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Mathematics Practices and Progressions

Mathematics Practices and Progressions. Jean Howard, OPI Mathematics Curriculum Specialist. August2011. INSTRUCTION. INSTRUCTION. INSTRUCTION. What does it look and sound like in classroom where all students are engaged in learning mathematics?. INSTRUCTION. INSTRUCTION. INSTRUCTION.

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Mathematics Practices and Progressions

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  1. MathematicsPractices and Progressions Jean Howard, OPI Mathematics Curriculum Specialist August2011

  2. INSTRUCTION INSTRUCTION INSTRUCTION What does it look and sound like in classroom where all students are engaged in learning mathematics? INSTRUCTION INSTRUCTION INSTRUCTION

  3. Mathematical rigor is an elusive term with multiple meanings. To a pure mathematician, rigor is a mark of excellence. To a K-12 educator, “rigorous” often means “difficult,” as in “AP calculus is rigorous.” In the Montana Standards for Mathematical Practices . . .

  4. Rigor is a process where students: • approach mathematics with a dispositionto accept challenge and apply effort; • engage in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and • emerge fluent in the language of mathematics, proficient with the tools of mathematics, and empowered as mathematical thinkers.

  5. Standards for (Student) Mathematical Practice 1. Make sense of complex 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 repeated reasoning. (CCSS, 2010)

  6. NCTM – Principles & Standards for School Mathematics • Process Standards • The five standards address the processes of • Problem solving • Reasoning and proof • Connections • Communication • Representation

  7. Intertwined Strands of Proficiency Adding It Up: Helping Children Learn Mathematics By Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001). Washington, DC: National Academy Press p. 117

  8. Integration of Practices for Rigor and Relevance • Not “Problem Solving Fridays” • Not “enrichment” for advanced students • Is a process, not just one correct answer • Student’s proficiency in Content and Practice standards is part of every lesson

  9. Grade Level Overview Page

  10. Grouping the Standards for Mathematical Practices (McCallum, 2011)

  11. Standards for Mathematical Practice in a Classroom McDonald’s Claim Wikipedia reports that 8% of all Americans eat at McDonalds every day. In the US, there are approximately 310 million Americans and 12,800 McDonalds. Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position. (Briars, Feb 2011)

  12. Standards for Mathematical Practice in a Classroom Traditional U.S. Problem Which fraction is closer to 1: 4/5 or 5/4 ? Same Problem integrating content and practice standards 4/5 is closer to 1 than is 5/4. Using a number line, explain why this is so. (Daro, Feb 2011)

  13. Math Class Makeover(10 min) Curriculum Makeover(5 min)

  14. Standards for Mathematical Practice by Grade Level Linking Content and Practices (AZ) Consider the description of the Practices within the document and discuss within grade and/or grade band groups the following questions:

  15. Reflection • How will incorporating the Standards for Mathematical Practice impact teaching and learning, including: • Planning for instruction? • Rigor? • Student learning as they progress through the grades? • How will you begin to integrate these practices in your classroom?

  16. BREAK

  17. FOCUS

  18. Critical Areas • There are typically two to four Critical Areas for instruction in the introduction for each grade level or course. • They bring focus to the standards at each grade by grouping and summarizing the big ideas that educators can use to build their curriculum and to guide instruction.

  19. Critical Areas Warm-up How will it improve teaching and learning when each grade focuses on a few Critical Areas?

  20. Examine Critical Areas • Describe Critical Areas • Read your grade level introduction about Critical Areas. • Record the Critical Areas on individual Foldable. • Complete Poster to share with whole group: use words and/or pictures to describe the focus for your grade level • Complete Explore Focus Through Critical Areas record sheet.

  21. Relate content standards to Critical Areas • Search for standards within a grade level (or course) that connect to a particular Critical Area • √ when a standard strongly matches your Critical Area and • ? when you are not sure • Group members share a brief summary of their focus Critical Area.

  22. Reflection • How do the Critical Areas help organize and bring focus to your grade level standards? • How should we as a school (or district) use what we have learned today about Critical Areas in planning for the implementation of the new standards?

  23. Tools You Can Use • Standards for Mathematical Practice • Inside Mathematics • Linking Content and Practices (Arizona) • Office of Public Instruction http://www.opi.mt.gov/Curriculum/Index.html?gpm=1_7#gpm1_7 • Resource on Wiki http://ccssmtteam.wikispaces.com/message/list/home • Other states • Blogs • Assessment • Projects • Reports, Articles, Documents • Presentations • Miscellaneous

  24. Jean Howard (406) 444-0706 jhoward@mt.gov

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