinachievementbyethnicity,familyincome,anddisabilities.Whatrecommendationswouldyoumaketo
raisethemathematicalachievementofallstudentsingeneralandspecialeducationandclosetheachievementgaps?
58.ExplainhowmathematicscanbetaughtusingUDLprinciplesandgiveexamplesofthevarioustoolsandinstructional
techniquestosupportyouranswer.