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Teaching for Understanding: Discourse and Purposeful Questioning


TEACHING FOR UNDERSTANDING: DISCOURSE AND PURPOSEFUL QUESTIONING March 21, 2016 Session 2A Vickie Inge vickieinge_at_gmail.com Joleen Lambert joleen.lambert ... – PowerPoint PPT presentation

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Title: Teaching for Understanding: Discourse and Purposeful Questioning

Teaching for Understanding Discourse and
Purposeful Questioning
  • March 21, 2016
  • Session 2A
  • Vickie Inge vickieinge_at_gmail.com
  • Joleen Lambert joleen.lambert_at_leecountyschools.net

Welcome Table Group Introductions
  • Who are You
  • Where do You Work

Teaching for Understanding Discourse and
Purposeful Questioning Framing Questions
  • How can purposeful questions and patterns of
    questions move students to math talk that
    promotes reasoning and sense making for deep
  • What are the five mathematics talk moves that
    support classroom discourse?
  • How can mathematics specialist and teacher
    leaders support teachers in being purposeful in
    their questioning?

With a shoulder partner, pick one of the aqua
hexagons each person has 1 minute to share what
they think it means.
Conceptual Understanding
Strategic Competence/ Problem Solving
Procedural Fluency
Adaptive Reasoning
Productive Disposition
Mathematical Proficiency
Mathematical Proficiency
Students with deep understanding are Mathematical
A student who is Mathematical Proficient
  • conceptual understanding - comprehension
    mathematical concepts, operations, and relations.
  • procedural fluency - skill in carrying out
    procedures flexibly, accurately, efficiently, and
  • strategic competence - ability to formulate,
    represent, and solve mathematical problems.
  • adaptive reasoning - capacity for logical
    thought, reflection, explanation, and
  • productive disposition - habitual inclination to
    see mathematics as sensible, useful, and
    worthwhile, coupled with a belief in diligence
    and ones own efficacy.

NCTM, Principles to Actions, p. 10
Effective Mathematics Teaching Practices NOVICE APPRENTICE EFFECTIVE PROFICIENT
Establish mathematics goals to focus learning
Implement tasks that promote reasoning and problem solving.  
Use and connect mathematical representations  
Facilitate meaningful mathematical discourse  
Pose purposeful questions
Build procedural fluency from conceptual understanding.  
Elicit and use evidence of student thinking  
Specialist and teacher leader decisions How to
help teachers move along a teacher practice
Questions are teachers tools to promote
classroom discourse and set up that lightbulb
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 brain engagement, thinking
    each set brings out in a student and develop a
    word or phrase that could be used to categorize
    the type of questions in each set.

Group Sharing
  1. What descriptions for the classifications did
    your table group identify?
  2. What discussions did you and your partner have
    about how to group the questions?
  3. Does anyone have an example of a question that
    caused some differences of opinion?

Question Type For What Purpose
  • Reaching a common understanding and language for
    discussing the type of brain engagement,
    thinking that different questions types elicit.
  • Principles to Actions Ensuring Mathematical
    Understanding for All (page 36-37)

Question Type For What Purpose
  • Identify what a student has to think about and
    demonstrate for each question type.
  • What seems to be an important distinction between
    type 1 and 2 questions and type 3 and 4
  • Read -- Pair -- Share
  • Principles to Actions Ensuring Mathematical
    Understanding for All (page 36-37)

(No Transcript)
Making Sense of Mathematics
  • 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

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

Virginia Standard of Learning 2009
Mathematical Progression for Functional Thinking
  • 3.19 --recognize and describe a variety of
    patterns formed using numbers, tables, and
    pictures, and
  • extend the patterns, using the same or
    different forms.
  • 4.15 --recognize, create, and extend numerical
    and geometric patterns.
  • 5.17 --describe the relationship found in a
    number pattern and express the relationship.
  • 5.18 --b) write an open sentence to represent a
    given mathematical relationship, using a
  • 6.17 --identify and extend geometric and
    arithmetic sequences.
  • 7.12 --represent relationships with tables,
    graphs, rules, and words.
  • 8.14 -- make connections between any two
    representations (tables, graphs, words, and
    rules) of a given relationship.
  • 8.16 --graph a linear equation in two variables.

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.


Pose Purposeful Questions
  • Effective Questions should
  • Gather information about and reveal students
    current understandings
  • Probe thinking and encourage students to explain,
    elaborate, or clarify their thinking
  • Make the mathematics more visible and accessible
    for student examination and discussion and
    connect mathematical structures and
  • Encourage reflection and justification to reveal
    deeper understanding including making
    generalizations and developing arguments.

Deeper Understanding

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
  • 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.

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
  • What do you notice about the student actions?

Patterns of Questioning
  • Initiate-Response-Evaluate (IRE) Questioning
  • Teacher asks a question to quickly gather factual
    information with a specific response in mind. A
    student responds and then the teacher evaluates
    the response.
  • Student has limited opportunity to think.
  • Teacher has no access to whether or how students
    are making sense of the mathematics.

Patterns of Questioning
  • Funneling Questioning
  • A teacher asks a series of questions to guide
    students through a procedure or to a desired
  • Teacher engages in cognitive activity about the
    idea and determining the next question to ask to
    guide or lead the student to a particular idea.
  • Student merely answering questions often
    without seeing connections.

Patterns of Questioning
  • Focusing Questioning
  • A teacher listens to student responses and uses
    student response to probe their thinking rather
    than leading them to how the teacher would solve
    the problem.
  • Allows teacher to learn about student thinking.
  • Requires students to articulate and explain their
  • Promotes making connections.

Patterns of Questioning
  • Funneling Questions
  • How many sides does that shape have?
  • Which side is longer?
  • Is this angle larger?
  • How do you know?
  • 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?

Another reason for Purposeful Questioning!
  • formative assessment requires considerable
    changes in what teachers do daily
  • More basketball and less ping-pong.
  • Dylan Wiliam
  • https//youtu.be/029fSeOaGio

Video Clip 2 focuses on the discussion between
teacher and students regarding the patterns they
  • 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

Lens for Watching Video Clip 2
  • As you watch the second video this time, pay
    attention to the questions the teacher asks.
  • To what extent do the questions encourage
    students to explain, elaborate, or clarify their
  • 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?

Managing Effective Student Discourse
  1. Why is high level classroom discourse so
    difficult to facilitate?
  2. What knowledge and skills are needed to
    facilitate productive discourse?

Walk and Talk Meet up with someone from a
different table to discuss the question the
facilitator indicates.
Pose Purposeful Questions Teacher and Student
Actions ( Principles to Actions page 41)
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.
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
Planning for Mathematical Discussion
  • What do We Talk About
  • Productive Talk Formats
  • 1. Mathematical Concepts
  • 2. Computational Procedures
  • 3. Solution Methods and Problem-Solving
  • 4. Mathematical Reasoning
  • 5. Mathematical Terminology, Symbols, and
  • 6. Forms of Representation
  1. Whole-Class Discussion
  2. Small-Group Discussion
  3. Partner Talk What Do We Talk About?

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

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

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
Change is Not Easy or Comfortable
Come on team we can do this together for the good
of the students!
Transition from toword
Less Of More Of
Rapid fire teacher questions   Questions directed to the whole class, with few students responding.   Questions that ask students to state small pieces of knowledge unrelated to the larger context.   Questions that ask what students know   Questions with quick answers.   Questions limited to current understanding   Plan activities in a lesson   Thoughtful questions that are linked to push student thinking   Questions directed to student partners or small groups.   Questions that require connections between and among concepts   Questions that ask how students know.   Questions with wait time for student thinking   Questions that extend understanding to a new context   Plan questions in the activities based on expected and unexpected student responses.
Question Types to Avoid
  • yes-no (These draw one-word -- Yes or No --
    responses "Does the square root of 9 equal 3?")
  • tugging (These place emphasis on rote "Come on,
    think of a third reason.")
  • guessing (These encourage speculation rather
    than thought "How many ways can ½ be written?")
  • leading (These tend to give away answers "How
    do right angles and parallel sides help to build
  • vague (These don't give students a clue as to
    what is called for "Tell us about graphs.")

8 ways teachers can talk less and get kids
talking more
  • http//thecornerstoneforteachers.com/2014/09/8-way

"Whats The Big Idea?" November 2006 ?K-12
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