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Mathematical Practices Overview

Mathematical Practices Overview. November 2011. Expected Outcomes. Explore the Standards for Mathematical Practice Identify characteristics of a student and classroom that exemplifies mathematical practice. Plan professional development to take a closer look to

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Mathematical Practices Overview

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  1. MathematicalPractices Overview November 2011

  2. Expected Outcomes • Explore the Standards for Mathematical Practice • Identify characteristics of a student and classroom that exemplifies mathematical practice. • Plan professional development to take a closer look to • make sense of each mathematical practice. • connect practices to content for rigor and relevance.

  3. INSTRUCTION INSTRUCTION INSTRUCTION What does a classroom look and sound like when all students are engaged in learning mathematics? INSTRUCTION INSTRUCTION INSTRUCTION

  4. Interpreting Distance–Time Graphs adapted from the Mathematics Assessment Project (MAP) Materials for this activity were obtained through the Mathematics Assessment Project (MAP). Original materials for this lesson can be found at: http://map.mathshell.org/materials/

  5. Tom’s journey to the Bus Stop Write a narrative (describe) what is happening. Is the graph realistic? Explain.

  6. Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education. - Montana Common Core Standards

  7. NCTM – Principles and Standards for School Mathematics Process Standards • Problem solving • Reasoning and proof • Connections • Communication • Representation

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

  9. 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 . . .

  10. 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.

  11. Integration of Practices for Rigor and Relevance Is: • a process, not just one correct answer. • part of each lesson. • not “Problem Solving Fridays”. • not “enrichment” for advanced students.

  12. Standards for 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)

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

  14. Connections to Practices • What opportunities were there for you to engage in the practice standards in the Distance Time Task? • Did explaining give opportunities to engage in additional practices? Or deepen the ones identified above. • Are there any words/phrases you want to add to our list that describe a classroom with students engaged in mathematical practice?

  15. 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)

  16. Math Class Makeover

  17. A Closer Look a Mathematical Practice Oregon State Mathematical Practice Module 1: • Part 1:Making Sense of the Mathematics • Doing mathematics • Examining mathematical practice • Part 2: Student dispositions and Teacher Actions • Identify student outcomes • Identify teaching strategies • Part 3: Looking for the Practices through Observation • Create your own “look for” tool • Look for MCCS Mathematical Practice in Classroom videos http://www.ode.state.or.us/search/page/?id=3406 Oregon DOE

  18. Reflection and Planning • Does our list of words/phrases describe a classroom where students are engaged in mathematical practice? • Use Reflection Sheet capture key thoughts about the practice standards

  19. Jean Howard Mathematics Curriculum Specialist (406) 444-0706; jhoward@mt.gov • Cynthia Green ELA Curriculum Specialist (406) 444-0729; cgreen4@mt.gov • Judy Snow State Assessment Director (406) 444-3656; jsnow@mt.gov

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