Student response shows clear evidence of

 CRITERIA FOR ASSESSING MATHEMATICS LEVEL 1Emerging LEVEL 2Approaching LEVEL 3Proficient LEVEL 4Exemplary Claim 1 Concepts & Procedures “Students can explain and apply mathematicalconcepts and carry out mathematical procedures with precision and fluency.” Use of invalid procedures, may not address learning targetLimited conceptual understandingAttempts to use a model Use of valid procedures, may not always be carried out correctly Some conceptual understanding Some use of models Use of valid procedures, carried out correctlyConceptual understanding Some use of / connections between various models Consistent, independent use / evaluation of multiple methodsThorough, concise conceptual understandingClear, precise connections between various models Claim 2 Problem Solving “Students can frame and solve a range of complex and real-world problems in pure and applied mathematics.  This is accomplished with the use of problem solving strategies and mathematical models” Difficulty reaching a valid solutionLimited attention to precision and thoroughnessDifficulty finding / applying strategies Solution reached, may not make senseLittle attention to precision and thoroughnessSome strategies used, may not be appropriate Valid solution reached, makes sense in contextSome attention to precision and thoroughnessAppropriate problem solving strategies Results examined / solutions verifiedPrecise, thorough responseEfficient problem solving strategies Claim 3 Communication and Reasoning“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others through the use of mathematical language and/or models.” Limited  mathematical reasoning Lack or incorrect use of mathematical language and symbolic notationNo justification of reasoning Attempts to show mathematical reasoning using models; connection between reasoning and model may not be clearSome appropriate mathematical language and symbolic notationLimited justification of reasoning Correct mathematical reasoning including models;  some connection between reasoning and modelCorrect mathematical language and appropriate symbolic notationJustification of mathematical reasoning Concise, thorough mathematical reasoning using models; clear connection between reasoning and modelPrecise mathematical language and symbolic notationThorough justification of  mathematical reasoning using multiple pieces of evidence Claim 4 Modeling interwoven throughout