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Purposeful Questioning 6-8 September 24, 2015

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Title: Purposeful Questioning 6-8 September 24, 2015


1
Purposeful Questioning 6-8 September 24, 2015
The Virginia Council of Mathematics Specialist
Conference NASA Langley Research Center, Hampton,
VA
  • Vickie Inge vickieinge_at_gmail.com

2
Overview of the Session
  • Examining the types of questions and the patterns
    of questioning teachers use in the classroom.
  • Watch video clips of an 8th grade pre-algebra
    class working on the Calling Plans Task.
  • Relate teacher and student actions in the video
    to the effective teacher and student actions as
    well as the types of questions for purposeful
    questioning.
  • Consider how to support teachers in using
    purposeful questioning.

3
Effective
NCTM, Principles to Actions, p. 10
4
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 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.

5
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.
  • 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

National Council of Teachers of Mathematics.
(2014). Principles to actions Ensuring
mathematical success for all. Reston, VA Author.
(p. 7)
6
Overview of the Relationship Between Question
Types and Patterns of Questioning Table, HO page
3
  • In the 2nd 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.

7
  • Principles to Actions Professional Learning
    Toolkit Website with Resources
  • http//www.nctm.org/ptatoolkit

8
Ms. Boverys Mathematics Learning Goals
  • Students will understand that
  • the point of intersection is a solution to each
    equation (Companies A, B, and C)
  • the rate of change (cost per minute) determines
    the steepness of the line
  • if the y-intercept (monthly base rate) is lowered
    then the rate of change (cost per minute) must
    increase in order for the new equation to
    intersect the other two at the same point.

9
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.

10

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.
  •  

11
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 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.
12

The Calling Plans Task The Context of the Video
Segment
School Pittsburgh Classical Academy,
Pittsburgh, PA Principal Valerie
Merlo Teacher Mrs. Elizabeth Brovey, Math
Coach Class Pre-Algebra 8th Grade Class
Curriculum Connected Mathematics Project
2 Size 27 students At the time the video was
filmed, Elizabeth Brovey was a coach at Classical
Academy in the Pittsburgh Public School District.
The students are mainstream eighth grade
Pre-Algebra students. The lesson occurred in
April.
13
The Calling Plans Task Part 2 The 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.

14
Lens for Watching Video Clip 1
  • As you watch the first video clip, pay attention
    to the teacher and student indicators associated
    with Pose Purposeful Questioning .
  • Think Abouts
  • 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?

15
Video Clip 2 focuses on the discussion between
teacher and students regarding the patterns they
notice.
  • Following individual and small group work, Mrs.
    Brovey pulls the class together for a whole group
    discussion. Several different equations that
    satisfy the conditions of the problem are offered
    by students. Jake, a student in the class then
    proposed a theory that every time the rate
    increases by 1 cent the base rate decreases by 50
    cents. Mrs. Brovey records the four possible
    phone plans for Company C (shown below) on the
    board and ask the class what patterns they
    see. C .14m
  • C .13m .50
  • C .12m 1.00
  • C .11m 1.50

16
Lens for Watching Video Clip 2
  • As you watch the second video this time, pay
    attention to the questions the teacher asks.
    Specifically
  • To what extent do the questions encourage
    students to explain, elaborate, or clarify their
    thinking?
  • To what extent do the questions make mathematics
    more visible and accessible for student
    examination and discussion?
  • How are the questions similar to or different
    from the questions asked in video clip 1?

17
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?)

18
Questioning Techniques
  • Funneling Questions
  • How many sides does that shape have?
  • Is this angle larger?
  • What is the product?
  • 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?

19
Questioning Funneling or Focusing
  • 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

20
Questioning Funneling or Focusing
  • 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
  • Promotes making connections

21
Our goal is not to increase the amount of talk
in our classrooms, but to increase the amount of
high quality talk in our classroomsthe
mathematical productive talk. Classroom
Discussions Using Math Talk to Help Students
Learn, 2009
22
Planning for Mathematical Discussion
  • Productive Talk Formats
  • What do We Talk About
  1. Whole-Class Discussion
  2. Small-Group Discussion
  3. Partner Talk 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

Chapin S., OConnor, C., Canavan Anderson, N.
(2003). Classroom discussions Using math talk to
help students learn. Sausalito, CA Math
Solutions.
23
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.

24
Bridging to Practice
  • How can we support teachers in purposeful
    questioning. (HO 7)

25
Bridging to Practice
Analyzing the Challenging Situation Some Ideas for Trouble Shooting Challenges
My students will not talk
The same few kids do all the talking
3. Should I call on students who _______
4. My students will talk, but they will not listen
5. What to do if students provide a response I do not understand
6. I have students at different levels
7. What to do when students are wrong
8. The discussion is not going anywhere--or at least not where I planned
9. Answers or responses are superficial
10. What if the first speaker gives the right answer
11. What to do for English Language Learners
26
Change is Not Easy or Comfortable
27
SupportSupport--Support
Come on team we can do this together for the good
of the students!
OR
28
Resources
  • Chapin S., OConnor, 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
    http//www.nctm.org/ptatoolkit/.
  • Reinhart, S. D. (2000). Never say anything a kid
    can say. Mathematics Teaching in the Middle
    School, 5(8) 478483.

29
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.
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