1. Transition to PA Common Core: Rigor in Learning and Assessment of Learning Copyright ©2010 Commonwealth of Pennsylvania 1

2. PA Common Core Toolbox Local Curriculum Copyright ©2010 Commonwealth of Pennsylvania 2

3. Please do the Following: Connect to the Internet Navigate to: http://www.pdesas.orghttp://www.pdesas.org – If a registered user, sign-in – If not a registered user, join now Place your name and school district/organization on your name tent Copyright ©2010 Commonwealth of Pennsylvania 3 Your Name Your School District/Organization

4. PA Common Core Introduction Essential Questions What is rigor and how is it represented in mathematical assessments? What does engagement look like for students in mathematics and how is this captured in assessments? What does relevance look like in terms of assessment design? How can teachers design assessments that are rigorous, engaging, and relevant that capture the features of the “PA Common Core Standards?” Copyright ©2010 Commonwealth of Pennsylvania 4

5. Rethinking Assessment Activity #1 How do you define rigorous assessment? Think-pair-share to create a working definition. Read 4 Myths about Rigor in the Classroom by Ronald Williamson and Barbara R. Blackburn. http://tinyurl.com/4RigorMyths http://tinyurl.com/4RigorMyths With your partner, revise your shared working definition of rigorous assessment. Be prepared to report out to the group. Copyright ©2010 Commonwealth of Pennsylvania 5

6. Depth of Knowledge (DOK) Adapted from the model used by Norman Webb, University of Wisconsin, to align standards with assessments Used by the Council of Chief State School Officers (CCSSO) for assessment alignment in more than ten states 6 Copyright ©2010 Commonwealth of Pennsylvania

7. Why Depth of Knowledge? Mechanism to ensure that the intent of the standard and the level of student demonstration required by that standard matches the assessment items (required under NCLB) Provides cognitive processing ceiling (highest level students can be assessed) for item development Designed for use with formative and summative assessments 7 Copyright ©2010 Commonwealth of Pennsylvania

8. Depth of Knowledge (DOK) Copyright ©2010 Commonwealth of Pennsylvania 8

9. Depth of Knowledge (DOK) Recall and Reproduction: Level 1 DOK 1 requires recall of information, such as a fact, definition, term, or performance of a simple process or procedure, as well as performing a simple algorithm or applying a formula. Answering a Level 1 item can involve following a simple, well-known procedure or formula. Simple skills and abilities or recall characterize DOK 1. Copyright ©2010 Commonwealth of Pennsylvania 9

10. Depth of Knowledge (DOK) DOK Level 1 Examples 1.Identify a diagonal in a geometric figure. 2.Multiply two numbers. 3.Find the area of a rectangle. 4.Convert scientific notation to decimal form. 5.Measure an angle. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 10

11. Depth of Knowledge (DOK) Skills/Concepts: Level 2 DOK 2 includes the engagement of some mental processing beyond recalling or reproducing a response. Items require students to make some decisions as to how to approach the question or problem. Keywords distinguishing Level 2 may include classify, organize, estimate, make observations, collect and display data, and compare data. These actions imply more than one mental or cognitive process/step. Copyright ©2010 Commonwealth of Pennsylvania 11

12. Depth of Knowledge (DOK) DOK Level 2 Examples 1. Classify quadrilaterals. 2. Compare two sets of data using the mean, median, and mode of each set. 3. Determine a strategy to estimate the number of jelly beans in a jar. 4. Extend a geometric pattern. 5. Organize a set of data and construct an appropriate display. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 12

13. Depth of Knowledge (DOK) Strategic Thinking: Level 3 DOK 3 requires reasoning, planning, using evidence, and more demanding cognitive reasoning. The cognitive demands at Level 3 are complex and abstract. An assessment item that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3. Copyright ©2010 Commonwealth of Pennsylvania 13

14. Depth of Knowledge (DOK) DOK Level 3 Examples 1.Solve a multiple-step problem and provide support with a mathematical explanation that justifies the answer. 2.Write a mathematical rule for a non-routine pattern. 3.Explain how changes in the dimensions affect the area and perimeter/circumference of geometric figures. 4.Provide a mathematical justification when a situation has more than one outcome. Interpret information from a series of data displays. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 14

15. Depth of Knowledge (DOK) Extended Thinking: Level 4 DOK 4 requires high cognitive demand and is very complex. It requires complex reasoning, planning, developing, and thinking. Students are expected to make connections - relate ideas within the content or among content areas — and select or devise one approach among many alternatives on how the situation can be solved. Due to the complexity of cognitive demand, DOK 4 often requires an extended period of time. Copyright ©2010 Commonwealth of Pennsylvania 15

16. Depth of Knowledge (DOK) Extended Reasoning/Thinking Examples: Level 4 1. Specify a problem, identify solution paths, solve the problem, and report the results. 2. Collect data over time taking into consideration a number of variables and analyze the results. 3. Model a social studies situation with many alternatives and select one approach to solve with a mathematical model. 4. Develop a rule for a complex pattern and find a phenomenon that exhibits that behavior. 5. Complete a unit on formal geometric constructions, such as nine-point circles or the Euler line. 6. Construct a non-Euclidean geometry. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 16

17. Depth of Knowledge (DOK) NOT The Depth of Knowledge is NOT determined by the verb, but the context in which the verb is used and the depth of thinking required. 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) DOK 2- Describe the difference between metamorphic and igneous rocks. (requires cognitive processing to determine the differences in the two rock types) DOK 1- Describe three characteristics of metamorphic rocks. (simple recall) Copyright ©2010 Commonwealth of Pennsylvania 17

18. Depth of Knowledge (DOK) Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK 1: Students will identify a transformation within a plane. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 18

19. Depth of Knowledge (DOK) Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK 2: Students will perform a compound transformation of a geometric figure within a coordinate plane. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 19

20. Depth of Knowledge (DOK) Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK 3: Students will perform a geometric transformation to meet specified criteria and then explain what does or does not change about the figure. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 20

21. Depth of Knowledge (DOK) Students will identify and describe properties of and apply geometric transformations within a plane to solve real-world and mathematical problems. DOK 4: Students will abstract the transformations occurring in an Escher woodprint and then create a simplified tessellation of their own. Source: Kentucky Department of Education (2007). Support Materials for Core Content for Assessment. Copyright ©2010 Commonwealth of Pennsylvania 21

22. Depth of Knowledge (DOK) Applying Webb’s Depth of Knowledge to Bloom’s Cognitive Process Dimensions for Math and Science Hess’ Cognitive Rigor Matrix & Curricular Examples for Math and Science www.nciea.org/publications/CRM_math-sci_KH11.pdf Source: Karen Hess (2009) Copyright ©2010 Commonwealth of Pennsylvania 22

23. Depth of Knowledge (DOK) Activity #2 Depth of Knowledge Math Sorting Activity 1.Working individually, classify each mathematical assessment task according to its DOK level. 2.Work with a partner to arrive at consensus as to what DOK level each task reflects. 3.Report out responses and the rationale of such responses. Copyright ©2010 Commonwealth of Pennsylvania 23

24. Assessment Analysis- Rigor Activity #3: Your Turn! Assessment Analysis - Rigor 1.Using the DOK levels, analyze one of your assessments and classify each assessment item according to one of the DOK levels. 2.Choose one question representing a DOK 1. How might you revise that question to elevate the rigor? Copyright ©2010 Commonwealth of Pennsylvania 24

25. Depth of Knowledge (DOK) Questions to Consider When Assessing Learning… 1.What DOK levels should you be targeting with assessment questions? 2.What would you consider to be an appropriate distribution of the different DOK levels in an assessment? 3.What concerns do you have regarding the different levels of DOK? 4.How might you build DOK Level 4 questions into your unit/lesson/assessment design? Copyright ©2010 Commonwealth of Pennsylvania 25

26. Depth of Knowledge (DOK) Questions to Consider When Designing Learning… 1.What DOK levels should you be targeting in learning activities? 2.What would you consider to be an appropriate distribution of instructional time across the four DOK Levels? 3.What concerns do you have regarding the different levels of DOK with respect to learning? 4.How might you build DOK Level 4 activities into your unit/lesson design? Copyright ©2010 Commonwealth of Pennsylvania 26

27. Assessment Analysis- Engagement Standards for Mathematical Practice Apply across Grades K-12. Describe ways in which students should engage with the content, process, and proficiencies of mathematics. Copyright ©2010 Commonwealth of Pennsylvania 27

28. Assessment Analysis- Engagement PACC Standards of Mathematical Practice Make sense of problems and persevere in solving them. Use appropriate tools strategically. Reason abstractly and quantitatively. Attend to precision. Construct viable arguments and critique the reasoning of others. Look for and make use of structure. Model with mathematics. Look for and make sense of regularity in repeated reasoning. Copyright ©2010 Commonwealth of Pennsylvania 28

29. Assessment Analysis- Engagement Activity #4: Your Turn! Assessment Analysis-Engagement 1.Analyze assessment items through the lens of the mathematical practices (www.pdesas.org/Standard/CommonCore). 2.Choose an assessment item to revise to better target one specific mathematical standard of practice. 3.Share with a partner as to what that assessment item may look like once it is revised. 4.Work with your partner to revise/expand the assessment item to further address the mathematical standard of practice. Copyright ©2010 Commonwealth of Pennsylvania 29

30. Assessment Analysis- Relevance Characteristics of PA Common Core State Standards Building on a foundation before moving on. Hands-on exploration. Real world application emphasizing mathematical modeling. Creating students who know math, do math, and use math. Requiring students to make connections and relate ideas within the content or among content areas while selecting or devising one approach among many alternatives on how the situation can be solved. Copyright ©2010 Commonwealth of Pennsylvania 30

31. Assessment Analysis-- Relevance PACC 2.3.7.A.1 (Geometry) Solve real-world and mathematical problems involving angle measure, area, surface area, circumference, and volume. Copyright ©2010 Commonwealth of Pennsylvania 31

32. Assessment Analysis- Relevance Assessment Task Examples Perhaps high school students may build a swimming pool that can meet the needs of ALL people who want to use it - from those who have special needs to children; but at the same time, it needs to meet certain criteria in terms of standard amounts of water and size. Perhaps middle school students may be in charge of designing a new and improved pyramid to be presented to the pharaoh - complete with a variety of antechambers. Perhaps elementary students may be in charge of creating an organic garden to sell certain products at the local farmer's market. Source: Andrew Miller (2012) http://www.andrewkmiller.com/2011/07/assessing-the-common-core- standards-real-life-mathematics/ Copyright ©2010 Commonwealth of Pennsylvania 32

33. Assessment Analysis- Relevance Activity #5: Your Turn! Assessment Analysis of Relevance 1.Analyze assessment items through the lens of relevance and real world contexts. Do your assessments reflect real world learning contexts for your students? 2.Choose an assessment item to revise to embed more of a real world, relevant context. 3.Share with a partner as to what that assessment item may look like once it is revised. 4.Work with your partner to revise/expand the assessment item to reflect a real world, relevant context. Copyright ©2010 Commonwealth of Pennsylvania 33

34. Building Assessment Teams Working collaboratively to improve assessments to capture rigor, engagement, and relevance – Analyzing DOK levels of assessment – Analyzing mathematical standards of practice in assessments and assessment tasks – Analyzing assessment design to reflect real-world context Using team members as a fidelity check to ensure that assessment questions are written that align to the teacher’s intent of the design of the task Copyright ©2010 Commonwealth of Pennsylvania 34

35. Building Assessment Teams Use each other as a resource. Writing DOK Levels of 3 or 4 assessment tasks may be different and more difficult than writing DOK Levels 1 or 2. Create assessment questions based upon same Assessment Anchor. Compare with colleagues to review differences in assessment questions. Determine individual assessment areas of strength and areas of need. As assessment teams, understand each other’s strengths and use those strengths when designing assessment items. Copyright ©2010 Commonwealth of Pennsylvania 35

36. Building Assessment Teams Questions for consideration and extensions of assessment teams: 1.What should be considered the target score on an assessment in order to move forward with instruction? – What score is considered acceptable showing that your students get it? 2.What actions should be taken as a result of the assessment score? (remediation, enrichment, etc.) 3. How might these changes in assessment drive changes in instruction? Copyright ©2010 Commonwealth of Pennsylvania 36

37. Building Assessment Teams What additional questions should assessment teams be asking each other? What additional questions should teachers be asking of their assessments? Copyright ©2010 Commonwealth of Pennsylvania 37

38. Building Assessment Teams Copyright ©2010 Commonwealth of Pennsylvania 38 Activity #6: Assessment Teams - Successes and Challenges 1.Write down two successes that you have experienced or would like to experience as a result of working with an assessment team. 2.On another card, write down two challenges that you have experienced or might anticipate as a result of working with an assessment team. 3.Share your successes and challenges with a shoulder partner. Discuss strategies that could help assure the successes and minimize the challenges.

39. Assessment Questions??? Copyright ©2010 Commonwealth of Pennsylvania 39