Elementary Mathematics Standard 1: Knowledge of ...Elementary Mathematics Standard 1: Knowledge of...

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.