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Cucamonga Math Presentation

Cucamonga Math Presentation. Outcomes. Identify the core components and organization of the Mathematics CCSS Understand the design of the “Next Generation Assessments” Implications for practice. Common Core State Standards. Next Generation Assessments.

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Cucamonga Math Presentation

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  1. Cucamonga Math Presentation

  2. Outcomes • Identify the core components and organization of the Mathematics CCSS • Understand the design of the “Next Generation Assessments” • Implications for practice

  3. Common Core State Standards Next Generation Assessments

  4. Smarter Balanced assessments will go beyond multiple-choice questions to include extended response and technology enhanced items, as well as performance tasks that allow students to demonstrate critical-thinking and problem-solving skills.

  5. Smarter Balanced Item Formats • Selected Response • Assessment items where students select from a given set of response options • Constructed Response/Extended Response • Assessment items where students produce the response instead of selecting from a list • Performance Tasks • Assessment items where students perform a skill or create a product • Technology-Enhanced / Technology-Enabled • Assessment items that employ technology to elicit a response from a student.

  6. Examples of Stimuli • Which of the numbers is • A factor of 100. • A multiple of 5. • 4 • 40 • 50 • 500 The table below shows the number of students in each third-grade class at Lincoln School. Students in the Third-Grade There are 105 fourth-grade students at Lincoln School. How many more fourth-grade students than third grade students are at Lincoln School? Show your work or explain how you know.

  7. Selected Response (SR) Items scored based on single or multiple answers

  8. Traditional Selected Response Items • Traditional Selected Response Item • Key and Distractor Analysis Which number is both a factor of 100 and a multiple of 5? A. 4 B. 40 C. 50 D. 500 Did not consider criteria of “multiple of 5” Did not consider criteria of “factor of 100” Correct Multiplied 100 and 5 Which number is both a factor of 100 and a multiple of 5? RATIONALE A. 4 B. 40 C. 50 D. 500 STEM Statement ofthe question KEY DISTRACTOR OPTIONS: Possible answers the students must select from

  9. Sample Math Non-Selected Response (SR) 4th grade STIMULUS STEM DOK 2: Skills and Concepts OPTIONS Rubric

  10. Sample Math Non-Selected Response (SR) 7th grade STEM DOK 2: Skills and Concepts OPTIONS Rubric

  11. Constructed Response (CR) Items scored on a rubric

  12. Sample Math Constructed Response (CR) 5th grade STIMULUS STEM DOK 2: Skills and Concepts RESPONSE 120 1 point item

  13. Sample Math Constructed Response (CR) High School STIMULUS STEM DOK 2: Skills and Concepts RESPONSE 0.4 (or equivalent) STEM RESPONSE 0.2 (or equivalent) 1 point item

  14. Technology Enhanced Items scored on a rubric

  15. Sample Math Technology Enhanced 3rd Grade STIMULUS DOK 2: Skills and Concepts STEM 1 point item

  16. Sample Math Technology Enhanced 8th grade STEM DOK 1: Recall and Reproduction STIMULUS Multiple Solution Path (64, 8) (1000, 10) (100, 100) (64, 4) 1 point item

  17. Performance Task (PT) Items scored on a rubric

  18. Sample Math Performance Task 5th Grade ç 18 point item Rubric scoring for each section DOK 4: Extended Thinking

  19. Sample Math Performance Task High School ç DOK 3: Strategic Thinking and Reasoning 16 point item Rubric scoring for each section

  20. Common Core State Standards CCSS Mathematics

  21. Math Standards

  22. Content Standards Grade level Focus or Priority • Identified in CCSS document not in the California Common Core document Domains • Content topics Cluster Heading • Identifies standard Cluster Standards • Group of related standards • CA added 15% are in italics and bold Progressions across grade levels

  23. Grade Level Focus or Priority d For each grade level from kindergarten through grade 8, the Critical Areas outline the essential mathematical ideas for each grade level. d

  24. Reading of K-8 Standards Domain Domain Domain Domain Domain

  25. Reading of K-8 Standards Cluster Heading Standards Cluster Stem: if standard is followed by a,b,c, etc. Domain

  26. Examples of Additional 15%: • Added language to existing standard • Grade 2-Measurement and Data • Grade 4-Geometry

  27. Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the understanding 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

  28. Standards for Mathematical Practice Locate the CCSS for Mathematics and read the first three words for each mathematical practice and notice the similarities. What do they begin with? Mathematically proficient students… Briars & Mitchell (2010) Getting Started with the Common Core State Standards 28 28 CISC Mathematics Toolkit

  29. 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 on important “processes and proficiencies” with longstanding importance in mathematics education.” (CCSS, 2010)

  30. The Standards for [Student] Mathematical Practice What are the verbs that illustrate the student actions for your assigned mathematical practice? Circle, highlight or underline them for all eight practices… Discuss with a partner: What stands out?

  31. Common Core State Standards CLASSROOM STRATEGY: POSE MEANINGFUL TASKS

  32. Not only this 7 x 5 = ___ But also….

  33. Amber didn’t know what 7 x 5 equals, but she know 5 x 5 = 25 and 2 x 5 = 10. Use drawings, words and/or equations to explain why Amber can add 25 and 10 to find out what 7 x 5 equals. Source: PARCC Item Department ITN, Appendix F

  34. Multiplication Problem • Which mathematical practices are needed to complete the task? • What mathematics content is needed to complete the task?

  35. Not only this Find 20% of 350,000. But also….

  36. Claim A fast food chain reports that 8% of people in the U.S. eat at its restaurants each day. The chain has 12,800 stores. According to the 2010 Census Bureau report approximately 310 million people live in the U.S.. Make a conjecture as to whether or not you believe the report from the fast food chain to be accurate. Create a mathematical argument that validates your conclusion.

  37. Claim Problem • Which mathematical practices are needed to complete the task? • What mathematics content is needed to complete the task?

  38. Not only this A rectangle has side lengths of 7 m and 9 m. A square with side length 5 m is cut out of the rectangle. Find the area of that rectangle after the square is cut out. But also….

  39. Here is a satellite photo of Geoff’s yard. He is interested in re-sodding his entire yard. Help him out by providing a cost estimate. Develop a list of questions you would need answered before you can solve the problem. Bristol Central Geometry Teachers

  40. Claim Problem • Which mathematical practices are needed to complete the task? • What mathematics content is needed to complete the task?

  41. Daily Instruction MATHEMATICAL DISCOURSE

  42. Mathematical Discourse The ability to read, write, listen, ask questions, think, and communicate about math will develop and deepen students’ understanding of mathematical concepts. Students should read text, data, tables, and graphs with comprehension and understanding. Their writing should be detailed and coherent, and they should use correct mathematical vocabulary. Students should write to explain answers, justify mathematical reasoning, and describe problem-solving strategies. Indiana Department of Education, 2006

  43. Language in CCSS Mathematics • 505 math standards K-12 • 89 math standards • 11 cluster headings • Standards for Mathematical Practice Require Language in Math

  44. Math Verbs

  45. Mathematically Speaking • a = math teacher • b = guides students towards use of specialized oral and written language to communicate content • c = English teacher then a = b and b = c therefore a = c Krajicek, Stephanie Writing in Mathematics: Common Objections & FAQ’s Volume 2, Number 2 issue of the Write Connections

  46. Mathematical Discourse • Where to begin…. • Start with why and because • Teacher: Start asking why? • Why did you choose that step? • Student: Explain their thinking. • ______is correct because_____.

  47. Mathematical Discourse • Think Alouds • Number Talks • Think-Pair-Share • Response Frames • Language Objectives • Writing in Math • Support for EL Learners

  48. Common Core State Standards Cognitive Rigor

  49. Cognitive Rigor Matrix

  50. Depth of Knowledge

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