Teaching for Understanding: Discourse and Purposeful Questioning

1. Teaching for Understanding: Discourse and Purposeful Questioning March 21, 2016 Session 2A Vickie Inge vickieinge@gmail.com Joleen Lambert joleen.lambert@leecountyschools.net

2. Welcome & Table Group Introductions Who are You Where do You Work

3. Teaching for Understanding: Discourse and Purposeful QuestioningFraming Questions • How can purposeful questions and patterns of questions move students to math talk that promotes reasoning and sense making for deep understanding? • What are the five mathematics talk moves that support classroom discourse? • How can mathematics specialist and teacher leaders support teachers in being purposeful in their questioning?

4. With a shoulder partner, pick one of the aqua hexagons;each person has 1 minute to share what they think it means. Relational Thinking Higher Order Thinking Skills Critical Thinking Teaching for Deep Understanding Making Sense of Mathematics Proficient in Math Higher Level Questioning

5. Conceptual Understanding Strategic Competence/ Problem Solving Procedural Fluency Adaptive Reasoning Productive Disposition Mathematical Proficiency Mathematical Proficiency Students with deep understanding are Mathematical Proficient.

6. A student who is Mathematical Proficient demonstrates-- • conceptual understanding- comprehension mathematical concepts, operations, and relations. • procedural fluency- skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. • strategic competence - ability to formulate, represent, and solve mathematical problems. • adaptive reasoning- capacity for logical thought, reflection, explanation, and justification • productive disposition- habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Handouts, page 2

7. Effective NCTM, Principles to Actions, p. 10

8. Specialist and teacher leader decisions: How to help teachers move along a teacher practice continuum.

9. Questions are teachers’ tools to promote classroom discourse and set up that lightbulb moment!

10. Question Sort • Open the envelop on your table and work as table groups to sort the questions into exactly 4 non-overlapping groups or sets. • Analyze the type of “brain engagement,” thinking each set brings out in a student and develop a word or phrase that could be used to categorize the type of questions in each set.

11. Group Sharing • What descriptions for the classifications did your table group identify? • What discussions did you and your partner have about how to group the questions? • Does anyone have an example of a question that caused some differences of opinion?

12. Question Type– For What Purpose Reaching a common understanding and language for discussing the type of “brain engagement,” thinking that different questions types elicit. Principles to Actions: Ensuring Mathematical Understanding for All (page 36-37)

13. Question Type– For What Purpose • Identify what a student has to think about and demonstrate for each question type. • What seems to be an important distinction between type 1 and 2 questions and type 3 and 4 questions. Read -- Pair -- Share Principles to Actions: Ensuring Mathematical Understanding for All (page 36-37)

15. Making Sense of Mathematics Teachers’ questions are crucial in helping students make connections and learn important mathematics concepts. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding Weiss & Pasley, 2004

16. Principles to Actions Professional Learning Toolkit Website with Resources http://www.nctm.org/ptatoolkit

17. Virginia Standard of Learning 2009 Mathematical Progression for Functional Thinking 3.19 --recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. 4.15 --recognize, create, and extend numerical and geometric patterns. 5.17 --describe the relationship found in a number pattern and express the relationship. 5.18 --…b) write an open sentence to represent a given mathematical relationship, using a variable; 6.17 --identify and extend geometric and arithmetic sequences. 7.12 --represent relationships with tables, graphs, rules, and words. 8.14 -- make connections between any two representations (tables, graphs, words, and rules) of a given relationship. 8.16 --graph a linear equation in two variables.

18. The Calling Plans Task Long-distance company A charges a base rate of $5.00 per month plus 4 cents for each minute that you are on the phone. Long-distance company B charges a base rate of only $2.00 per month but charges you 10 cents for every minute used. • Part 1: How much time per month would you have to talk on the phone before subscribing to company A would save you money? • Part 2: Create a phone plane, Company C, that costs the same as Companies A and B at 50 minutes, but has a lower monthly fee than either Company A or B.

19. Pose Purposeful Questions • Effective Questions should: • Gather information about and reveal students’ current understandings; • Probe thinking and encourage students to explain, elaborate, or clarify their thinking; • Make the mathematics more visible and accessible for student examination and discussion and connect mathematical structures; and • Encourage reflection and justification to reveal deeper understanding including making generalizations and developing arguments. Deeper Understanding

20. The Calling Plans Task – Part 2The Context of Video Clip 1 • Prior to the lesson: • Students solved the Calling Plans Task – Part 1. • The tables, graphs and equations they produced in response to that task were posted in the classroom. • Video Clip 1 begins immediately after Mrs. Brovey explained that students would be working on the Calling Plans Task – Part 2 and read the problem to students. Students first worked individually and subsequently worked in small groups.

21. Lens for Watching Video Clip 1 As you watch the first video clip, pay attention to the teacher and student indicators associated withPose Purposeful Questioning . Think About’s: • What types of questions is the teacher using? • What can you say about the pattern of questions? • What do you notice about the student actions?

22. Patterns of Questioning Initiate-Response-Evaluate (IRE) Questioning Teacher asks a question to quickly gather factual information with a specific response in mind. A student responds and then the teacher evaluates the response. • Student has limited opportunity to think. • Teacher has no access to whether or how students are making sense of the mathematics. Principles to Actions, page 37

23. Patterns of Questioning: FunnelingQuestioning A teacher asks a series of questions to guide students through a procedure or to a desired result. • Teacher engages in cognitive activity about the idea and determining the next question to ask to guide or lead the student to a particular idea. • Student merely answering questions – often without seeing connections. Principles to Actions, page 37

24. Patterns of Questioning Focusing Questioning A teacher listens to student responses and uses student response to probe their thinking rather than leading them to how the teacher would solve the problem. • Allows teacher to learn about student thinking. • Requires students to articulate and explain their thinking. • Promotes making connections. Principles to Actions, page 37

25. Patterns of Questioning Funneling Questions • How many sides does that shape have? • Which side is longer? • Is this angle larger? • How do you know? Focusing Questions • What have you figured out? • Why do you think that? • Does that always work? If yes, why? If not, why not? When not? • Is there another way? • How are these two methods different? How are they similar? Principles to Actions, page 37 \

26. Another reason for Purposeful Questioning! ……formative assessment requires considerable changes in what teachers do daily… More basketball and less ping-pong. Dylan Wiliam https://youtu.be/029fSeOaGio

27. Managing Effective Student Discourse • Why is high level classroom discourse so difficult to facilitate? • What knowledge and skills are needed to facilitate productive discourse? Walk and Talk: Meet up with someone from a different table to discuss the question the facilitator indicates.

28. Pose Purposeful QuestionsTeacher and Student Actions ( Principles to Actions page 41)

29. “Our goal is not to increase the amount of talk in our classrooms, but to increase the amount of high quality talk in our classrooms—the mathematical productive talk.” –Classroom Discussions: Using Math Talk to Help Students Learn, 2009

30. Planning for Mathematical Discussion Productive Talk Formats What do We Talk About 1. Mathematical Concepts 2. Computational Procedures 3. Solution Methods and Problem-Solving Strategies 4. Mathematical Reasoning 5. Mathematical Terminology, Symbols, and Definitions 6. Forms of Representation • Whole-Class Discussion • Small-Group Discussion • Partner Talk What Do We Talk About? Chapin S., O’Connor, C., & Canavan Anderson, N. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions.

31. A survey of multiple studies on questioning support the following: • Plan relevant questions directly related to the concept or skill being taught. • Phrase questions clearly to communicate what the teacher expects of the intent and quality of students’ responses. • Do not direct the question to anyone until after it is asked so that all students pay attention. • Allow adequate wait time to provide students time to think before responding. • Encourage and design for wide student participation.

32. Bridging to Practice How can we support teachers in purposeful questioning. (HO 7)

33. Bridging to Practice

34. Change is Not Easy or Comfortable

35. Support—Support--Support Come on team we can do this together for the good of the students! OR

36. Transition fromtoword

37. Question Types to Avoid • yes-no (These draw one-word -- Yes or No -- responses: "Does the square root of 9 equal 3?") • tugging (These place emphasis on rote: "Come on, think of a third reason.") • guessing (These encourage speculation rather than thought: "How many ways can ½ be written?") • leading (These tend to give away answers: "How do right angles and parallel sides help to build rectangles?") • vague (These don't give students a clue as to what is called for: "Tell us about graphs.")

38. 8 ways teachers can talk less and get kids talking more • http://thecornerstoneforteachers.com/2014/09/8-ways-teachers-can-talk-less-get-kids-talking.html

39. Teacher to Student Student toStudent Student Product "What’s The Big Idea?" November 2006 K-12 Alliance/WestEd