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Transition to PA Common Core Mathematical Practices Copyright ©2011 Commonwealth of Pennsylvania 1 PA Common Core Local Curriculum Toolbox Copyright ©2011 Commonwealth of Pennsylvania 2 Please Do the Following • Connect to the Internet • Navigate to: http://www.pdesas.org – If a registered user, sign-in – If not a registered user, join now • Place your name and school district/organization on your name tent Your School District/Organization Your Name Copyright ©2011 Commonwealth of Pennsylvania 3 PA Common Core Introduction Essential Questions • What are the Standards for Mathematical Practices and how do they relate to the PA Common Core? • Can the characteristics of a student and classroom that exemplify mathematical practices be identified and implemented? Copyright ©2011 Commonwealth of Pennsylvania 4 Math Class Makeover Dan Meyer describes why we need to makeover math classrooms. Copyright ©2011 Commonwealth of Pennsylvania 5 Expected Outcomes Explore the Standards for Mathematical Practice. Identify characteristics of a student and classroom that exemplify mathematical practice. Copyright ©2011 Commonwealth of Pennsylvania 6 Looks Like/Sounds Like When all students are engaged in learning mathematics, what does a classroom... Look Like Copyright ©2011 Commonwealth of Pennsylvania Sound Like 7 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 ‘processes and proficiencies’ with longstanding on important importance in mathematics education. (CCSS, 2010) Copyright ©2011 Commonwealth of Pennsylvania 8 NCTM – Principles and Standards for School Mathematics o Problem solving o Reasoning and proof o Connections o Communication o Representation Copyright ©2011 Commonwealth of Pennsylvania 9 Standards of Proficiency of Mathematical Practice Adding It Up: Helping Children Learn Mathematics By Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001). Washington, DC: National Academy Press p. 117 Copyright ©2011 Commonwealth of Pennsylvania 10 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. Copyright ©2011 Commonwealth of Pennsylvania 11 Grouping the Standards for Mathematical Practice (McCallum, 2011) Copyright ©2011 Commonwealth of Pennsylvania 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. What implications might the standards of mathematical practice have on your classroom? Copyright ©2011 Commonwealth of Pennsylvania 13 Rigor Is o approaching mathematics with a disposition to accept challenge and apply effort; o engaging in mathematical work that promotes deep knowledge of content, analytical reasoning, and use of appropriate tools; and o emerging fluent in the language of mathematics, proficient with the tools of mathematics, and being empowered as mathematical thinkers. Copyright ©2011 Commonwealth of Pennsylvania Rigor Is Not o “difficult,” as in “AP calculus is rigorous.”; o enrichment activities for advanced students; o Problem Solving Friday o Adding two word problems to the end of a worksheet; and o adding more numbers to a problem. 14 Buttons Task Gita plays with her grandmother’s collection of black & white buttons. She arranges them in patterns. Her first 3 patterns are shown below. Pattern #1 Pattern #2 Pattern #3 Pattern #4 1. Draw pattern 4 next to pattern 3. 2. How many white buttons does Gita need for Pattern 5 and Pattern 6? Explain how you figured this out. 3. How many buttons in all does Gita need to make Pattern 11? Explain how you figured this out. 4. Gita thinks she needs 69 buttons in all to make Pattern 24. How do you know that she is not correct? How many buttons does she need to make Pattern 24? CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003 Copyright ©2011 Commonwealth of Pennsylvania 15 Buttons Task 1. Individually complete parts 1 - 3. 2. Then work with a partner to compare your work and complete part 4. Look for as many ways to solve parts 3 and 4 as possible. 3. Consider each of the following questions and be prepared to share your thinking with the group: a) What mathematics content is needed to complete the task? b) Which mathematical practices are needed to complete the task? National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Copyright ©2011 Commonwealth of Pennsylvania CTB/McGraw-Hill; Mathematics Assessment Resource Services, 2003 16 www.Inside Mathematics.org A reengagement lesson using the Button Task Francis Dickinson San Carlos Elementary Grade 5 • http://www.insidemathematics.org/index.php/classroom-video-visits/publiclessons-numerical-patterning/218-numerical-patterning-lessonplanning?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8 Copyright ©2011 Commonwealth of Pennsylvania 17 Learner A Pictorial Representation What does Learner A see staying the same? What does Learner A see changing? Draw a picture to show how Learner A sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy. Verbal Representation Describe in your own words how Learner A sees this pattern growing. Be sure to mention what is staying the same and what is changing. Copyright ©2011 Commonwealth of Pennsylvania 18 Learner B Pictorial Representation What does Learner B see staying the same? What does Learner B see changing? Draw a picture to show how Learner B sees this pattern growing through the first 3 stages. Color coding and modeling with square tiles may come in handy. Verbal Representation Describe in your own words how Learner B sees this pattern growing. Be sure to mention what is staying the same and what is changing. Copyright ©2011 Commonwealth of Pennsylvania 19 Buttons Task Revisited • Which of the Standards of Mathematical Practice did you see the students working with? Cite explicit examples to support your thinking. • What value did Mr. Dickinson generate by using the same math task two days in a row, rather than switching to a different task(s)? • How did the way the lesson was facilitated support the development of the Standards of Mathematical Practice for students? • What classroom implications related to implementation of CCSS resonate? Copyright ©2011 Commonwealth of Pennsylvania 20 Standards for Mathematical Practice Standard 1: Make sense of problems and persevere in solving them. 4th Grade Copyright ©2011 Commonwealth of Pennsylvania 21 Standards for Mathematical Practice Standard 4: Model with mathematics. 9th Grade/10th Grade Copyright ©2011 Commonwealth of Pennsylvania 22 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) Copyright ©2011 Commonwealth of Pennsylvania 23 End of the Day Reflections 1. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain. 2. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain. Copyright ©2011 Commonwealth of Pennsylvania Slide 24 Reflection and Planning • Does our list of words/phrases describe a classroom where students are engaged in mathematical practice? • Use the reflection sheet to capture key thoughts about the practice standards. Copyright ©2011 Commonwealth of Pennsylvania 25 References • Jean Howard Mathematics Curriculum Specialist (406) 444-0706; [email protected] • Cynthia Green ELA Curriculum Specialist (406) 444-0729; [email protected] • Judy Snow State Assessment Director (406) 444-3656; [email protected] • http://www.insidemathematics.org/index.php/class room-video-visits/public-lessons-properties-ofquadrilaterals/300-properties-of-quadrilateralstuesday-group-work-part-a? • http://insidemathematics.org/index.php/classroom -video-visits/public-lesson-number-operations/182multiplication-a-divison-problem-4-part-c • http://www.insidemathematics.org/index.php/class room-video-visits/public-lessons-numericalpatterning/218-numerical-patterning-lessonplanning?phpMyAdmin=NqJS1x3gaJqDM-18LXtX3WJ4e8 Copyright ©2011 Commonwealth of Pennsylvania • National Council of Supervisors of Mathematics • CCSS Standards of Mathematical Practice: Reasoning and Explaining • www.mathedleadership.org • http://www.youtube.com/watch?v=SjsfHTuZ14 w • Adding It Up: Helping Children Learn Mathematics By Jeremy Kilpatrick, Jane Swafford, & Bob Findell (Editors). (2001). Washington, DC: National Academy Press 26