Elementary Mathematics
Standard 1: Knowledge of Mathematical Problem Solving
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Candidates know,understand, and applythe process ofmathematical problemsolving.
Candidates can:
• Apply and adapt a varietyof appropriate strategiesto solve problems.
• Solve problems that arisein mathematics and thoseinvolving mathematics inother contexts.
• Build new mathematicalknowledge throughproblem solving.
• Monitor and reflect on theprocess of mathematicalproblem solving.
Standard 2: Knowledge of Reasoning and Proof
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Candidates reason,construct, and evaluatemathematicalarguments and developan appreciation formathematical rigor andinquiry.
Candidates can:
• Recognize reasoning andproof as fundamentalaspects of mathematics.
• Make and investigatemathematical conjectures.
• Develop and evaluate
mathematical argumentsand proofs.
• Select and use varioustypes of reasoning andmethods of proof.
Standard 3: Knowledge of Mathematical Communication
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Candidatescommunicate theirmathematical thinkingorally and in writing topeers, faculty, andothers.
Candidates can:
• Communicate theirmathematical thinkingcoherently and clearly topeers, faculty, and others.
• Use the language ofmathematics to expressideas precisely.
• Organize mathematicalthinking throughcommunication.
• Analyze and evaluate themathematical thinking andstrategies of others.
Standard 4: Knowledge of Mathematical Connections
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Candidates recognize,use, and makeconnections betweenand amongmathematical ideas and
Candidates can:
• Recognize and useconnections among
in contexts outsidemathematics to buildmathematicalunderstanding.
mathematical ideas.• Recognize and apply
mathematics in contextsoutside of mathematics.
• Demonstrate howmathematical ideasinterconnect and build onone another to produce acoherent whole.
Standard 5: Knowledge of Mathematical Representation
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Candidates use variedrepresentations ofmathematical ideas tosupport and deepenstudents' mathematicalunderstanding.
Candidates can:
• Use representations tomodel and interpretphysical, social, andmathematical phenomena.
• Create and userepresentations toorganize, record, andcommunicatemathematical ideas.
• Select, apply, andtranslate amongmathematicalrepresentations to solveproblems.
Standard 6: Knowledge of Technology
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Candidates embracetechnology as anessential tool forteaching and learningmathematics.
Candidates can:
• Use knowledge ofmathematics to select anduse appropriatetechnological tools, suchas but not limited to,spreadsheets, dynamicgraphing tools, computeralgebra systems, dynamicstatistical packages,graphing calculators, data-collection devices, andpresentation software.
Standard 7: Dispositions
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Candidates support apositive dispositiontoward mathematicalprocesses andmathematical learning.
Candidates can:
• Attention to equity• Use of stimulating
curricula• Effective teaching• Commitment to learning
with understanding• Use of various
assessments
• Use of various teachingtools including technology
Standard 8: Knowledge of Mathematics Pedagogy
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Candidates possess adeep understanding ofhow students learnmathematics and of thepedagogical knowledgespecific to mathematicsteaching and learning.
The candidate:
• Selects, uses, anddetermines suitability ofthe wide variety ofavailable mathematicscurricula and teachingmaterials for all studentsincluding those withspecial needs such as thegifted, challenged andspeakers of otherlanguages.
• Selects and usesappropriate concretematerials for learningmathematics.
• Uses multiple strategies,including listening to andunderstanding the waysstudents think aboutmathematics, to assessstudents' mathematicalknowledge.
• Plans lessons, units andcourses that address
appropriate learninggoals, including those thataddress local, state, andnational mathematicsstandards and legislativemandates.
• Participates inprofessional mathematicsorganizations and usestheir print and on-lineresources.
• Demonstrates knowledgeof research results in theteaching and learning ofmathematics.
• Uses knowledge ofdifferent types ofinstructional strategies inplanning mathematicslessons.
• Demonstrates the abilityto lead classes inmathematical problemsolving and in developingin-depth conceptualunderstanding, and tohelp students develop andtest generalizations.
• Develop lessons that usetechnology's potential forbuilding understanding ofmathematical conceptsand developing importantmathematical ideas.
Standard 9: Knowledge of Number and Operation
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Candidatesdemonstratecomputationalproficiency, including aconceptualunderstanding ofnumbers, ways ofrepresenting number,relationships amongnumber and numbersystems, and meaningsof operations.
Candidates can:
• Develop the meaning ofaddition, subtraction,multiplication, and divisionand provide multiplemodels for whole numberoperations and theirapplications.
• Recognize the meaningand use of place value inrepresenting wholenumbers and finitedecimals, comparing andordering numbers, andunderstanding the relativemagnitude of numbers.
• Demonstrate proficiencyin multi-digit computationusing algorithms, mentalmathematics, andcomputational estimation.
• Analyze integers andrational numbers, theirrelative size, and howoperations with wholenumbers extend tointegers and rationalnumbers.
• 9.5 Demonstrateknowledge of the historical
development of numberand number systems
• Includes contributionsfrom diverse cultures.
Standard 10: Knowledge of Different Perspectives on Algebra
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Candidates emphasizerelationships amongquantities includingfunctions, ways ofrepresentingmathematicalrelationships, and theanalysis of change.
Candidates can:
• Explore and analyzepatterns, relations, andfunctions.
• Recognize and analyzemathematical structures.
• Investigate equality andequations.
• Use mathematical modelsto represent quantitativerelationships.
• Analyze change in variouscontexts.
• Demonstrate knowledgeof the historicaldevelopment of algebraincluding contributionsfrom diverse cultures.
Standard 11: Knowledge of Geometries
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Candidates use spatialvisualization andgeometric modeling toexplore and analyzegeometric shapes,structures, and theirproperties.
Candidates can:
• Use visualization, theproperties of two- andthree-dimensional shapes,and geometric modeling.
• Build and manipulaterepresentations of two-and three-dimensionalobjects using concretemodels, drawings, anddynamic geometrysoftware.
• Specify locations anddescribe spatialrelationships usingcoordinate geometry.
• Apply transformations anduse symmetry,congruence, andsimilarity.
• Demonstrate knowledgeof the historicaldevelopment of Euclideanand non-Euclideangeometries includingcontributions from diversecultures.
Standard 12: Knowledge of Data Analysis, Statistics, and Probability
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Candidatesdemonstrate anunderstanding ofconcepts and practicesrelated to data analysis,statistics, andprobability.
Candidates can:
• Design investigations thatcan be addressed bycreating data sets andcollecting, organizing, anddisplaying relevant data.
• Use appropriate statisticalmethods andtechnological tools toanalyze data and describeshape, spread, andcenter.
• Apply the basic conceptsof probability.
• Demonstrate knowledgeof the historicaldevelopment of probabilityand statistics includingcontributions from diversecultures.
Standard 13: Knowledge of Measurement
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Candidates apply anduse measurementconcepts and tools.
Candidates can:
• Recognize and applymeasurable attributes ofobjects and the units,
systems, and processesof measurement.
• Employ estimation as away of understandingmeasurement units andprocesses.
• Demonstrate knowledgeof the historicaldevelopment ofmeasurement andmeasurement systemsincluding contributionsfrom diverse cultures.
Standard 14: Field-Based Experiences
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Candidates completefield-based experiencesin mathematicsclassrooms.
Candidates can:
• Engage in a sequence ofplanned opportunitiesprior to student teachingthat includes observingand participating in middlegrades mathematicsclassrooms under thesupervision ofexperienced and highlyqualified teachers.
• Experience full-timestudent teaching inelementary grades
mathematics that issupervised by anexperienced and highlyqualified teacher and anorganizational supervisorwith elementary gradesmathematics teachingexperience.
• Demonstrate the ability toincrease students'knowledge ofmathematics.