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Gilroy Unified School District Common Core Implementation Team-Math K-5 April 23, 2013

Gilroy Unified School District Common Core Implementation Team-Math K-5 April 23, 2013. Objectives. Establish norms for our work together Determine next steps Understand Webb’s DOK and how the new SBAC assessments will measure student understanding in Math

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Gilroy Unified School District Common Core Implementation Team-Math K-5 April 23, 2013

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  1. Gilroy Unified School District Common Core Implementation Team-Math K-5 April 23, 2013

  2. Objectives • Establish norms for our work together • Determine next steps • Understand Webb’s DOK and how the new SBAC assessments will measure student understanding in Math • Consider instructional implications for 21st century learning GUSD K-5 CCSS-Math Implementation Team Session 1

  3. Agenda • Welcome and Objectives • Establish norms for our work together • CCSS in the classroom • Determine needs and next steps • Webb’s Depth of Knowledge • Smarter Balanced Assessments for Math • 21st century skills GUSD K-5 CCSS-Math Implementation Team Session 1

  4. Agreements for our work together GUSD K-5 CCSS-Math Implementation Team Session 1 • Active Participation • Ask questions • Be honest and respectful • Equity of Voice • Safety & Confidentiality • Focus on what we can do

  5. CCSS in the Classroom GUSD K-5 CCSS-Math Implementation Team Session 1

  6. Instructional Shifts Combined

  7. A Classroom Example Common Core Mathematics Lesson- Grades 4/5 GUSD K-5 CCSS-Math Implementation Team Session 1

  8. 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 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.

  9. Confident Problem Solvers • How can we teach our students to be problem solvers, deep thinkers and feel confident in math? • What do we need? GUSD K-5 CCSS-Math Implementation Team Session 1

  10. SBAC and Webb’s DOK GUSD K-5 CCSS-Math Implementation Team Session 1

  11. New Assessment System: 2014-2015 GUSD K-5 CCSS-Math Implementation Team Session 1

  12. Smarter Balanced Assessment Consortium (SBAC) GUSD K-5 CCSS-Math Implementation Team Session 1

  13. Assessment: What We Know • Assessments will begin in 2014-15. • California is a governing state in the Smarter Balanced Assessment Consortium (www.smarterbalanced.org) • Assessments will include: • Selected Response (computer adaptive) rubric scored • Technology Enhanced • Constructed Response rubric scored • Performance Task rubric scored • may extend beyond one class session

  14. SBAC’s Mathematics Assessment Claims • Claim 1: Concepts and Procedures • Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency • Claim 2: Problem Solving • Students can solve a range of complex well-posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies • Claim 3: Communicating Reasoning • Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others • Claim 4: Modeling and Data Analysis • Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems

  15. SBAC Claims and Tasks

  16. Formats and Components ofSelected 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

  17. Non-Traditional Selected Response Item STIMULUS STEM A multiplication problem is shown below. 17 × 12 Which model(s) below could represent the solution to this problem? Select all that apply. 17 × 12 Which model(s) below could represent the solution to this problem? Select all that apply. A. B. C. (1×1)+(1×7)+(1×2)+(2×7) D. E. F. (17×2)+(17×1)

  18. Non-Traditional Selected Response Item Key and DistractorAnalysis: • Does not understand how to modelmultiplication of two two-digitnumbers using area models. • Correct • Did not account for the valuesof the digits in the tens places. • Correct • Did not understand that the 1 represents 10 in the multiplication problem • Showed multiplication of 17 and (1 + 2) instead of 17 and 12 Responses to this item will receive 0–2 points, based on the following: 2 points: B, D 1 point: Either B or D 0 points: Any other combination of selections.

  19. Non-Traditional Selected Response Item Scoring Rule: Students who properly match the four shapes to their name will receive two points. Students who make two or three correct matches will receive partial credit of one point All other connections will receive a score of 0. Match each shape below to its name.

  20. Purpose of Constructed Response Items • ConstructedResponse Items • Address assessment targets and claims that are of greater complexity • Require more analytical thinking and reasoning • Administered during the computer-adaptive component

  21. Components of aConstructed Response Item A teacher asked her students to use estimation to decide if the sum of the problem below is closer to 4,000 or 5,000. 496 + 1,404 + 2,605 + 489 = One student replied that she thinks the sum is closer to 4,000. She used the estimation shown below to support her reasoning. Is the student’s reasoning correct? In the space below, use numbers and words to explain why or why not. If the student’s reasoning is not correct, explain how she should have estimated. STIMULI STEM

  22. Components of aConstructed Response Item • Sample Top-Score Response: • The student’s reasoning is incorrect. She was rounding to the thousands place. She had 2 numbers that were less than 500, and she decided to round these numbers to 0. This is like saying these numbers were not in the problem at all. She needs to account for these two numbers. Together, they have a sum that is very close to 1,000. I think adding 1,000 + 1,000 + 3,000 is a better strategy. This means the sum is closer to 5,000 than to 4,000. Scoring Rubric: • Responses to this item will receive 0–2 points, based on the following: • 2 points: Student has thorough understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is incorrect and provides reasoning that shows a better estimation strategy. • 1 point: Student has partial understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is incorrect, but alternate estimation strategy is also flawed. • 0 points: Student has little or no understanding of how to estimate and how improper estimation can lead to flawed reasoning. Student states that the student in the scenario used reasoning that is correct. TOP-SCORE SCORING RUBRIC

  23. Extended ResponseClaim 3 – Communicating Reason Claim 3: Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others. • Test propositions or conjectures with specific examples. • Construct, autonomously, chains of reasoning that justify or refute propositions or conjectures. • State logical assumptions being used. • Use the technique of breaking an argument into cases. • Distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in the argument—explain what it is.

  24. Purpose of Performance Tasks (SBAC) Challenge students to apply their knowledge and skills to respond to real-world problems Collections of questions and activities meant to measure capacities such as depth of understanding, research skills, and complex analysis

  25. Claim 4 – Modeling and Data Analysis Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems. • Apply mathematics to solve problems arising in everyday life, society, and the workplace. • Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem. • State logical assumptions being used. • Interpret results in the context of a situation.

  26. Parts of an Extended Performance Task (Grade 5) Storage Facility • Part A: Student uses problem-solving strategies to organize information (storage units of different sizes in a grid). • Part B: Student uses numeric operations to find the volume of rectangular prisms, the monthly cost and the average cost per unit.

  27. Extended Performance Task (continued) • Part C: Student justifies why the original mathematical model is insufficient and makes improvements to the data. • Part D: Student uses problem-solving strategies based upon new data they created to answer various mathematical concepts.

  28. Test Administration Maximum Time Requirements for Performance Tasks • Grade 3–8: • 105 minutesPart 1: 35 min.Part 2: 70 min. • High School • 120 minutes Part 1: 35-45 min.Part 2: 75-85 min.

  29. Depth of Knowledge (DOK) • A scale of cognitive demand (thinking)to align standards with assessments • Based on the research of Norman Webb, University of Wisconsin Center for Education Research and the National Institute for Science Education • Defines the “ceiling” or highest DOK level for each Core Content standard for the CCSS assessment • Guides item development for CCSS assessments GUSD K-5 CCSS-Math Implementation Team Session 1

  30. DOK Webb’s Depth of Knowledge Webb’s DOK Model • Level 1 — Recall • Level 2 — Basic Application • Level 3 — Strategic Thinking/Reasoning • Level 4 — Extended Thinking/Creating GUSD K-5 CCSS-Math Implementation Team Session 1

  31. Depth of Knowledge (DOK)

  32. Webb’s Depth of Knowledge (DOK) GUSD K-5 CCSS-Math Implementation Team Session 1

  33. Webb’s Depth of Knowledge (DOK) GUSD K-5 CCSS-Math Implementation Team Session 1

  34. Common Core Big IdeasDepth of Knowledge (DOKs) Yuan & Le (2012); Herman & Linn (2013) from Linda Darling-Hammond, Assembly Hearing, 3.6.13

  35. DOK is about what follows the verb... What comes after the verb is more important than the verb itself. “Analyze this sentence to decide if the commas have been used correctly” does not meet the criteria for high cognitive processing.” The student who has been taught the rule for using commas is merely using the rule. GUSD K-5 CCSS-Math Implementation Team Session 1

  36. Same Verb—Three Different DOK Levels DOK 1-Describe three characteristics of metamorphic rocks. (Requires simple recall) DOK 2-Describe the difference between metamorphic and igneous rocks. (Requires cognitive processing to determine the differences in the two rock types) DOK 3-Describe a model that you might use to represent the relationships that exist within the rock cycle. (Requires deep understanding of rock cycle and a determination of how best to represent it) GUSD K-5 CCSS-Math Implementation Team Session 1

  37. DOK Depth of Knowledge • Level 1 — Identify this utensil. (fork) • Level 2 — Explain the function of the fork. • Level 3 — Identify two examples of when a fork would not be the best utensil for a type of food and explain why. • Level 4 — Design an investigation to determine the optimal number and length of tines for a salad fork. GUSD K-5 CCSS-Math Implementation Team Session 1

  38. DOK Level 1: Recall and Reproduction • Determine the perimeter or area of rectangles given a drawing or labels. • Retrieve information from a table or a graph. GUSD K-5 CCSS-Math Implementation Team Session 1

  39. DOK Level 2: Skills and Concepts • Classify plane and three-dimensional figures. • Retrieve information from a table or a graph and use it to solve a problem requiring multiple steps. GUSD K-5 CCSS-Math Implementation Team Session 1

  40. DOK Level 3: Strategic Thinking • You have a given amount of money. A) Show the different combinations of coins to make that amount of money. B) Show the different combinations of bills and coins to make that amount of money. C) Use the fewest possible number of coins to make that amount of money. • Draw conclusions from observations or data, citing evidence. GUSD K-5 CCSS-Math Implementation Team Session 1

  41. DOK Level 4:Extended Thinking • Collect data on the population of your school over the last tem years. Graph the information. What would you predict the school population will be in six years? What trends do you see in the population and what are a few reasons for the trends? Would enrollment figures suggest a need to increase the size of your school facility in the next ten years? Why or why not? • Conduct a project that specifies a problem, identifies solutions paths, solves the problem, and reports results. GUSD K-5 CCSS-Math Implementation Team Session 1

  42. Examples of DOK tasks Topic = Chocolate Chip Cookies

  43. Introduction to 21st Century Classrooms GUSD K-5 CCSS-Math Implementation Team Session 1

  44. Think Time • How would you define 21st century instruction? • What does a 21st century classroom look like? GUSD K-5 CCSS-Math Implementation Team Session 1

  45. GUSD K-5 CCSS-Math Implementation Team Session 1 1…………………...............10 20th Century 21st Century Where is your district or site on the scale?

  46. We are Shifting from sitting & getting  to creating professional learners GUSD K-5 CCSS-ELA Early Adopters Session 1

  47. Creativity & Innovation 21st Century Learning Critical Thinking & Problem Solving Communication & Collaboration Social & Cross-Cultural Skills Information, Communication, & Technology Literacy Productivity & Accountability Leadership & Responsibility Information Literacy Flexibility & Adaptability Media Literacy Initiative & Self Direction Financial, Economic, Business, Literacy Global Awareness Civic Literacy Health Literacy Environmental Literacy GUSD K-5 CCSS-Math Implementation Team Session 1

  48. P21 and the 4Cs • Collaboration and Interdependence • Communication • Creativity and Innovation • Critical Thinking and Problem Solving GUSD K-5 CCSS-Math Implementation Team Session 1

  49. 21st Century Curriculum and Instruction • Teaches 21st century skills discretely in the context of core subjects and 21st century interdisciplinary themes. • Focuses on providing opportunities for applying 21st century skills across content areas and for a competency-based approach to learning. • Enables innovative learning methods that integrate the use of supportive technologies, inquiry- and problem-based approaches and higher order thinking skills. • Encourages the integration of community resources beyond school walls. GUSD K-5 CCSS-Math Implementation Team Session 1

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