Productive Struggle to Grow Stronger Mathematics Students in Grades K–12

1. Productive Struggle to Grow Stronger Mathematics Students in Grades K–12 November 30th , 2012 National Council of Teachers Mathematics Regional Meeting - Chicago, IL www.jennyray.net http://debbiewaggoner-ckecmath.weebly.com

2. Who are we? KDE Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners Debbie.waggoner@education.ky.gov CKEC, Lexington Katrina.slone@education.ky.gov KVEC, Hazard Jenny.ray@education.ky.gov NKECS, No.Kentucky

3. REAL • Think of a time when you learned something outside of school. • Why and how did you learn it? • Was there a struggle? • Do you still remember it?

4. Productive Struggle

5. Don’t Prevent Students’ Mistakes, Prepare for Them David Ginsberg ASCD Smart Brief January 2, 2012

6. Today’s Learning Targets • I can experience productive struggle and explain its purpose and benefits. • I can explain the purpose of Formative Assessment Lessons (FALs). • I can describe the process of implementing a FAL. • I can access and use the materials to plan and perform a FAL.

7. Formative Assessment??? Exit Slipsentrance slips bell ringers Thumbs up/down Common Assessments Clickers White Boards

8. Why Now?

9. Five “Key Strategies” for Effective Formative Assessment • Clarifying, sharing, and understanding goals for learning and criteria for success with learners • Engineering effective classroom discussions, questions, activities, and tasks that elicit evidence of students’ learning. • Providing feedback that moves learning forward. • Activating students as owners of their own learning. • Activating students as learning resources for one another.

10. Typology of Kinds of Formative Assessment Formative Assessment Lessons

12. What’s a Problem For? • What would students need to know to get started on this problem? • Background knowledge, choose carefully based on where my students are…ZONE a little above • Is there more than one way to approach the problem? • Make sure the task is OPEN and has multiple possible solution strategies… • How do I introduce the problem? • Frame the task, relating to what we are learning… • What should I do after introducing the problem? • Stay quiet as much as possible, answer questions with questions only to move the learning forward…

21. FAL Outline: Determine FEEDBACK QUESTIONS • Pre-Assessment – Individual student work • Intro Lesson • Collaborative Activity • Whole Class Discussion • Post-Assessment Oral FEEDBACK QUESTIONS Written FEEDBACK QUESTIONS Formative Assessment Lesson

23. What do we really want our studentsto know and be able to do? • “And I’m calling on our nation’s governors and state education chiefs to develop standards and assessments that don’t simply measure whether students can fill in a bubble on a test, but whether they possess 21st Century skills like problem solving and critical thinking and entrepreneurship and creativity.” • President Obama, 1 March 2009

24. Mathematics Assessment Project • Designed and developed well-engineered assessment tools (FALs) to support US schools in implementing the Common Core State Standards for Mathematics (CCSS). • Funding is provided by the Bill and Melinda Gates Foundation through the University of California, Berkeley. • http://map.mathshell.org/materials/lessons.php • KDE mathematics specialists are developing FALs for grades K-5. • http://debbiewaggoner-ckecmath.weebly.com • www.jennyray.net

25. Re-teaching vs. Re-engagement

26. Two Kinds of FALs Problem Solving Focused Activity draws on knowledge about a variety of content Sometimes a number of answers are plausible but must be defended Usually includes a small group/pairs activity that requires analyzing sample student work in order to look at different strategies for solving the problem at hand. Concept Focused Both types include both concepts and problem solving, but each puts more emphasis on one than the other. • Specific content is central to the activity • Generally one correct answer, but may be a variety of ways to get that answer • Usually includes a small group/pairs activity that requires manipulation of mathematical information (often in the form of card sorts, etc.)

27. Learning by Doing!

28. What does teacher do during this time? Independent Work

29. Pre-Assessment

30. As I walk around, take note of the questions I ask you and the comments I make to you. Are they questions or comments that encourage you to engage in productive struggle, or do I GPS you to an answer?

31. What’s the teacher doing now? Moving around to groups, taking notes, asking questions and answering questions with questions!

32. Misconceptions & Feedback Questions • What misconceptions might your students have with this FAL or an activity like this one? • What possible feedback questions could you ask to move their learning forward?

33. Provide feedback that moves students forward.

34. Provide feedback that moves students forward.

36. Independent Work

37. Post-Assessment

38. Common Core Standards • 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. • 7.NS.2 Apply and extend previous understandings of multiplication and division of fractions to multiply and divide rational numbers. • 7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

39. Learning Targets of Unit If I gave an exit slip, quiz question, or other short cycle formative assessment for each of these targets, would it tell me if they really got and were able to do the standard? • Compute unit rates associated with ratios of fractions in like or different units. • Know that a proportion is a statement of equality between two ratios. • Define constant of proportionality as a unit rate. • Recognize situations in which percentage proportional relationships apply. • Apply proportional reasoning to solve multistep ratio and percent problems • Apply the properties of operations, particularly distributive property, to multiply rational numbers. • Interpret the products of rational numbers by describing real-world contexts. • Solve real-world mathematical problem by adding, subtracting, multiplying, and dividing rational numbers, including complex fractions.

41. How does the FAL structure provide for differentiation & productive struggle? Don’t Prevent Students’ Mistakes, Prepare for Them

42. Today’s Learning Targets • I can experience productive struggle and explain its purpose and benefits. • I can explain the purpose of Formative Assessment Lessons (FALs). • I can describe the process of implementing a FAL. • I can access and use the materials to plan and perform a FAL.

43. Who are we? KDE Regional Mathematics Content Specialist Kentucky Department of Education Office of Next Generation Learners Debbie.waggoner@education.ky.gov CKEC, Lexington Katrina.slone@education.ky.gov KVEC, Hazard Jenny.ray@education.ky.gov NKECS, No.Kentucky