Common Core Standards

1. Common Core Standards Fewer, Clearer, Higher . . What Exactly Does That Mean?

2. Solve the Following Problem: 3 ÷ ½ =

3. Relate to Knowledge Package What “Knowledge” is needed to solve this problem?

4. How did you learn to work this problem? ½ ÷ ¼ = How might you get your students to “reason why”?

5. Invert and Multiply:Just “DO IT” Mathematics “Yours is not to reason why, just invert and multiply” is all about memorizing a procedure. Multiplying across the numerators and denominators (never mind why that works in multiplication but not in addition!), you get the answer 4/2 or 2. Reasoning why was not part of the equation. It is easy to reason through that question by asking, “How many fourths are in a half?” You might illustrate the question by creating a diagram of a whole square, and then shading in one half of it (Figure 3.6). How many fourths are inside that half? It’s easy to see that there are two of them.

6. A good teacher makes you think even when you don’t want to. -Fisher, 1998 Teaching Thinking

8. The Intent of the Common Core Standards . . . . • bring greater rigor to standards driving instruction and expectations for ALL students, • focus curriculum and instruction on deeper student understanding of a few critically important areas rather than skimming a multitude of topics, • provide clearer direction to teachers on what American students should know and be able to do as they leave high school for college or career purposes.

9. Before we begin . . . • Take a couple of minutes to write your personal definition of “cognitive rigor” as it relates to instruction, learning, and assessment. • At your table, discuss the following: • Your definition of cognitive rigor? • What does “rigor” look like in the classroom? • Be prepared to share your group’s definition. • Reflect on your definition of RIGOR as we discuss this morning . . . . 9

11. Quality Instruction:Students achievement is more highly correlated with the nature of classroom instruction- HOW the content is taught and HOW teachers use the curriculum--rather than with WHAT curriculum is used. The ♥ of the matter is the Depth of Knowledge

12. Challenging Tasks There is no other decision that teachers make that has a greater impact on students’ opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics. (Lappan & Briars)

13. The Bottom Line . . . . Our students won’t learn What they need to learn, if we don’t give them opportunities to learn it.

14. “Higher” Standards=Common CoreDeveloping the Cognitive Rigor Matrix • Different states/schools/teachers use different models to describe cognitive rigor. Each addresses something different. • Bloom – What type of thinking (verbs) is needed to complete a task? • Webb – How deeply do you have to • understand the content to successfully interact with it? How complex is the content? (What follows the verbs?)

15. Webb’s Depth of Knowledge Webb’s Depth of Knowledge (DOK): scale of cognitive demand There are 4 Levels of Cognitive Complexity Depth of Knowledge refers to the cognitive demand required for the task or problem or the “type of thinking” required. It is the depth and complexity of the task or problem, not difficulty level. The intended student learning outcome determines the DOK level. What mental processing must occur? While verbs may appear to point to a DOK level, it is what comes AFTER the verb that is the best indicator of the rigor/DOK level.

16. Common Core Standards = “Higher” Expectations Depth of Knowledge is the degree of depth or complexity of knowledge. DOK is NOT.....about Verbs - Verbs are not always used appropriately. about "difficulty" - It is not about the student or level of difficulty for the student - it requires looking at the assessment item not student work in order to determine the level. DOK is about the item/standard - not the student. DOK is....about what FOLLOWS the verb. What comes after the verb is more important than the verb itself. It’s about the complexity of mental processing that must occur to answer a question. Remember DOK... Descriptive, not a taxonomyFocuses on how deeply the student has to know the content in order to respond.Not the same as difficulty.

17. Webb’s Depth of Knowledge Levels • DOK-1 – Recall & Reproduction - Recall of a fact, term, principle, concept, or perform a routine Procedure • DOK-2 - Basic Application of Skills/Concepts -Use of information, conceptual knowledge, select appropriate procedures for a task, two or more steps with decision points along the way, routine problems, organize/display data, interpret/use simple graphs • DOK-3 - Strategic Thinking - Requires reasoning, developing a plan or sequence of steps to approach problem; requires some decision making and justification; abstract, complex, or non-routine; often • more than one possible answer • DOK-4 - Extended Thinking - An investigation or application to real world; requires time to research, problem solve, and process multiple conditions of the problem or task; non-routine manipulations, across disciplines/content areas/multiple sources

18. Cognitive Rigor Matrix

19. Cognitive Rigor & Implications for Examining Resources & Assessments • Assessing only at the highest DOK level will miss opportunities to know what students do & don’t know—go for a range and end “HIGH” in Critical Areas. • Performance assessments can offer varying levels of DOK embedded in a larger, more complex task.

21. Revisit 3 ÷ ½ = Individually: Write a mathematics word problem for which 3 ÷ ½ would be the method of solution. NAEP, 8th grade-2011

22. Student Samples: Student A: Student B:

23. How Did Kansas 8th Graders Do? 66% Incorrect 14% Correct 20% Omitted

24. TwizzlerProblem What is … ½ x ½ ÷ ½= ? Justify your answer with the Twizzler.

25. Step one: ½ x ½ ÷ ½= ? ¼ (half of one-half)

26. Step two: ¼ ÷ ½= ? How much of the ½ fits into ¼? ¼ ½ ½ of the ½ fits into ¼ This is why ½ is the answer.

27. Compare the 2 problems—Where were opportunities to: • Make sense of problems and persevere in solving them • Reason abstractly and quantitatively • Construct viable arguments and critique the reasoning of others • Model with mathematics • Use appropriate tools strategically • Attend to precision • Look for and make use of structure • Look for and express regularity in repeated reasoning Implications for Depth of Knowledge? How does this relate to your knowledge package?

29. Time to Assess Your Learning Are You Ready! You’ve heard new information about the CCSS -DOK Levels -Expectations -Examples, etc. In your team • Analyze SBAC of KS Assessment item for rigor • Use DOK Poster to Justify your choice for DOK Level • Reach Consensus • Show your DOK Analysis (1, 2, 3, 4) • You MUST defend your choice!

30. Math 4th Grade (KS State Assessment) • Each day that Jasmine turns in her homework on time, she earns 5points. Jasmine has turned in her homework on time for the last 8 days. How many points has Jasmine earned altogether? a)30 b)35 c)40 d)45

31. Math, 3rd Grade Look at the number below: 6,593 Which digit is in the tens place? • 3 • 9 • 6 • 5

32. 6th Grade , Math Sample, SBAC

33. 8th Grade, Math Sample SBAC

34. HS Math Sample, SBAC

36. 3rd Grade Diego buys a greeting card that costs $1.29. He pays for the card with two $1.00 bills and receives the correct amount of money as change. Which group of coins could Diego have received as change?

37. 3rd Grade, SBAC

38. 6th Grade SBAC

39. High School SBAC

40. THINK FOR A MOMENT . . . DoALL of your sudents have the opportunity to grapple with challenging tasks, everyday? • Do you have resources that embed the Habits of Mind in every lesson? • Are the tasks you choose for your students cognitively challenging? • Are ALL students exposed to rich tasks that promote higher order thinking? • Are at least 80% of your test questions (Formatives & Summatives) written at “higher” DOK levels?

41. Putting it all together . . . . . Revisit your definition of “rigor” and what this looks like in the classroom– have your ideas changed? If so, in what ways? 41