The Virginia Council of Mathematics Specialist Conference NASA

The Virginia Council of Mathematics Specialist Conference NASA Langley Research Center, Hampton, VA Purposeful Questioning K-5 September 25, 2015 Vickie Inge vickieinge@gmail. com

Overview of the Session • Examining the types of questions and the patterns of questioning teachers use in the classroom. • Watch video clips of an teacher working on the Donuts Task with a class of kindergarten students. • Relate teacher and student actions in the video to the effective teacher and student actions as well as the types of questions that leads to purposeful questioning. • Consider how to support teachers in using purposeful questioning.

Effective NCTM, Principles to Actions, p. 10

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

Patterns in Teacher Questioning • Funneling Questions • Focusing Questions • How many sides does that shape have? • What have you figured out? • Is this angle larger? • Does that always work? If yes, why? If not, why not? When not? • What is the product? • Why do you think that? • Is there another way? • How are these two methods different? How are they similar?

Patterns in Teacher Questioning • Funneling occurs when a teacher asks a series of questions to guide students through a procedure or to a desired result. • Teacher engages in cognitive activity • Student merely answering questions – often without seeing connections

Patterns in Teacher Questioning • Focusing requires the teacher to listen to student responses and guide them based on what students are thinking rather than how the teacher would solve the problem. • Allows teacher to learn about student thinking • Requires students to articulate their thinking • Supports making connections

Making Sense of Mathematics An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author. (p. 7) 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

Overview of the Relationship Between Question Types and Patterns of Questioning Table, HO page 3 • In the 2 nd Column you will see the identifying name for each type of question that the authors of Principles to Actions: Ensuring Mathematical Success for All use. • Column 3 provides a description or purpose of each type of question. • Column 4 provides examples of specific questions representing each type. • Column 1 identifies the two patterns of questioning observed in most classrooms and the set up of the table suggests the type of question that typically is used in each pattern. Work with a partner to explore the information contained in he table.

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

Ms. Smith’s Mathematics Learning Goals Students will understand that: • the sum of two or more sets can be combined in many different ways (counting, counting on, or the use of known facts); • two addition expressions can have the same sum although the addends appear in a different order (the commutative property of addition); and • more sets of smaller amounts can still add up to the same amount as fewer sets with more items.

The Donuts Task, HO page 10 1. Dion chooses 3 chocolate donuts and 4 vanilla donuts. Draw a picture and write an equation to show Dion’s donuts. 2. Tamika has 4 vanilla donuts and 3 chocolate donuts. Draw a picture and write an equation to show Tamika’s donuts. 3. Tamika claims that she has more donuts than Dion. Who has more donuts, Dion or Tamika? Draw a picture and write an equation to show you know who has more donuts. Extensions • Tamika changes her mind and she gets 3 chocolate, 2 vanilla, and 2 sprinkle donuts. Draw a picture and write an equation to show Tamika’s donuts. • Tamika claims that she has more donuts than Dion because she has three kinds of donuts. What do you think about Tamika’s claim? Who has more donuts and how do you know?

Pose Purposeful Questions Effective Questions should: • Reveal students’ current understandings; • Encourage students to explain, elaborate, or clarify their thinking; and • Make the mathematics more visible and accessible for student examination and discussion.

Pose Purposeful Questions Teacher and Student Actions (HO page 2) What are teachers doing? What are students doing? • Advancing student understanding by asking questions that build on, but do not take over or funnel, student thinking. • Making certain to ask questions that go beyond gathering information to probing thinking and requiring explanation and justification. • Asking intentional questions that make the mathematics more visible and accessible for student examination and discussion. • Allowing sufficient wait time so that more students can formulate • Expecting to be asked to explain, clarify, and elaborate on their thinking. • Thinking carefully about how to present their responses to questions clearly, without rushing to respond quickly. • Reflecting on and justifying their reasoning, not simply providing answers. • Listening to, commenting on, and questioning the contributions of their classmates.

The Donuts Task The Context of the Video Segment Teacher: Amanda Smith Grade: Kindergarten School: Sam Houston Elementary School District: Lebanon School District, Tennessee Date: April 10, 2013 The teacher poses a problem to the students. Students work with manipulatives to represent and solve the problem. The teacher circulates, asking students what they know and pressing students to tell her the number of chocolate and vanilla donuts. The teacher also works to help students understand the goals for their learning.

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

Lens for Watching Video Clip 2 As you watch the second video clip of the students engaged with the extension problems, pay attention these questions. • What type of questions is the teacher using? • What can you say about the pattern of questions? • What do you notice about the student actions?

Why be INTENTIONAL about Asking PURPOSEFUL Questions? • Assess knowledge and learning. • Encourage students to articulate and extend their thinking and make predictions. • Prompt students to clarify, expand, and support their claims. • Encourage students to question their thought process or reasoning. • Apply class concepts to real-world scenarios.

Managing Effective Student Discourse • Why is high level classroom discourse so difficult to facilitate? • What knowledge and skills are needed to facilitate productive discourse? • Why is it important? (i. e. Why do we care? )

“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

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

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. And communicate what the teacher expects of the students’ responses. • Do not direct the question to anyone until it is asked so that all students pay attention • Encourage wide student participation, distribute questions to involve the majority of students. • Allow adequate wait time to provide students time to think before responding.

A survey of multiple studies on questioning support the following: • Probe student responses in a non-judgmental way. • Do not repeat students’ responses. Ask other students to “re-voice” or “add on”, or “apply their reasoning to someone else’s reasoning. ” Let students have to listen for themselves.

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

Change is Not Easy or Comfortable 25

Support—Support--Support Come on team we can do this together for the good of the students! OR 26

Resources Chapin S. , O’Connor, C. , & Canavan Anderson, N. (2003). Classroom discussions: Using math talk to help students learn. Sausalito, CA: Math Solutions. Huinker, D. , & Freckmann, J. L. (2004). Focusing conversations to promote teacher thinking. Teaching Children Mathematics, 10(7) 352 -357. National Council of Teachers of Mathematics. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, VA: National Council of Teachers of Mathematics. (n. d. ) Principles to Actions Professional Learning Toolkit. Retrieved September 2015. From http: //www. nctm. org/ptatoolkit/. Reinhart, S. D. (2000). Never say anything a kid can say. Mathematics Teaching in the Middle School, 5(8) 478– 483.

Resources Sullivan, P. , & Lilburn, P. (2002). Good questions for math teaching: Why ask them and what to ask. Grades K-6. Sausalito, CA: Math Solutions. Schuster, L. , & Anderson, N. C. (2005). Good Questions for math teaching: Why ask them and what to ask. Grades 5 -8. Sausalito, CA: Math Solutions. Small, M. (2012). Good Questions – Great Ways to Differentiate Mathematics Instruction. New York, NY: Teachers College Press. Smith, M. S. , & Stein, M. K. (2011). 5 Practices for Orchestrating Productive Mathematics Discussions. Reston, VA: National Council of Teachers of Mathematics and Thousand Oaks, CA: Corwin Press. Smith, M. S. , Hughes, E. K. , & Engle, R. A. , & Stein, M. K. (2009). Orchestrating discussions. Mathematics Teaching in the Middle School, 14 (9), 549 -556.