Unwrapping The Common Core Standards For Elementary Math Leaders Elementary Math C.L.A.S.S. Session 1 Networks 604 and 609 - Greg Jaenicke & Debra VanNostrand Cluster 6 Jose Ruiz Helen Ponella, Facilitator November 15, 2010 Petrides Learning Complex, Conference Room C Staten Island, NY
8:30 a.m. – 9:00 a.m. Breakfast 9:00 a.m. – 9:30 a.m. Introduction to the CCS in Mathematics 9:30 a.m. – 10:00 a.m. Activity 1.1: Unwrapping the Common Core State Standards 10:00 a.m. – 10:45a.m. Activity 1.2: CCSS for Mathematical Practice 10:45 a.m. – 11:00 p.m. BREAK 11:00 a.m. – 12:00p.m. Activity 1.3: Problem Solving and the Mathematics Content and Practice Standards 1:00 p.m. – 2:15 p.m. Activity 1.4: Mathematical Standards and Looking at Student Work and Rigorous Math Task Alignment to the CCS 2:15 p.m. – 2:30 p.m. Reflections and Next Steps
Why Common Core State Standards? • Preparation: The standards are college- and career-ready. They will help prepare students with the knowledge and skills they need to succeed in education and training after high school. • Competition: The standards are internationally benchmarked. Common standards will help ensure our students are globally competitive. • Equity: Expectations are consistent for all – and not dependent on a student’s zip code. • Clarity:The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them. • Collaboration:The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials.
Process and Timeline • K-12 Common Standards: • Core writing teams in English Language Arts and Mathematics (See www.corestandards.orgfor list of team members) • External and state feedback teams provided on-going feedback to writing teams throughout the process • Draft K-12 standards were released for public comment on March 10, 2010; 9,600 comments received • Validation Committee of leading experts reviews standards • Final standards were released June 2, 2010
Feedback and Review • External and State Feedback teams included: • K-12 teachers • Postsecondary faculty • State curriculum and assessments experts • Researchers • National organizations (including, but not limited, to):
Common Core State Standards Design • Building on the strength of current state standards, the CCSS are designed to be: • Focused, coherent,clearand rigorous • Internationally benchmarked • Anchored in college and career readiness* • Evidence and research based *Ready for first-year credit-bearing, postsecondary coursework in mathematics and English without the need for remediation.
Common Core State Standards Evidence Base • Evidence was used to guide critical decisions in the following areas: • Inclusion of particular content • Timing of when content should be introduced and the progression of that content • Ensuring focus and coherence • Organizing and formatting the standards • Determining emphasis on particular topics in standards Evidence includes: • Standards from high-performing countries, leading states, and nationally-regarded frameworks • Research on adolescent literacy, text complexity, mathematics instruction, quantitative literacy • Lists of works consulted and research base included in standards’ appendices
DESPITE GAINS, ONLY 39% OF NYC 4TH GRADERS AND 26% OF 8TH GRADERS ARE PROFICIENT ON NATIONAL MATH TESTS NAEP & NY STATE TEST RESULTS NYC MATH PERFORMANCE PERCENT AT OR ABOVE PROFICIENT 4th Grade 8th Grade 2003 2009 2003 2009 2003 2009 2003 2009 NAEP NY State Test NAEP NY State Test
Many NYC Public School Graduates struggle in college • 40,549 students graduated from NYC public high schools in 2007 • 39% enrolled at CUNY in Fall 2007 • 45% of these students required remediation in reading, writing, or math
The Research on College Readiness • “The academic intensity of the high school curriculum counts more than anything else towards moving students toward completing a bachelor’s degree.” • Source: Adelman, C. The Toolbox Revisited: Paths to Degree Completion From High School Through College, February 2006
Factors that Lead to College Readiness during High School • Diploma type: Local, Regents, Advanced Regents and Advanced Regents with Honors • Advanced math coursework beyond Algebra II • Participation in Advanced Placement (AP) and/or College Now courses
Math Coursework Completed Diploma Type Individually, each high school indicator is predictive of passing out of remedial classes N= 4,627 8,922 3,583 634 N= 2,085 10,172 1,851 1,155 1,679 AP Participation College Now N= 11,430 5,740 Note: Based on Class of 2008 entering CUNY in Fall of 2008.
Why are the Common Core STATE Standards important for students, teachers, and parents? The Common Core State Standards: • Prepare students with the knowledge and skills they need to succeed in college and work • Ensure consistent expectations regardless of a student’s zip code or ELL or SWD status • Provide educators, parents, and students with clear, focused guideposts • Will lead to new, more rigorous assessments that will drive changes in curriculum and teacher practice
Criteria for the standards • Fewer, clearer, and higher • Aligned with college and work expectations • Include rigorous content and application of knowledge through high-order skills • Build upon strengths and lessons of current state standards • Benchmarked internationally, so that all students are prepared to succeed in our global economy and society • Based on evidence and research
Key differences between Nys and Common Core state Standards: math • Fewer topics; more generalizing and linking of concepts • Well-aligned with the way high-achieving countries teach math • Emphasis on both conceptual understanding and procedural fluency starting in the early grades • More time to teach and reinforce core concepts from K-12 • Some concepts will now be taught later • Focus on mastery of complex concepts in higher math (e.g., algebra and geometry) via hands-on learning • Emphasis on mathematical modeling in the upper grades
The most important ideas in CCSS that will be overlooked • Properties of operations: their role in arithmetic and algebra • Units and unitizng • Quantities-variables-functions-modeling • Number-expression-equation-function • Modeling • Practices Phil Daro, 2010 NCSM 2010, Used with permission
Common Core Standards • Text Rendering Protocol • Common Core Introduction Pages 3-4 • Common Core Expanded Version Pages i – x • Task: Highlight a sentence, a phrase, and a word from these introductory pages that are particularly significant and/or relevant to you as it relates to your past work, present state, and future work around instructional coherence and ensuring college and career readiness for all students via the rollout of the Common Core State Standards.
Common Core State Standards for Mathematical Practice How can the CCSS for Mathematical Practice promote instructional change? How do we change the focus in the classroom from mechanical facility to conceptual understanding?
Block Stack 25 layers of blocks are stacked; the top four layers are shown. Each layer has two fewer blocks than the layer below it. How many blocks are in all 25 layers? Math Olympiad for Elementary and Middle Schools
Why Standards? • Looking at the Standards - Practice • Looking at the Standards - Content • Using the Lens of CCSS: • Looking at Student Work • Examine a Lesson – and Compare
What Are Standards? • Standards define what students should understand and be able to do. • The US has been a jumble of 50 different state standards. Race to the bottom or the top? • Any country’s standards are subject to periodic revision. • Math, however, is more than a list of topics.
What Does “Higher Standards” Mean? • More topics? But the U.S. curriculum is already cluttered with too many topics. • Earlier grades? But this does not follow from the evidence. In Singapore, division of fractions: grade 6 whereas in the U.S.: grade 5 (or 4)
Lessons Learned • TIMSS: math performance is being compromised by a lack of focus and coherence in the “mile wide. Inch deep” curriculum. • Hong Kong students outscore US students in the grade 4 TIMSS, even though Hong Kong only teaches about half the tested topics. US covers over 80% of the tested topics. • High-performing countries spend more time on mathematically central concepts: greater depth and coherence. Singapore: “Teach less, learn more.”
Answer Getting vs. Learning Mathematics • United States • How can I teach my kids to get the answer to this problem? • Use mathematics they already know. Easy, reliable, works with bottom half, good for classroom management. • Japan • How can I use this problem to teach mathematics they don’t already know?
Three Responses to a Math Problem • Answer getting • Making sense of the problem situation • Making sense of the mathematics you can learn from working on the problem
Answer Getting • Getting the answer one way or another and then stopping • Learning a specific method for solving a specific kind of problem (100 kinds a year)
Use Butterflies on This TIMSS Item • 1/2 + 1/3 +1/4 =
Foil FOIL • (a + b)(c +d) = ac + bc + ad + bd • Use the distributive property • This IS the distributive property when a is a sum: a(x + y) = ax + ay • It works for trinomials and polynomials in general
Answers Are a Black Hole: Hard to Escape the Pull • Answer getting short circuits mathematics, especially making mathematical sense • Very habituated in US teachers versus Japanese teachers • High-achieving countries devise methods for slowing down, postponing answer getting
A dragonfly can fly 50 meters in 2 seconds. What question can we ask?
Posing the Problem • Whole class: pose problem, make sure students understand the language, no hints at solution • Focus students on the problem situation, not the question/answer game. Hide question and ask them to formulate questions that make situation into a word problem • Ask 3-6 questions about the same problem situation; ramp questions up toward key mathematics that transfers to other problems
What Problem to Use? • Problems that draw thinking toward the mathematics you want to teach. NOT too routine, right after learning how to solve • Ask about a chapter: what is the most important mathematics students should take with them? Find problems that draw attention to this math • Begin chapter with this problem (from lesson 5 thru 10, or chapter test). This has diagnostic power. Also shows you where time has to go. • Near end of chapter, external problems needed, e.g. Shell Centre
What Do We Mean by Conceptual Coherence? • Apply one important concept in 100 situations rather than memorizing 100 procedures that do not transfer to other situations: • Typical practice is to opt for short-term efficiencies, rather than teach for general application throughout mathematics. • Result: typical students can get B’s on chapter tests, but don’t remember what they ‘learned’ later when they need to learn more mathematics • Use basic “rules of arithmetic” (same as algebra) instead of clutter of specific named methods • Curriculum is a ‘mile deep’ instead of a ‘mile wide’
Mental Math 145 145 -100- 98
Math Standards • Mathematical Practice: • Varieties of expertise that math educators should seek to develop in their students. • Mathematical Content: • Mathematical Performance: what kids should be able to do. • Mathematical Understanding: what kids need to understand.
The Common Core Standards: Understanding the Mathematical Practices Standards These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep. — CCSS (2010, p.5) 45 NCSM 2010, Used with permission
The Standards for [Student] 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” for mathematics education. 46 NCSM 2010, Used with permission
The Standards for [Student] Mathematical Practice The first of these are the NCTM (2000) process standards of problem solving, reasoning and proof, communication, representation, and connections spelled out in PSSM… • Problem Solving • Reasoning and Proof • Communication • Representation • Connections 47 NCSM 2010, Used with permission
The Standards for [Student] Mathematical Practice The second are the strands of mathematical proficiency specified in the National Research Council’s report (2001) Adding It Up: Adaptive reasoning; Strategic competence; Conceptual understanding (comprehension of mathematical concepts, operations and relations); Procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately); and Productive disposition 48 NCSM 2010, Used with permission
The Standards for [Student] Mathematical Practice Take a moment to examine the first three words of each of the 8 mathematical practices… what do you notice? (Pages 6-8 in CCS) 49 NCSM 2010, Used with permission
The Standards for [Student] Mathematical Practice The 8 Standards for Mathematical Practice – place an emphasis on student demonstrations of learning… What we as teachers do, doesn’t matter nearly as much as what our students do Daily, we know what it is we do… how do we know how the students experience it? 50 NCSM 2010, Used with permission