Transcript The Common Core Mathematical Practices go to college

THE COMMON CORE MATHEMATICAL
PRACTICES GO TO COLLEGE
Scott Adamson, Ph.D.
Chandler-Gilbert Community College
Ted Coe, Ph.D.
Achieve
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
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
COMMON CORE STANDARDS FOR MATHEMATICS
What they are:
• Math Standards
• Practice Standards
• Content Standards
What they are not:
• Anything else
CBMS SUPPORTED
http://www.nctm.org/uploadedFiles/New_and_Noteworthy/CB
MS%20Support%20Statement%20for%20CCSSM.pdf
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
CONTENT STANDARDS
• By grade for K-8
• By Conceptual Category for High School:
• Number and Quantity
• Algebra
• Modeling
• Functions
• Geometry
• Statistics and Probability
KEY SHIFTS IN THE CCSS-M
• Focus
• Coherence
• Rigor
• Procedural skill and fluency
• Conceptual understanding
• Application
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
BEYOND WAYS OF DOING
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.
WHAT DOES AVERAGE MEAN?
• 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?
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
ANGLES
• What is an angle?
• What am I measuring when I measure an angle?
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
CCSS: GRADE 8 (8.EE.6)
• Imagine what this might look like.
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
16
FROM THE PROGRESSIONS DOCUMENTS
Source: http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf p.5
FROM THE PROGRESSIONS DOCUMENTS
Source: http://commoncoretools.me/wp-content/uploads/2013/07/ccss_progression_functions_2013_07_02.pdf p.5
http://tedcoe.com/math/algebra/constant-rate
http://tedcoe.com/math/algebra/constant-rate
Assume
http://tedcoe.com/math/geometry/similar-triangles
CCSS: GEOMETRY (G-SRT.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.77
21
ISSUE: ALIGNED CURRICULUM
MATERIALS
SOURCE: HTTP://IME.MATH.ARIZONA.EDU/PROGRESSIONS/
23
MATERIALS
SOURCE: ENGAGENY HTTPS://WWW.ENGAGENY.ORG/RESOURCE/ALGEBRA-I-MODULE-3
24
EQUIP/IMET
SOURCE: WWW.ACHIEVE.ORG/EQUIP
EQUIP/IMET
SOURCE: HTTP://ACHIEVETHECORE.ORG/PAGE/783/INSTRUCTIONAL -MATERIALS-EVALUATION-TOOL-IMET
ISSUE: ASSESSMENT
NEXT GENERATION MATH ASSESSMENT
EXAMPLE
Source: http://www.azed.gov/standards-development-assessment/aims/sample-for-students/ (April 2014)
SMARTER BALANCED CLAIMS
http://www.smarterbalanced.org/wordpress/wp-content/uploads/2012/09/Smarter-Balanced-Mathematics-Claims.pdf
PARCC MATHEMATICS CLAIMS (2013)
SOURCE: PARCC (2013)
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
SOURCE: CCSS
32
PARCC SAMPLE ITEMS
Source: http://www.parcconline.org/samples/math
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
34
PARCC SAMPLE ITEMS
• Grade Level?
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
36
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
37
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
38
PARCC SAMPLE ITEMS
• Grade Level?
39
PARCC SAMPLE ITEMS
•
Algebra I
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
40
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
41
PARCC SAMPLE ITEMS
• Grade Level?
42
PARCC SAMPLE ITEMS
SOURCE: HTTP://WWW.PARCCONLINE.ORG/SAMPLES/MATH
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ISSUE: INSTRUCTION
THINKING
“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
“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
“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
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
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.
COMMUNITY COLLEGE IMPACT?
• Placement
• Assessment
• Content
• Instruction
• Preservice