Peg Smith University of Pittsburgh Teachers Development Group Leadership Seminar on Mathematics Professional Development February 13, 2009 Learning to Ask Good Questions

2 Why Focus on Questioning? Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask (NCTM, 1991). Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge (NCTM, 2000). Questions are one of the only tools teachers have for finding out what students are thinking (Michaels, 2005).

3 Why Focus on Questioning? Teachers’ questions are crucial in helping students make connections and learn important mathematics and science 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

4 Overview of Activities Solve and discuss the Calling Plans task Watch an excerpt of a classroom discussion and identify “good questions” asked by the teacher. Identify the characteristics of good questions. Read the Boaler & Brodie article and discuss the categories of questions identified therein. Discuss the value of considering the types of questions that teachers ask and of planning specific questions to ask in preparation for teaching. Brainstorm ways that teachers could practice in situations of reduced complexity

Calling Plans (blue version 1) Long-distance company A charges a base rate of $5 per month, plus 4 cents per minute that you are on the phone. Long-distance company B charges a base rate of only $2 per month, but they charge you 10 cents per minute used. How much time per month would you have to talk on the phone before it would save you money to subscribe to company A?

The Calling Plans Task Work on the task individually for about five minutes (Private Think Time). Continuing working on the task in your group. Once you have a solution, discuss what you see as the key mathematical ideas that you would want to emerge from work on this task.

Number of Minutes Plan APlan B 0$5.00$ $5.40$ $5.80$ $6.20$ $6.60$ $ $7.40$ $7.80$ $8.20$ $8.60$ $9.00$12.00 Plan A C =.04m + $5 Plan B C =.10m + $2

Consider… Will any two phone plans (that are linear functions) have a shared point (i.e., the same cost for the same number of minutes)? Why or why not?

9 Identifying Good Questions Watch a clip from a classroom discussion facilitated by Cheryl Anderson featuring the Calling Plans task (see the yellow transcript) Identify a question (or two) that Cheryl Anderson asked during the lesson that you consider good Discuss the questions identified by folks at your table and come to agreement on 2 or 3 questions that you think are good. (Mark your selections on the group transcript.) Create a list of the characteristics of a good question

10 Identifying Good Questions What makes a question “good”?

11 Considering the Questions Teachers Ask During Instruction Read the Boaler and Brodie article ( ). Identify the findings of the Boaler and Brodie study that you found most intriguing and discuss these briefly at your table. Consider how the Boaler and Brodie categories match the characteristics of questions we identified (see page 776 of the article). white

Teacher Questioning Exploring mathematical meaning and relationships (type 3) Probing (type 4) Generating discussion (type 5)

13 All Question Types Are Not Equally Important … the question type that is arguably the most important of all - type 3, targeting key concepts - was observed very rarely…Such questions orient students to the central mathematical ideas. They do not necessarily follow up on students’ ideas; they often come from the teacher, and they serve a very particular and deliberate purpose: challenging students to consider a critical mathematical concept. Boaler & Humphreys, 2005, p.38

Importance of Questions The questions teachers ask guide students through particular pathways in the mathematical environment…We find that some teachers ask surface questions that do not take students deeper into mathematical issues; we think of those students as walking on a path that surrounds a beautiful forest without ever stepping into the forest to look at the trees. Other teachers ask questions that are more probing but that do not build carefully toward key concepts. We think of these students as stepping in and out of the forest, catching glimpses of trees and flowers but not learning where they are in relation to each other or how they may navigate their way through the forest. Other teachers ask questions that target key concepts and build carefully to enable students to find their way around. Those students experience the forest fully – they walk through, looking at the trees and flowers, and they also climb some trees and look at the whole terrain, getting a sense of where they are….the questions that teachers use to guide students become the pathways that students walk along and that shape their experience of the terrain. Boaler & Humphreys, 2005

15 Are Good Questions Enough? We have been focusing our attention so far on the types of questions a teacher asks during instruction. Does the task that forms the basis for instruction matter? Why or why not?

16 The Value of Asking a Range of Question Types What value, if any, do you see in thinking about the types of questions teachers ask using the Boaler and Brodie categories? How can you help teachers expand their questioning repertoire to include a broader range of question types?

Building Teachers’ Capacity to Ask Good Questions Engage in an activity similar to the one we just did where teachers first identify questions, discuss characteristics of good questions, and then consider a questioning framework Create a record of practice from their own teaching and analyze the questions they ask (pink sheet). [The Karen Zigmond example I gave the other night is one version of how this could play out.] Analyze student work and create questions that you would ask the students who produced the work that would probe their thinking and help make the mathematics salient.

Using Student Work to Generate Questions Analyze the responses produced by the two groups of students in Cheryl Anderson’s class (green). Create questions that you would ask the students who produced the response that would clarify and extend their thinking.

Questioning: Is it a High-Leverage Practice? I SAY YES!!!

Calling Plans Plan A C =.04m + $5 Plan B C =.10m + $2

Number of Minutes Plan APlan B 0$5.00$ $5.40$ $5.80$ $6.20$ $6.60$ $ $7.40$ $7.80$ $8.20$ $8.60$ $9.00$12.00

Graph of Companies A and B