# Procedures - Explaining procedures CI 401 M&M2 Fall 2009...

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Explaining procedures CI 401 M&M2 Fall 2009

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Mathematical Proficiency Graphic From: “Addning it Up”, 2001, Jeremy Kilpatrick, Jane Swafford, Bradford Findell, Editors ; Mathematics Learning Study Committee, National Research Council
Mathematical Proficiency Conceptual understanding : comprehension of mathematical concepts, operations, and relations Procedural fluency: skill in carrying out procedures, flexibly, accurately, efficiently, and appropriately Strategic competence: ability to formulate, represent, and solve mathematical problems Adaptive reasoning: capacity for logical thought, reflection, explanation, and justification Productive disposition: habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

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Mathematical procedures, strategies, or skills Examples of procedures – Find the slope of a line, simplify an algebraic expressions, find the roots of a quadratic equation, find the area of a trapezoid,find the prime factorization of a number. Examples of strategies – Draw an auxiliary line – Add zero x 2 -2x-24+ 1-1 = (x - 1) 2 - 25 – Multiply by one (sin 2 θ +cos 2 θ =1) – Multiply an equation with fractions by the lcm – Use a table to record information with word problems (mixture problems) – Draw a diagram to model a physical situation Examples of skills – Identify relevant information in a word problem
Rubric for Explaining Procedures © Patricio Herbst; University of Michigan

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To explain a procedure, strategy, or skill a teacher would: Focus the Procedure • Establish clearly what kind of problem the procedure targets. • Demonstrate circumstances when students may encounter such problem (and thus need to use the procedure). • Promote flexibility by comparing pros and cons of the target procedure with those of alternative ones that might be used in similar situations.
Example: The procedure for finding x - and y -intercepts The procedure has the purpose of identifying solution

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Procedures - Explaining procedures CI 401 M&M2 Fall 2009...

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