Learning to Ask Good Questions: A Key to Effective Teaching

Peg SmithUniversity of Pittsburgh

Teachers Development Group Leadership Seminar on Mathematics Professional DevelopmentFebruary 13, 2009Learning to Ask Good Questions

2Why 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).

2The last quote is particularly interesting. It doesnt come from a research study or even a published article. It is the comment made by one of the preservice secondary teachers in our certification program during a discussion of questioning.

When he made the comment he left Peg completely speechless (if you can imagine that).

3Why 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, 200434Overview of ActivitiesSolve and discuss the Calling Plans taskWatch 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 complexity4These are the activities in which we will engage this morning.

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.

6Identify folks to put their solutions on the document projector

Table is the first strategy I am afterGraph -- would work better with a graphing calcualtor

DO YOU HAVE TO USE SYSTEMS? NOOOOOOOO

Chart math ideas on newsprint

Number of MinutesPlan APlan B0$5.00$2.0010$5.40$3.0020$5.80$4.0030$6.20$5.0040$6.60$6.0050$7.00$7.0060$7.40$8.0070$7.80$9.0080$8.20$10.0090$8.60$11.00100$9.00$12.00Plan A C = .04m + $5

Plan B C = .10m + $2ConsiderWill 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?

9Identifying Good QuestionsWatch 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 question9HERE WE ARE INTERESTED IN ANY UTTERANCES THAT HAVE BOTH THE FORM AND FUNCTION OF QUESTIONS (AND WHICH ARE MATHEAMTICAL).

FOR EXAMPLE A STATEMENT LIKE YOU KNOW THAT THE SLOPE IS 3 BECAUSE IS A QUESTION ALTHOUGH IT IS NOT IN THE FORM OF A QUESTION HOW DO YOU KNOW THAT THE SLOPE IS 3?10Identifying Good QuestionsWhat makes a question good?

10Look across posters and see if there are commonalities in what they identify.

Ask what makes the question in lines xx-yy GOOD. (Chart responses)

Pick another question. What makes it good. Are some of the reasons the same as those previously identified or are there additional reasons?

[You dont need to talk about every question just enough to get at some of the key ideas that will come out in Boaler.]

The goal of the whole-group discussion is to make salient that a good question is one that helps advance students engagement with and understanding of the mathematical ideas. In looking at the Boaler and Brodie categories good questions -- types 3, 4, 5, and 7 primarily - get students to explain their thinking, make connections, extend their thinking, etc.

Review your color coded transcript in advance. The questions in RED are type 3, blue are type 4 and green are type 5. You may want to be on the look out for type 3 questions. There are actually more of these than any other type.11Considering the Questions Teachers Ask During InstructionRead 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).white11Three key points:

what is most important isnt the amount of time spent in particular activities it is how they work, what the teacher says and how they respond. the questions teachers ask shape the nature and flow of classroom discussions and the cognitive opportunities offered to students.

the questions teachers ask teach students to ask important questions of their own work.

It is also important to make the point about the importance of type 3 questions. See the next slide.Teacher QuestioningExploring mathematical meaning and relationships (type 3)

Probing (type 4)

Generating discussion (type 5)

12I would like to do is have you go through the questions you identified -- or back to the transcript -- and see if you can find questions that would fit into each of these categories.

Exploring Mathematical Relationships 17,33,37,64, 82, 102 129, 132, 156, 166

Probing 8,11, 85, 69, 121, 138

Generating Discussion 4, 12, 43, 101, 124

13All 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 rarelySuch 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.3813Boaler and Humphreys go on to say that this type of question could not be used exclusively and that the range they have witnessed is very useful in helping students develop understanding, manipulate methods, learn vocabulary, and so on. But the questions that target mathematical meanings and relationships are critical, and surprisingly rare.

Importance of QuestionsThe questions teachers ask guide students through particular pathways in the mathematical environmentWe 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

14Consider the question I asked you initially -- about whether any two plans intersected. What did that questions do for you?15Are 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?

15The point here is to make sure that they dont focus so much on the questioning that they miss the fact that if the task is not rich to begin with then asking good questions may be a wasted effort. Consider the following:

Mr. Johnsons seventh-grade class were completing a task that required them to express various rations, presented in a variety of formats (e.g., 4:12, 15/25, 1/5 to 1/2, and verbal problems) in simplest terms. Mr.. J modeled the solution of a few examples and then in order to have students experience mathematics as a collaborative activity he encourage his students to work and talk with one another in small groups. As they worked, he circulated around the room, stopping periodically to ask questions, When most of the class had completed the assignment, Mr..J orchestrated a large-group discussion to review the solutions. To provide thoughtfulness in the classroom discourse, Mr.. J frequently asked students questions about their answer (e.g., How do you know? Does It make sense? Can you justify your reasoning?).

In this episode, MR. Js choice of task and types of questioning limited what students could discuss in class. Many tasks, such as the one used by Mr.. J do not lend themselves to rich discourse. Hence it is important to consider the task and the questions TOGETHER.

(This excerpt comes from Silver and Smith, 1996, pp.20 - 29).16The Value of Asking a Range of Question TypesWhat 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?

16The poiint here isnt to work on all nine categories. That is overkill.

Teachers ask some of these questions quite naturally, particularly type 1. BUT we probably need to help teachers ask more questions that get at students thinking. I include type 5 in that group because it is about making thinking public.

ASSIGNMENT -- Here is an assignement that Peg gave in her class in the fall.

Identify a 10-minute segment of the lesson in which the teacher is interacting with the students in class (e.g., the share, discuss and analyze segment of a lesson that follows small group work). Transcribe this segment of tape verbatim (i.e., make a record of all utterances of the teacher and students during this period).

Analyze the segment you identified with respect to: 1) the types of the questions asked and the purposes they served; 2) what students do or not appear to understand based on their talk or their responses to the questions that were posed by the teacher; and 3) the role you think questions play in student learning. Use a subset of the Boaler and Humphreys (2005) question types to frame your discussion.

Building Teachers Capacity to Ask Good QuestionsEngage 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 frameworkCreate 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 QuestionsAnalyze the responses produced by the two groups of students in Cheryl Andersons 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 PlansPlan A C = .04m + $5

Plan B C = .10m + $2Number of MinutesPlan APlan B0$5.00$2.0010$5.40$3.0020$5.80$4.0030$6.20$5.0040$6.60$6.0050$7.00$7.0060$7.40$8.0070$7.80$9.0080$8.20$10.0090$8.60$11.00100$9.00$12.00Graph of Companies A and B