Proficiency Are you confused ?

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?

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.

What tools do students need? Those would be the 5 steps to proficiency

Essential Components  procedural fluency  conceptual understanding  adaptive reasoning  strategic competence  productive disposition

procedural fluency—  Recall of basic addition and multiplication facts  Formulas and procedures committed to memory  Speed and accuracy at procedures

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…

adaptive reasoning—  Logical thought  Reflection  Justification  Communication

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, …

productive disposition—  Recognize the utility of mathematics  Believe you can do mathematics  Understand the need for engagement  Struggle with ideas  Learn to love math

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!!

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

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?

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.