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Scott Adamson, Ph.D. Chandler-Gilbert Community College Ted Coe, Ph.D. Achieve THE COMMON CORE MATHEMATICAL PRACTICES GO TO COLLEGE

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YOUR CLASSROOM Close your eyes and imagine your classroom What are YOU doing? What are your STUDENTS doing? What is the nature of the mathematics? Share for 1 minute each with a partner

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TEACHING GOALS Previously, emphasis has been on ways of DOING Now, we emphasize also developing ways of THINKING These ways of thinking lead to HABITS of THINKING This will lead to effective, efficient, flexible, and fluent ways of DOING

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COMMON CORE STANDARDS FOR MATHEMATICS What they are: Math Standards Practice Standards Content Standards What they are not: Anything else

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CBMS SUPPORTED http://www.nctm.org/uploadedFiles/New_and_Noteworthy/CB MS%20Support%20Statement%20for%20CCSSM.pdf

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National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. P.4

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CONTENT STANDARDS By grade for K-8 By Conceptual Category for High School: Number and Quantity Algebra Modeling Functions Geometry Statistics and Probability

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KEY SHIFTS IN THE CCSS-M Focus Coherence Rigor Procedural skill and fluency Conceptual understanding Application

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SAMPLE: HS National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.p.70

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BEYOND WAYS OF DOING

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STANDARDS FOR MATHEMATICAL PRACTICE Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.

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Titans have won a total of 36 games over the past 5 seasons (2009-2013) What is the average (mean) number of games won each year? What does the average mean in this context? WHAT DOES AVERAGE MEAN?

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COMMON CORE STANDARDS What Mathematical Practices were visible during the last conversation? Grade 6: National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. P.39

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ANGLES What is an angle? What am I measuring when I measure an angle?

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4.MD.5 National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. P.31

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Imagine what this might look like. CCSS: GRADE 8 (8.EE.6) 16 National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. P.54

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FROM THE PROGRESSIONS DOCUMENTS Source: http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf p.5

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FROM THE PROGRESSIONS DOCUMENTS Source: http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf p.5http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf

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http://tedcoe.com/math/algebra/constant-rate

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Assume http://tedcoe.com/math/geometry/similar-triangles

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CCSS: GEOMETRY (G-SRT.6) 21 National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors. P.77

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ISSUE: ALIGNED CURRICULUM

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MATERIALS 23 SOURCE: HTTP://IME.MATH.ARIZONA.EDU/PROGRESSIONS/

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MATERIALS 24 SOURCE: ENGAGENY HTTPS://WWW.ENGAGENY.ORG/RESOURCE/ALGEBRA-I-MODULE-3HTTPS://WWW.ENGAGENY.ORG/RESOURCE/ALGEBRA-I-MODULE-3

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EQUIP/IMET SOURCE: WWW.ACHIEVE.ORG/EQUIP

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EQUIP/IMET SOURCE: HTTP://ACHIEVETHECORE.ORG/PAGE/783/INSTRUCTIONAL-MATERIALS-EVALUATION-TOOL-IMET

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ISSUE: ASSESSMENT

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NEXT GENERATION MATH ASSESSMENT

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EXAMPLE Source: http://www.azed.gov/standards-development-assessment/aims/sample-for-students/ (April 2014)

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SMARTER BALANCED CLAIMS http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/Smarter-Balanced-Mathematics-Claims.pdf

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PARCC MATHEMATICS CLAIMS (2013) SOURCE: PARCC (2013)

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SOURCE: CCSS 32 STANDARDS FOR MATHEMATICAL PRACTICE Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the understanding of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning

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Source: http://www.parcconline.org/samples/math PARCC SAMPLE ITEMS

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34 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH PARCC SAMPLE ITEMS

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Grade Level? PARCC SAMPLE ITEMS

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36 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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PARCC SAMPLE ITEMS 37 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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PARCC SAMPLE ITEMS 38 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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Grade Level? PARCC SAMPLE ITEMS 39

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Algebra I PARCC SAMPLE ITEMS 40 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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PARCC SAMPLE ITEMS 41 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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Grade Level? PARCC SAMPLE ITEMS 42

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PARCC SAMPLE ITEMS 43 SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH

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ISSUE: INSTRUCTION

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“People are naturally curious, but we are not naturally good thinkers; unless the cognitive conditions are right, we will avoid thinking.” Willingham, Daniel T. (2009-06-10). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom THINKING

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“There is a great danger in the present day lest science-teaching should degenerate into the accumulation of disconnected facts and unexplained formulae, which burden the memory without cultivating the understanding.” —J. D. Everett, writing in 1873 Willingham, Daniel T. (2009-06-10). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom THINKING

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“Memory is the residue of thought.” Willingham, Daniel T. (2009-06-10). Why Don't Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom THINKING

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A PEEK IN A CLASSROOM Brainstorm… Thinking about the math practices, focusing on ways of thinking, good assessment of learning, relationships and challenge, what do you think a classroom should/does look like? Share for 1 minute each with a partner

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MATHEMATICS TEACHING PRACTICES Establish mathematics teaching goals to focus learning. Implement tasks that promote reasoning and problem solving. Use and connect mathematical representations. Facilitate meaningful mathematical discourse. Pose purposeful questions. Build procedural fluency from conceptual understanding. Support productive struggle in learning mathematics. Elicit and use evidence of student thinking. National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: Authors.

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COMMUNITY COLLEGE IMPACT? Placement Assessment Content Instruction Preservice

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