The Common Core State Standards For Mathematics: An Overview

1. The Common Core State Standards For Mathematics:An Overview NJASCD/FEA Common Core Cadre Presenters

2. Agenda Introductions Rationale and Purpose Examining the CCS Standards for Math Prioritizing the Standards The Math Standards and Curriculum Samples Why new standards? How do they compare with the NJ State Standards? How are they different? What does this mean for my classroom instruction? Why new standards? How do they compare with the NJ State Standards? How are they different? What does this mean for my classroom instruction?

3. The Common Core . . . State-led and developed Common Core Standards for K-12 in English/language arts and mathematics Fewer, clearer, and higher Aligned with college and/career training Internationally benchmarked Standards are the beginning . . . Main Stakeholders: CCSSO= Council of Chief State School Officials NGA= National Governors Association Universities, Experts in Educational Research and Publication Adopted in 44 of the 50 states. (Not Tx, WV, Alaska, Montana,Nebr, Minnesoa) Private and parochial schools not accountable. Charter Schools receiving state funds are required. Higher = appendix of ELA describes complexity Based upon release of test data placing us 17th in the world behind Finland, Singapore, Hong Kong, South Korea. The three-yearly OECD (Organization for Economic Cooperation and Development, 34 countries) Program for International Student Assessment (PISA) report, which compares the knowledge and skills of 15-year-olds in 70 countries around the world, ranked the United States 14th out of 34 OECD countries for reading skills, 17th for science and a below-average 25th for mathematics. EPIC (Educational Policy Improvement Center in Eugene, Org) recently compared the standards against those of leading state standards, international standards and university standards at high-school exit level; found them even more rigorous in some areas. Assessments for grades 3- high school. Main Stakeholders: CCSSO= Council of Chief State School Officials NGA= National Governors Association Universities, Experts in Educational Research and Publication Adopted in 44 of the 50 states. (Not Tx, WV, Alaska, Montana,Nebr, Minnesoa) Private and parochial schools not accountable. Charter Schools receiving state funds are required. Higher = appendix of ELA describes complexity Based upon release of test data placing us 17th in the world behind Finland, Singapore, Hong Kong, South Korea. The three-yearly OECD (Organization for Economic Cooperation and Development, 34 countries) Program for International Student Assessment (PISA) report, which compares the knowledge and skills of 15-year-olds in 70 countries around the world, ranked the United States 14th out of 34 OECD countries for reading skills, 17th for science and a below-average 25th for mathematics. EPIC (Educational Policy Improvement Center in Eugene, Org) recently compared the standards against those of leading state standards, international standards and university standards at high-school exit level; found them even more rigorous in some areas. Assessments for grades 3- high school.

4. The Launch America’s quest to be #1 in Education again ~a shared vision of what students, teachers and administrators should know and be able to do/deliver ~consistency of high expectations for all ~flexibility: states may add up to 15% Discuss flexibility.Discuss flexibility.

5. ~ New expectations ~ 2010-2011~ time for planning 2014-2015~ Common assessments will be operational Between now and then~ ~ Transitions in assessment systems ~ Phase-in the Standards - Curriculum development and alignment - Professional development Test this year (2012) in grades 3-5 has field tested CCStandards Math transitional tests in grades 3-5 will be in 2013, 2014. 2012- Field tested questions on math 3-5 2013- Questions which overlap both NJ Standards and CC 2014- Based on CC, given by NJ 2014-2015 – PARCC testTest this year (2012) in grades 3-5 has field tested CCStandards Math transitional tests in grades 3-5 will be in 2013, 2014. 2012- Field tested questions on math 3-5 2013- Questions which overlap both NJ Standards and CC 2014- Based on CC, given by NJ 2014-2015 – PARCC test

6. Limitations What the standards do not define~ How teachers should teach All that can or should be taught The nature of advanced learning beyond the core The interventions needed for students below level The full range of support for English language learners and students with special needs

7. Language and Lay-out of the Standards Core Content English Language Arts ~Reading ~Writing ~Speaking and Listening ~Language Conventions ~Standards for literacy in history/ social studies, science, and technical subjects Shared Responsibility for ELA @ Social Studies and Science TeachersShared Responsibility for ELA @ Social Studies and Science Teachers

8. Language & Layout Mathematics ~Focus and Coherence ~A few key topics at each grade level ~Progressions across grade levels: some content may have been moved to a different grade ~Domain and Code ~Standards for Content and Standards for Practice Aim for clarity and specificity – “not a mile wide and an inch deep” They don’t spiral, they overlap and build upon previous grade. Teach for in depth understanding,, not memorizing rules and tricks. Stress conceptual understanding of key ideas and return frequently to the organizing principles to structure the ideas. Require higher level Blooms thinking at all grade levels. Do not stop at knowledge and comprehension. Teachers will need to understand “why” it works and lead students to that understanding also. Students asked to “explain”, demonstrate, often with hands-on materials, and apply knowledge to real world problems. (BLOOMS) Based on current research into developmental levels of students Aims for an understanding level which asks for explanations and justification of answers, not rote recitation of rules. What they do not do: give intervention methods for students below grade level, ELL students, or suggestions for enrichment for students well above grade level. Intentions and explanations given in the introduction to the standards. Advise reading these. Show White Packet Aim for clarity and specificity – “not a mile wide and an inch deep” They don’t spiral, they overlap and build upon previous grade. Teach for in depth understanding,, not memorizing rules and tricks. Stress conceptual understanding of key ideas and return frequently to the organizing principles to structure the ideas. Require higher level Blooms thinking at all grade levels. Do not stop at knowledge and comprehension. Teachers will need to understand “why” it works and lead students to that understanding also. Students asked to “explain”, demonstrate, often with hands-on materials, and apply knowledge to real world problems. (BLOOMS) Based on current research into developmental levels of students Aims for an understanding level which asks for explanations and justification of answers, not rote recitation of rules. What they do not do: give intervention methods for students below grade level, ELL students, or suggestions for enrichment for students well above grade level. Intentions and explanations given in the introduction to the standards. Advise reading these. Show White Packet

9. Explain how each Grade Level Section is Organized: First paragraph prepares you for the “biggies” at your grade level. Underneath that you get the rationale and explanation of the skills Notice how they are written around “understanding”, not just computing. Explain how each Grade Level Section is Organized: First paragraph prepares you for the “biggies” at your grade level. Underneath that you get the rationale and explanation of the skills Notice how they are written around “understanding”, not just computing.

10. Note the opportunities to include instruction in the mathematical practices skills Mathematics Practices are HABITS OF MIND. They’re the ‘not so soft’ skills that correspond to the anchor standards in the ELA document. We’ll look at them in more depth later. Note the opportunities to include instruction in the mathematical practices skills Mathematics Practices are HABITS OF MIND. They’re the ‘not so soft’ skills that correspond to the anchor standards in the ELA document. We’ll look at them in more depth later.

11. If time- also show Grade 1- p. 13 in the standards Grade 6- p. 39 in the standards If time- also show Grade 1- p. 13 in the standards Grade 6- p. 39 in the standards

12. Mathematics Document At the end of the Standards document are: Glossary of Terms Tables of Comparison Sample of Works Consulted Suggest that they read over overview of high school courses to understand the progression of skills leading through high school. No particular order is suggestion for high school courses. All foundational knowledge is provided by Grade 8 for success in the high school courses and career readiness. Suggest that they read over overview of high school courses to understand the progression of skills leading through high school. No particular order is suggestion for high school courses. All foundational knowledge is provided by Grade 8 for success in the high school courses and career readiness.

13. Samples Mathematics Operations & Algebraic Thinking (OA) K-5 The Number System (NS) 6-8 Geometry (G) K-8 Conceptual Categories – high school An Overall View of the Standards Themselves DOE Packet Explain what symbols mean. Highlight domains Write the domain names on chart Write the number of standards in that domain to the right Circle the number if there are 2 or more + or N standards in that domain 2) Share Chart of Standards Moves- What does this show? Pair share. The Progressions Activity: (Purple Sheet) Language. Discuss how skills progress progress. Activity: Geometry Progression: [Whiteboards]. Draw a picture that represents the cluster standards content of what students will be expected to do at your grade level. Share. The Progression of Basic Operations K-8 5) Show Critical Focus Areas. Activity: Trace the Basic Operations K-8 An Overall View of the Standards Themselves DOE Packet Explain what symbols mean. Highlight domains Write the domain names on chart Write the number of standards in that domain to the right Circle the number if there are 2 or more + or N standards in that domain 2) Share Chart of Standards Moves- What does this show? Pair share. The Progressions Activity: (Purple Sheet) Language. Discuss how skills progress progress. Activity: Geometry Progression: [Whiteboards]. Draw a picture that represents the cluster standards content of what students will be expected to do at your grade level. Share. The Progression of Basic Operations K-8 5) Show Critical Focus Areas. Activity: Trace the Basic Operations K-8

14. Model Content Frameworks for Mathematics Final form to be published Fall of 2011 “The Model Content Frameworks are not a curriculum; rather, they are a voluntary resource to help teachers understand how to implement the standards.” Distribute Frameworks for each Grade Level Read over the format. Activity: By grade level. Come to the charts and put checks beside the domains of the first priority. Activity: Fluency. Place an asterisk in front of the domain in which students are expected to develop fluency. Then on your whiteboard create a problem and be able to explain to the group what the fluency is being required. Distribute Frameworks for each Grade Level Read over the format. Activity: By grade level. Come to the charts and put checks beside the domains of the first priority. Activity: Fluency. Place an asterisk in front of the domain in which students are expected to develop fluency. Then on your whiteboard create a problem and be able to explain to the group what the fluency is being required.

15. Math Practice Standards 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 White – Practice Standards Sheet Habits of Mind standards. A balanced combination of procedure and understanding. NCTM Process Standards + National Research Councils (strands of mathematical proficiency) White – Practice Standards Sheet Habits of Mind standards. A balanced combination of procedure and understanding. NCTM Process Standards + National Research Councils (strands of mathematical proficiency)

16. Math Practice Standards Use appropriate tools strategically. Attend to precision. Look for and make sense of structure. Look for and express regularity in repeated reasoning. Practice Standards Page Read bottom of back sheet of Practice Standards which says- In this sense…. Number off 1-8 by grade level Find a domain that is a natural spot to focus on that particular math practice standard. Write MPS in front of that standard on the chart. (At your grade level, look for a standard which says to “understand”. ) Practice Standards Page Read bottom of back sheet of Practice Standards which says- In this sense…. Number off 1-8 by grade level Find a domain that is a natural spot to focus on that particular math practice standard. Write MPS in front of that standard on the chart. (At your grade level, look for a standard which says to “understand”. )

17. The Common Core as the Lens through which Curriculum will be designed Instruction will be delivered Learning will be assessed and measured Discuss P21 Skills: 4 C’s and Workplace and Readiness Skills (Collaboration, Communication, Critical Thinking, Creativity) Show the Template Discuss P21 Skills: 4 C’s and Workplace and Readiness Skills (Collaboration, Communication, Critical Thinking, Creativity) Show the Template

18. Additional Resources Wordpress.com Lists progressions for each Domain. The Illustrative Mathematics Project Website for designing tasks. Eventually interactive Wordpress – contains documents which explain the progression of standards at each grade level Also contains clarifications by Jason Zimba, chief author of math standards.Wordpress – contains documents which explain the progression of standards at each grade level Also contains clarifications by Jason Zimba, chief author of math standards.

19. Curriculum Design Essential Components for 21st Century Learners The Common Core Standards as the Foundation Integrated Technology and Interdisciplinary Standards Integrated 21st Century Themes and Skills Formative and Summative Assessments Template contains places in the unit to bring all these ideas together in an integrated fashion. Discuss the Curriculum Project The Framework for 21st Century Learning presents four critical components to educate students for success in the future. (Share from author Diane Heacocks):   Deep content knowledge and the ability to apply this knowledge across disciplines.  Information, media, and technology skills that respond to new needs and interests of tech-savvy students  Life and career skills, including dispositions and attitudes such as personal initiative and self-direction  Learning and innovative skills, including creative and critical thinking, problem solving, and decision making ( 4 C’s) Show Math Units Template contains places in the unit to bring all these ideas together in an integrated fashion. Discuss the Curriculum Project The Framework for 21st Century Learning presents four critical components to educate students for success in the future. (Share from author Diane Heacocks):   Deep content knowledge and the ability to apply this knowledge across disciplines.  Information, media, and technology skills that respond to new needs and interests of tech-savvy students  Life and career skills, including dispositions and attitudes such as personal initiative and self-direction  Learning and innovative skills, including creative and critical thinking, problem solving, and decision making ( 4 C’s) Show Math Units

20. Assessment Measure standards that are rigorous, globally competitive, and consistent across the states New Jersey’s Choice The assessment consortium PARCC (Partnership for Assessment of Readiness for College and Careers) New assessments will replace current state NCLB tests in 2014-2015 PARCC- Web site should become more active and useful. 24 states, 10 of them Race to the Top recipients Four assessments possible. Two required. Both count toward summative grade. Science test being developed Two required, including one performance assessment. Pre and mid term available but not required. Performance assessment will be score before summative given so they can be averaged in. FYI. Speaking and listening component of ELA test. Separate score for “highlighted domain” at each grade level and then a summative score. Also available, high end and low end extended scores to use as prescriptive, diagnostic measures. Twice as many score points as on statewide tests. PARCC- Web site should become more active and useful. 24 states, 10 of them Race to the Top recipients Four assessments possible. Two required. Both count toward summative grade. Science test being developed Two required, including one performance assessment. Pre and mid term available but not required. Performance assessment will be score before summative given so they can be averaged in. FYI. Speaking and listening component of ELA test. Separate score for “highlighted domain” at each grade level and then a summative score. Also available, high end and low end extended scores to use as prescriptive, diagnostic measures. Twice as many score points as on statewide tests.

21. Ongoing Learning ~ the importance of continuous professional development for staff ~ the appropriateness of sharing curriculum, effective instructional strategies, and assessment processes, necessary for teachers and leaders to accomplish these goals PLC’s effective organizational strategies to tackle issues of standards PLC’s effective organizational strategies to tackle issues of standards

22. Leadership ~ the capacity to lead at every level The wisdom in building capacity at every level to stay ahead of the curve To know what works in your school/district and to design learning opportunities accordingly There is NO ONE RIGHT WAY; use these Standards as just that: the standard to begin this new work! Thank them for taking this step in informing everyone with the same information.Thank them for taking this step in informing everyone with the same information.

23. Linkages . . . the dimensions of implementing the Standards Leadership – from School Board to classroom teachers. Shared at all levels. Must be informed. Collaborative Curriculum Design- Rich, balanced, differentiated. Based on DOE template which incorporates Backward Design model, the importance of formative assessment and technology. 21st Century Learning and Skills - Integrating the 4 C’s ( Collaboration, Communication, Creativity and Critical Thinking) as well as workplace readiness skills . Assessment- Based on performance tasks, uses pre, formative and summative assessment. Multiple indicators that mirror real-world situations. Much to be done here on state, regional level as we receive more information from PARCC Effective Teaching – Instruction holds the greatest promise for increased achievement. Students are changing in their contextual background, technology has changed them and us, brain research tells us more about how we learn, and what effective teaching looks like in the classroom. Collaboration with fellow teachers, support staff, parents, community resources all critical to being able to teach effectively. Leadership – from School Board to classroom teachers. Shared at all levels. Must be informed. Collaborative Curriculum Design- Rich, balanced, differentiated. Based on DOE template which incorporates Backward Design model, the importance of formative assessment and technology. 21st Century Learning and Skills - Integrating the 4 C’s ( Collaboration, Communication, Creativity and Critical Thinking) as well as workplace readiness skills . Assessment- Based on performance tasks, uses pre, formative and summative assessment. Multiple indicators that mirror real-world situations. Much to be done here on state, regional level as we receive more information from PARCC Effective Teaching – Instruction holds the greatest promise for increased achievement. Students are changing in their contextual background, technology has changed them and us, brain research tells us more about how we learn, and what effective teaching looks like in the classroom. Collaboration with fellow teachers, support staff, parents, community resources all critical to being able to teach effectively.

24. Visit NJASCD Online  The Common Core Portal A Curriculum Design Format/Template Sample Curriculum Unit Plans Resources The Standards Documents Info-Brief on Implementation of the Common Core

25. We live in a time of vast changes that include accelerating globalization, mounting quantities of information, the dominating influence of science and technology, and the clash of civilizations. Those changes call for new ways of learning and thinking in school, business, and the professions. Howard Gardner . . .toward a more informed future