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Published byBrian Joseph Harrington Modified over 9 years ago
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Proficiency Are you confused ?
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Who says what it means? OPI has a definition (and an 8 page rubric) NCTM has a definition (and numerous books) ACT has a definition (and a poster) Where are you getting YOUR definition?
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Proficiency vs. Standards Any lesson I teach can fit into the standards somewhere. Following the “standards” isn’t enough. They need to guide us, but can’t be THE resource we use. What I need to do is to make the problems in that lesson use the 5 key proficiency “tools”. Every problem doesn’t need to use every tool, but every day, my students need to be given the opportunity to use each one. Giving those opportunities will allow the tools to become second nature.
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What tools do students need? Those would be the 5 steps to proficiency
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Essential Components procedural fluency conceptual understanding adaptive reasoning strategic competence productive disposition
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procedural fluency— Recall of basic addition and multiplication facts Formulas and procedures committed to memory Speed and accuracy at procedures
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conceptual understanding— Being able to understand how and why things work When do you add, when do you divide, when do you graph, when do you…. Why do you add, why do you divide…
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adaptive reasoning— Logical thought Reflection Justification Communication
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strategic competence— Ability to formulate, represent and solve problems with a wide variety of strategies Guess and check, lists, tables, make a model, determine patterns, make a sketch, equations, …
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productive disposition— Recognize the utility of mathematics Believe you can do mathematics Understand the need for engagement Struggle with ideas Learn to love math
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So how do we get there? We expose students to problems that need all 5 steps procedural fluency conceptual understanding adaptive reasoning strategic competence productive disposition Every problem doesn’t need every step, but every lesson does!!
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Translated into kid’s language “Proficiency” means: You must learn your basic facts and be able to compute with numbers You must work hard to understand what you are doing and why you are doing it You must be able to justify your thinking and explain your methods You must know how to change a problem into math symbols and sentences You must learn to love mathematics
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Need a rubric? 1 Point Each: Procedural – did they do it right? Conceptual – did they show the concept? Adaptive – did they communicate the “how”? Strategic – did they do it the “nicest” way? Disposition – did they stick with it to the end?
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How to get kids to use the tools We need to remind them of what they are. We need to encourage them to use them We need to give them problems that necessitate their use. We need to praise them when they make the tools a regular part of their problem solving.
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