Elementary Mathematics Standard 1: Knowledge of Mathematical Problem Solving Description Indicators Map to Field Experiences/ Map to Curriculum and Course Experiences Assessment Strategies Candidates know, understand, and apply the process of mathematical problem solving. Candidates can: • Apply and adapt a variety of appropriate strategies to solve problems. • Solve problems that arise in mathematics and those involving mathematics in other contexts. • Build new mathematical knowledge through problem solving. • Monitor and reflect on the process of mathematical problem solving. Standard 2: Knowledge of Reasoning and Proof Description Indicators Map to Field Experiences/ Map to Curriculum and Course Experiences Assessment Strategies Candidates reason, construct, and evaluate mathematical arguments and develop an appreciation for mathematical rigor and inquiry. Candidates can: • Recognize reasoning and proof as fundamental aspects of mathematics. • Make and investigate mathematical conjectures. • Develop and evaluate
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Elementary Mathematics Standard 1: Knowledge of ...Elementary Mathematics Standard 1: Knowledge of Mathematical Problem Solving Description Indicators Map to Field Experiences/ Map
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Elementary Mathematics
Standard 1: Knowledge of Mathematical Problem Solving
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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
Description IndicatorsMap to Field Experiences/
Map to Curriculum and Course ExperiencesAssessment Strategies
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.
• Demonstrates the abilityto lead classes inmathematical problemsolving and in developingin-depth conceptualunderstanding, and tohelp students develop andtest generalizations.
Map to Curriculum and Course ExperiencesAssessment Strategies
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.
• Engage in a sequence ofplanned opportunitiesprior to student teachingthat includes observingand participating in middlegrades mathematicsclassrooms under thesupervision ofexperienced and highlyqualified teachers.
mathematics that issupervised by anexperienced and highlyqualified teacher and anorganizational supervisorwith elementary gradesmathematics teachingexperience.
• Demonstrate the ability toincrease students'knowledge ofmathematics.