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Common Core Mathematics Core Academic Standards for Math Content

Common Core Mathematics Core Academic Standards for Math Content. Foundational Understanding of rhe Standards of Math Practice and the Common Core Math Content Standards. Today’s Key Outcomes.

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Common Core Mathematics Core Academic Standards for Math Content

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  1. Common Core MathematicsCore Academic Standards for Math Content Foundational Understanding of rhe Standards of Math Practice and the Common Core Math Content Standards

  2. Today’s Key Outcomes • Become familiar with Missouri’s Core Academic Standards for Math Content and Math Practices (Common Core State Standards) • Begin to process how you will begin to make the shifts necessary to meet these standards • Leave with some seeds planted in the place in your head where things grow

  3. Common Core State Standards • Define the knowledge and skills students need for college and career • Developed voluntarily and cooperatively by states; more than 40 states have adopted • Provide clear, consistent standards in English language arts/Literacy and mathematics Source: www.corestandards.org

  4. Math Risk Mapping State Proficiency Standards onto NAEP Scales, IES August 2011

  5. Math Risk Mapping State Proficiency Standards onto NAEP Scales, IES August 2011

  6. PISA 2009 Overall Math Scale

  7. Next Generation Assessments • More rigorous tests measuring student progress toward “college and career readiness” • Have common, comparable scoresacross member states, and across consortia • Provide achievement and growth information to help make better educational decisions and professional development opportunities • Assess all students, except those with “significant cognitive disabilities” • Administer online, with timely results • Use multiple measures Source: Federal Register / Vol. 75, No. 68 / Friday, April 9, 2010 pp. 18171-85

  8. Each state procures its own assessmentsystem • Each state bears the burden of test development; no economies of scale Summative Assessments Today Measure proficiency against state standards, not agreed-upon standards • Students often leave high school unprepared to succeed in entry-level college courses Usually heavy reliance on multiple choice questions • Poor measures of demonstration of skills and complex cognitive performance Results often delivered months after tests are given • Tests cannot be used to inform instruction or affect program decisions Accommodations for special education and ELL students vary • Difficult to interpret meaning of scores; concerns about access and fairness Most administered on paper • Costly, time consuming, and challenging to maintain security

  9. The Assessment Challenge ...to here? How do we get from here... Common Core State Standards specify K-12 expectations for college and career readiness All studentsleave high school college and career ready ...and what can an assessment system do to help?

  10. Yes, but • Gather in groups of four to six • One person volunteer in each group to be the idea person • Idea person, come up with a simple plan for an end of the year party for your school staff, place, theme, time, date etc—just an idea however plain or wild • Each other person, going around the group, offer a “yes, but”… to make an addition to that plan.

  11. Yes, and • Now go around the group again • Idea person state your plan exactly the same way you stated it the first time. • This time, each member of the group, contribute your addition, preceded by “Yes, and…”

  12. What happened • Share out the difference between the two interactions • How does this translate into

  13. Turn to the CCSS Document • Table of Contents • Introduction • In small group, read the paragraph at your table aloud—and write a summary statement about what you comprehend as a group • Move to the next table’s paragraph when directed, and read their paragraph, their summary statement, and add a “yes, and…” statement(s) from your group • Repeat around the room

  14. How to read the standards • How to read the standards • Read the statements beneath the diagram • With a partner, summarize the key points • Share out with the whole group—yes, and…

  15. Page 1 and 2 of the handout • Key points on this page • No specific order to these standards! • They are clustered, but some clusters can be connected…read paragraph 1 beneath diagram • Ideally it would read: “Students should already know…and should come next to learn….” • Promise that over time we will better understand and articulate the progressions to a greater extent • Best practice will be NEXT PRACTICE—this is a promise we intend to keep.

  16. How to Read the Common Core Standards  The development began with research-based learning progressions detailing what we know today about how students’ mathematical knowledge, skill and understanding develop over time.  The Standards define what students should understand and be able to do in their study of mathematics.

  17. Standards of Math Practice rest on NCTM’s Process Standards • Problem Solving • Reasoning and Proof • Communication • Representation • Connections

  18. Standards of Math Practice rest on the strands of Mathematical Proficiency from The National Research Council • Adaptive reasoning • Strategic competence • Conceptual understanding • Procedural fluency • Productive disposition

  19. Look at the diagram as a scale • How do we balance this scale?

  20. The MOST IMPORTANT PART OF THE CAS • Standards of Math Practice pp.6-8 in CCSS • This afternoon— • Quickly skim these pages for a preview • What do you see? What do you make of it? what makes you say that?

  21. Sketch a diagram that takes into account the background we now have • Include the following: • Need for Focus and Coherence • Need for progressions • Need for focus on number sense early • The foundational underpinnings of The NCTM Processes and the NRC proficiencies

  22. Let’s compare • Existing State • Current State

  23. Key Shifts for Math Core Academic Standards ( CAS) • Missouri will call the CCSS the CAS—Core Academic Standards because eventually they will include Science, Social Studies and other subjects besides the CCSS math and English Language Literacy

  24. Danger of Unpacking Standards • Grecian Urn Analogy

  25. Look at handout P. 3 • These are not the GLEs….we do not unpack them and put them on checklists for completion. • We do not assess them totally in isolation. • We do not create pacing charts and curriculum maps in absence of conversation amongst the people who will be teaching it.

  26. Common Core Format • High School • Conceptual Category • Domain • Cluster • Standards • K-8 • Grade • Domain • Cluster • Standards

  27. Example of Domain, Cluster, StandardGrades 6-8 Statistics and Probability 6.SP Develop understanding of statistical variability. • Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. 6.SP.1 • Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.2 • Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. 6>SP.3

  28. Elementary Domains • Counting and Cardinality CC • Operations and Algebraic thinking OA • Number and operations in Base Ten NBT • Measurement and Data MD • Geometry G • See p. 1 of your handout

  29. Grades 6-8 Domains • Ratios and Proportional Relationships ( Gr.6-7) RP • The Number System NS • Expressions and Equations EE • Functions ( Grade 8 only) F • Geometry G • Statistics and Probability SP

  30. Example of Conceptual Category, Domain, Cluster, Standard Algebra is the Conceptual Category Seeing Structure in expressions A-SSE is the Domain Interpret the structure of expressions (the Cluster) • Interpret expressions that represent a quantity in terms of its context.★ • Interpret parts of an expression, such as terms, factors, and coefficients. • Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. A-SSE.1 • Use the structure of an expression to identify ways to rewrite it. For example, see x4– y4mas (x )2– (y2)2 thus recognizing it as a difference of squares that can be factored as (x2– y2)(x2+ y2). A-SSE.2

  31. High School Domains ①Number and quantity N-RN ( the real number system) N-Q ( quantities) N-CN ( the complex number system) N-VM ( vector and matrix quantities) ②Algebra A-SSE (seeing structure in expresssions) A-APR (arithmetic with polynomial and rational expressions A-CED(creating Equations) A-REI( reasoning with equations and inequalities

  32. ③Functions F-IF(Interpreting functions) F-BF( Building Functions) F-LE( Linear, quadratic, exponential Models) F-TF( TrigometricFunctions) ④Modeling ⑤Geometry G-CO ( congruence) G-SRT ( similarity, right triangles, trigonometry) G-C ( circles) G-GPE( Expressing Geometric Properties and equations) G-GMD( Geometericmeasurement and dimension G-MG Modeling Geometry

  33. ⑥Statistics and Probability S-ID (Interpreting categorical and quantitative data) S-IC ( Making inferences and justifying conclusions) S-CP(Conditional probability and the rules of probability) S-MD( Using probability to make decisions)

  34. Let’s explore your standards • Jot down differences from GLEs • Jot down similarities to GLEs • Jot down all impressions • Be prepared to share

  35. Link to DESE and Crosswalk • http://dese.mo.gov/divimprove/curriculum/common-core-math.htm Let’s take a look at the crosswalk!

  36. Look at handout on p. 5 It shows areas of emphasis in the content domains over grades K-5 What do you see? What do you make of it? What makes you say that?

  37. Coherence: One Step at a Time 6. Individual standards 5. Units 4. Clusters 3. Progressions 2. Critical Focus Areas 1. Introduction to the CAS Relevance Relevance Relevance Relevance Relevance Relevance Rigor Rigor Rigor Rigor Rigor Rigor Rigor Rigor Rigor Rigor

  38. Look at handout P. 3 • These are not the GLEs….we do not unpack them and put them on checklists for completion. • We do not assess them totally in isolation. • We do not create pacing charts and curriculum maps in absence of conversation amongst the people who will be teaching it.

  39. Let’s compare • Existing State • Current State

  40. Focus strongly where the Standards Focus The Standards call for a greater focus in mathematics. Rather than racing to cover topics in today’s mile-wide, inch-deep curriculum, teachers use the power of the eraser and significantly narrow and deepen the way time and energy is spent in the math classroom. They focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.

  41. Critical Focus Areas • Take a look at handouts 6 and 7 to see thumbnails of what the focus areas are for each grade in K-8 and for Algebra, Algebra 2 and Geometry.

  42. See Thumbnails and Focus Documents • Focus will require teachers to have a better understanding of the math that is taught. • Focus will require that teachers can identify where student understanding is, in the progression of a concept. • Focus will require that teachers can integrate other concepts and skills while still maintaining a focus on the grade level focus points—this is tricky—it will take Professional Development and attention on the part of each teacher. • We learned more about teaching reading and writing in the 2000’s—now it is time to do the same with math.

  43. Carefully look at current curriculum. What can be “culled”? What’s being taught just because it’s in the textbook (more about textbooks tomorrow)? What’s being taught that will continue to be taught at the same grade with the CAS transition? What’s going to shift? Where’s it shifting – before or beyond? Where do teachers need the most support?

  44. Visual Synectics • What do you need to know to get the understanding of your photo? • What skills/dispositions do you need to stretch to gain more insight into why this connection was made when photoshopping this picture? • What new perspective do you have from putting what you know with what you don’t know? • Swap with someone and try it again.

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