Integrating Mathematical Practices K-12

1. Integrating Mathematical Practices K-12 Gila County Teacher Institute Gail Gorry & Deb Leverance June 1, 2012

2. Agenda Background of Common Core Explore the Mathematical Practices Discover Level of Knowledge Develop a Mathematical Practice Integrated Lesson

3. Where Are You Now? How comfortable do you feel implementing the 2010 Arizona Mathematics Standards? How knowledgeable are you about the components and how to access them?

4. True or False? ___The CCSS are a national curriculum. ___ The CCSS represent a modest change from current practice. ___ The CCSS will transform schools.

5. Background Information The Partnership for Assessment of Readiness for College and Careers (PARCC) Arizona: Is a PARCC Governing State Will be Pilot State for Assessment Development Starts Computer/Performance based testing in 2014/2015 Follows the 2008 Math Standards format

6. 45 States + DC Have Adopted the Common Core Math Standards 6

7. Video • Watch the David Coleman video. • Listen for the 3 main focuses of the Mathematics Common Core. • Discuss. Link: http://usny.nysed.gov/rttt/resources/bringing-the-common-core-to-life.html

8. Standards of 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.

9. Activity • Jigsaw with your table one of the Standards of Mathematical Practice. • Share your thoughts about what this practice means with your table group. • Record key ideas on easel paper. • Post your paper. • Gallery walk.

10. Mathematical Practices Take Home • How are the mathematical practices reflected in your daily instruction? • Move into integrated grade level groups. • Compare and contrast the grade level mathematical practices. • Share findings.

11. Grade Level Documents • Find a person who shares your grade level. • Locate the mathematical practices from the standards documents. • Any changes from your earlier discussion? K = p.21 1st = p.21 2nd = p.20 3rd = p.27 4th = p.33 5th = p.37 6th = p.44 7th = p.30 8th = p.31 9th-12th = p.122

12. Depth and Rigor Hess’ Cognitive Rigor Matrix describes the type of thinking involved, not whether it will be completed correctly applies Webb’s Depth of Knowledge to Bloom’s Cognitive Process Dimensions identifies cognitive levels of student activities and test questions Involves multiple levels (sometimes) in one activity

13. 13 Karin K. Hess, Ed.D., Senior Associate National Center for Assessment, Dove, NH khess@nciea.org

14. 14 Karin K. Hess, Ed.D., Senior Associate National Center for Assessment, Dove, NH khess@nciea.org

15. Identify the DOK Level Analyze the following chart entitled, “The Speed of Indy 500 Cars per Lap” and be ready to share your conclusions. Retrieve information from a table or graph.

16. Identify the DOK Level Gather information about the speed of vehicles in your neighborhood. Analyze and evaluate the information in a presentation of your choice to the class. Compare and contrast the data from 1985 to 2010 from the following table.

17. Your team will be assigned a verb from Bloom’s Revised Taxonomy. Design activities that will fill the matrix (Levels 1-4) for your assigned verb. Make a chart and be ready to share with the entire group. Design activities to fill the matrix 17

19. Cognitive Demand (Expectations for Student Performance) Use Extend Acquire Recall Skill/Concept Strategic Thinking Extended Thinking Memorize Perform Procedures Demonstrate Understanding Conjecture, Generalize Prove Solve non- routine/ make connections

20. Cognitive Demand Sorting Activity A Memorize Facts, Definitions, Formulas B Perform Procedures E Solve Non-Routine Problems, Make Connections C Demonstrate Understanding of Mathematical Ideas D Conjecture, Analyze, Generalize, Prove

21. SEC Math Expectations for Students

22. Mathematical Practices • Watch the video. • Note times during the lesson where mathematical practices were being implemented. • Watch teacher and student behaviors.

23. Video Here’s the link to the videos: http://www.learner.org/resources/series33.html?pop=yes&pid=921# hexominoes – 5th gr geometry http://www.learner.org/resources/series32.html?pop=yes&pid=879# 2nd gr marshmallows

24. Video • Here’s the link to the video: http://www.learner.org/resources/series33.html?pop=yes&pid=921# rods and rafts – surface area http://www.learner.org/vod/vod_window.html?pid=925 bungee jumping

26. Teacher/Student Insights Note mathematical practices. Discuss teacher/student actions and words. What DOK levels were illustrated? How do these activities compare to the learning activities in your classroom?

27. Activity Choose a math standard. Develop a lesson imbedding mathematical practices. Write the specific guiding questions. Share your common core math lesson outline.

34. Math Standard 7 NS 3 Solve real-world and mathematical problems involving the four operations with rational numbers, (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

37. Session Review Discover level of knowledge Investigate the format of the 2010 Math Standards Explore and use the Mathematical Practices Develop a “math practices” focused lesson

38. Closing Remarks • Questions • Evaluation • Now the work begins • State Resources - http://www.ade.az.gov/standards/CommonCoreStandards/default.asp • County Resources • Coaching • County Curriculum Specialist • Teacher Resource Library • Professional Development workshops • Differentiated Instruction • STEM Education and Training • Intel Math Training • Common Core

39. Gila County Education Service Agency • Globe • 1400 E Ash St. • 928-402-8783 • lowen@gilacountyaz.gov • ggorry@gilacountyaz.gov • Payson • 112 W. Cedar Ln. • 928-472-5374 • lowen@gilacountyaz.gov • ggorry@gilacountyaz.gov