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Mathematics Educators to the Career and College Ready Conference A Quick Look at Critical Topics in Mathematics Reform from Past Academies

 R educe Side Chatter  I nvolve Yourself in the Process  G ive Your Thoughts & Ideas  O pen Your Mind on how You Can Change Instruction  R emember to Silence Electronic Devices

 Reflect on how the Standards for Mathematical Practice will be infused into daily instruction.  Become familiar with the Maryland's College and Career-Ready Standards.  Analyze the instructional SHIFTS

Standards for Mathematical Practice 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others. 4.Model with Mathematics 5.Use appropriate tools strategically 6.Attend to precision 7.Look for and make use of structure. 8.Look for and express regularity in reasoning Apply to every Mathematics Unit in every grade/course

SMP Placemat Activity Behavior Cards Placemat

Conceptual Categories for High School: Number and Quantity Algebra Functions Geometry Modeling Probability and Statistics

Algebra I Arithmetic with Polynomials and Rational Functions  Perform arithmetic operations on polynomials  Understand the relationship between zeros and factors of polynomials  Use polynomial identities to solve problems  Rewrite rational expressions

 Focus  Coherence  Rigor SHIFTS in Mathematics Conceptual Understanding Procedural Skill Modeling/Application

FOCUS FOCUS is largely built into the CCSSM curriculum. The charge for the classroom teacher is to take opportunities to revisit major content frequently and make connections between the major and supporting and additional content.

New Learning Prior Learning COHERENCECOHERENCE Shift #2

Connects to Pythagorean Theorem Distance Formula Pythagorean Trig Identities Connects to

Progression Documents

Instruction in the mathematics classroom of the future must take advantage of every opportunity to make connections between topics both within a course and from course to course if the SHIFT toward COHERENCE is to be a achieved. COHERENCE

“ Rigor is the goal of helping students develop the capacity to understand content that is complex, ambiguous, provocative, and personally or emotionally challenging.” Shift #3

Rigorous Learning Experiences  Challenge students  Require effort and tenacity  Focus on quality  Have multiple paths  Not always “tidy”  Connect ideas in mathematics  Develop strategic, flexible thinking  Encourage reasoning and sense-making  Actively involve students Non-rigorous Learning Experiences  Awkward, difficult values  Minimal effort required  Focus on quantity, repetition  Scripted, includes pathway to the solution  No links to other mathematics  Routine, rote procedures  Memorized rules without understanding  Teachers do the work while students observe What are some characteristics of RIGOROUS learning experiences?

PARCC Model Content Framework documents include Fluency Recommendations

A.Drag into the box exactly three unique items whose sum is less than 10. B.Drag into the box exactly three unique items whose sum is between 10 and 20. C.Drag into the box exactly three unique items whose sum is greater than 20. A.Three unique items whose sum is less than 10 B.Three unique items whose sum is between 10 and 20 C. Three unique items whose sum is greater than 20 Items

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Standard A-REI.10 Conceptual Category: Algebra Domain: Reasoning with Equations and Inequalities Cluster: Represent and solve equations graphically

To help students develop conceptual understanding provide learning experiences that : see connections between the mathematics they are learning and what they already know. use manipulatives to model concepts, and then verbalize their results. show different representations of the same mathematical situation.

What does it mean to MODEL with mathematics?

SMP #4:Model with mathematics Conceptual Category :Modeling Modeling Standards: A.CED.1

Tasks assessing modeling / applications call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards. tasks may include a mix of innovative, machine scored and hand scored responses. will be included on the PBA component and generate evidence for measuring mathematical modeling/application with connections to content.

Report Modeling Cycle Problem Compute Validate Formulate Interpret

Report Modeling Cycle Problem Compute Validate Formulate Interpret

Procedural Skill Modeling/Application Conceptual Understanding

Illustrative Math Bill McCullum, CCSS lead writer Sample Lessons that illustrate specific standards Achieve The Core Jason Zimba, CCSS lead writer Multiple Resources – e.g. Lesson Plans, Assessments, Professional Development courses, Grade-at-a-Glance PARCC Information about PARCC Assessments Sample Lessons Practice Tests

Noticing and Wondering Annie Fetter

The greatest danger for most of us is not that our aim is too high and we miss it…. But that it is too low and we reach it. -- Michelangelo