Supporting Teachers in Posing Purposeful Questions

Supporting Teachers in Posing Purposeful Questions

“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—

theproductive mathematical talk.”
2009, Classroom Discussions: Using Math Talk to Help Students Learn

Prepared for Virginia Council of Mathematics Specialist 2015 Conference:

Copies of PowerPoint and handouts can be downloaded at vacms.org

Presenter Vickie Inge

Framing Questions;

How can using purposeful questions move students to math talk that promotes reasoning and sense making for deep understanding?
What are the four main purposes of questioning in the classroom?
What are the two main patterns of questioning in classrooms and how does each pattern impact student learning?
How can mathematics specialist and teacher leaders support teachers in being purposeful in the questions they ask students.
How can mathematics specialist and teacher leaders support teachers in using a pattern of questioning that promotes students reasoning and sense making?

The new NCTM publication, Principles to Actions: Ensuring Mathematical Success for All, reminds us that how important classroom discourse is to help students at all levels to make sense of mathematics and advance the mathematical understanding of all students.Also, mathematical discourse is a powerful tool for formative assessment; that is as a "window" for teachers into students thinking, their understandings and their misunderstandings. However, the value of the ideas and information shared during partner, small group, and whole group classroom discussions is heavily dependent on the type of questions posed and the pattern of questioning the teacher uses.

Teachers have various reasons for asking questions such as the following.

Assess knowledge and learning.
Encourage students to 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.

When teachers are consciously aware of the types of questions and the frequency of each type they are able to evaluate their classroom instruction. When posing too many lower-level thinking questions they can adjust their questioning and ask more higher-level thinking questions. Teacher who create specific questions during planning a lesson have higher-level thought provoking questions read to use without having to come up with them on-the-fly. Different researches use various terms to designate the types of questions but for the purposes of this work the four types are identified as the following.

Gathering information
Probing thinking

Making the mathematics visible
Encouraging reflection and justification

Not only does the type of question posed impact students' reasoning and sense making, but the pattern of questioning also has an influence on student learning. The two patterns of questioning are funneling and focusing.

FUNNELING: Pattern of questions that lead to a desired procedure or conclusion.

The teacher has decided on apath for discussion to follow, leading student(s) along the path.Higher level questions may be part of this pattern. However, student responses that stray from the teacher’s goal will be given limited attention. This may not allow students to make their own connections or build understanding.

Teacher engages in cognitive activity
Student merely answering questions – often without seeing connections

FOCUSING : Pattern of questions that press students to advance their understanding.

Teacher attends to what the students are thinking, pressing them to communicate more clearly, and expecting them to reflect on their thoughts and those of their classmates. Focusing questions requires the teacher to listen to student responses and probe or ask another question based on what students are thinking rather than how the teacher would solve the problem. The teacherplans questions and outlines key points that should become apparent during the lesson. This permits the teacherto analyze and understand better what the students are thinking and presses students to communicate their thinking more effectively and to reflect on their thoughts.

Allows teacher to learn about student thinking
Requires students to articulate their thinking
Supports students making connections

Observations in many classrooms employing more intentional and thoughtful purposeful questioning reveal some commonly occurring teacher actions and student actions.

Pose Purposeful Questions
Teacher and Student Actions
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 thethinking 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 and offer responses.

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.

Principles to Actions: Ensuring Mathematical Success for All, p. 41 Figure

Overview of the Relationship Between Question Types and Patterns of Questioning

Question Type / Description / Examples
Funneling Pattern of Questioning
(Assessing) / Gathering Information:
Checking for a method, leading students through a method /

Wants a direct answer, usually right or wrong
Rehearses known facts or procedures
Students recall/state facts, definitions, formulas, etc.

When you write an equation, what does the equal sign tell you?
What is the formula for finding the area of a rectangle?
What does the median indicate for a set of data?

Probing Thinking:
Getting students to explain their thinking /

Explains, elaborates, or clarifies student thinking including articulating the steps in solution methods or the completion of a task.
Enables students to elaborate their thinking for their benefit and the class.

As you drew that number line, what decisions did you make that so that you can represent fourths on it?
Can you show and explain more about how you used a table to find the answer to the ducks and cows task?
Help me understand how you found 29 x 12 using 30 x 12.

Focusing Pattern of Questioning
(Advancing) / Making the Mathematics
Visible /

Students discuss mathematical structures and make connections among mathematical ideas and relationships.
Points to relationships among mathematical ideas and mathematics and other areas of study or context.

When you look at your book, your desk, and the door what do you notice about how they are alike?
What does your equation have to do with the seating at the band concert situation?
How does that array relate to multiplication and division?
In what ways might the division of fractions be related to the division of whole numbers?

Encouraging Reflection andJustification /

Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.
Extends the situation under discussion, where similar ideas may be used.

How might you prove that 51 is the solution?
How do you know that the sum of two odd numbers will always be even?
Why does plan A in the Smartphone Plans task start out cheaper but become more expensive in the long run?

Compiled using the work of Boaler and Humphries (2005) Connecting Mathematical Ideas: Middle School Cases to Support Teaching and Learning and NCTM (2014) Principles to Actions: Ensuring Mathematical Understanding for All Students.

THE ART OF QUESTIONING IN MATH CLASS

Adapted from Compiled by Mary Gardner, Regional Office of Education,

Phrases for enhancing questions:

“Tell me more about what you were thinking.”
“How did you decide that?”
“Elaborate for others in the class so they can check their thinking.”
“Can you justify that?”
“Give us your insights about arriving at the answer.”
“What steps did you take?”
“Tell us more about what you are thinking.”
“What made you think of that?”
“To a person on the street who does not speak “Math,” tell how you decided that . . . “

A “Try-to” List:

Try to use effective pauses and wait time.

Try to avoid frequent questions that require only a yes/no answer or simple recall.

Try to avoid answering your questions.

Try not give verbal and non-verbal clues

Try to follow up student responses with questions and phrases such as, “why?” or “tell me how you know” or “think about how you can put Jim’s response into your words.”

Try to avoid directing a question to a student mainly for disciplinary reasons.

Try to follow up a student’s response by fielding it to the class or another student for a reaction.

Try to avoid giveaway facial expressions to student responses.

Try to make it easy for students to ask a question at any time.

Try to ask the question before calling on a student to respond.

Try not to call on a particular student immediately after asking a question.

Try to ask questions that are open-ended.

Try to leave an occasional question unanswered at the end of the period.

Try to keep the students actively involved in the learning process.

Try to keep questions neutral. Qualifiers such as easy or hard can shut down learning in students.

Encouraging Your Students to AskQuestions in Class.

Note the subtle difference. The first set sounds as if you do not want questions; the second set implies that you both want and expect questions.

Instead of you asking questions this way: / You might try asking questions this way:

"How many of you understood that?”
“Everybody see that?”
“This is a ______, isn’t it?”

“Are there any questions?”
“You do not have any questions, do you?”
“Would anyone like to see that again?”

"Thumbs up--I got this, Thumb sideways--I am still working on this, Thumbs down--I have questions" Have students hold thumbs close to their heart so only you can see. Note who has questions and get back to them later.
“Okay--I want three questions about ___ from the group that will help us all understand better?”
“Now, write a question on your white board and hold it up."
“Now, what questions may I answer?”

Phrases That Encourage Participation:It is useful to have a handful of effective ways to start your questions that will motivate all students to participate. Here are some to try.

What others can you think of?

“Don’t raise your hand--yet; just think about a possible answer. I will give you a minute . . . “ “Everyone—picture this figure in your mind. Is it possible to sketch a possible counterexample to this statement? I will walk around to look at your work and select three students to share their results with the class.”
“Find an example of this statement and write it down. In just a minute, I will tell you possible ways to check your example to see if it indeed makes the statement true.”
“Put the next step on your paper and write a reason to justify this step. Raise your hand when you are ready and I will be around to check in on you.”

Phrases That May Fail to Motivate: There are some questions that you might want to avoid. Why? Because often you end up answering your ownquestionsand “permitting” students NOT to participate—that is, students are not required to take responsibility to develop a response depending how the question is phrased.

“Does someone know if . . . “
“Can anyone here give me an example of . . . “
“Who knows the difference between . . . “
“Someone tell me the definition of . . . “
“OK, who wants to tell me about . . . “

POSE OPEN QUESTIONS

Successful questions provide a manageable challenge to students – one that is at their stage of mathematical development. Open questions are effective in supporting learning. An open question is one that encourages a variety of approaches and responses. Consider

“What is 4 + 6?” (closed question) versus “Is there another way to make 10?” (open question)
“How many sides does a quadrilateral figure have?” (closed question) versus “What do you notice about these figures?” (open question).

Open questions

Help teachers build student self-confidence as they allow learners to respond at their own stage of development.
Intrinsically allow for differentiation. Responses will reveal individual differences, which may be due to different levels of understanding or readiness, the strategies to which the students have been exposed and how each student approaches problems in general.
Signal to students that a range of responses is expected and, more importantly, valued.

Huinker and Freckman (2004, p. 256) suggest the following examples:

As you think about…

As you consider…

Given what you know about…

In what ways…

Regarding the decisions you made…

In your planning…

From previous work with students…

Take a minute…

When you think about…

How else could you have …?

How are these ____ the same?

How are these different?

What would you do if …?

What would happen if …?

What else could you have done?

What Teachers Can do to Build a Risk Free Classroom and Support Students

Plan relevant questions. The essence of good questioning is in planning questions that are directly related to the concept or skill being taught.
Phrase questions clearly. Clear and concise phrased questions communicate what the teacher expects of the students’ responses.
Do not direct the question to anyone until it is asked. This forces all students to pay attention and requires more students to answer the question mentally
Encourage wide student participation. Distribute questions to involve the majority of students. Balance responses from volunteering and non-volunteering students and encourage student-to-student interaction.
Allow adequate wait time. Give students time to think when responding. Allow three to five seconds of wait time after asking a question before requesting a student’s response, particularly when high-level questions are asked. The more time a teacher waits for a reply from the students the better the response and will encourage other students to participate.

TRANSITION TO PRACTICE and SUPPORTING TEACHERS:

Trouble-shooting some of the challenges teachers face when increasing the math talk in the classroom and using more open and focusing questions. An effective way to support teachers is to work with small groups or even one teacher and identify what they perceive as challenging situations, some frequent ones teachers name are listedbelow. Then brainstorm together the cause of the challenge think of some ways to address the challenges.

Analyzing the Challenging Situation / Some Ideas for Trouble Shooting Challenges
My students will not talk
The same few kids do all the talking
Should I call on students who
My students will talk, but they will not listen
What to do if students provide a response I do not understand
I have students at different levels
What to do when students are wrong
The discussion is not going anywhere--or at least not where I planned
Answers or responses are superficial
What if the first speaker gives the right answer
What to do for English Language Learners

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.

National Council of Teachers of Mathematics. (n.d.) Principles to actions professional learning toolkit. Retrieved September 2015. From

Reinhart, S. D. (2000). Never say anything a kid can say. Mathematics Teaching in the Middle School, 5(8) 478–483.

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.

Tasks for Sessions:

Grades K-5 SessionDonuts Task

Dion chooses 3 chocolate donuts and 4 vanilla donuts. Draw a picture and write an equation to show Dion’s donuts.
Tamika has 4 vanilla donuts and 3 chocolate donuts. Draw a picture and write an equation to show Tamika’s donuts.
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 how 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?

Grades 6-8 SessionThe Calling Plans

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.

1 | Compiled by Vickie Inge for the VACMS 2015