improving classroom questions in mathematics

Improving Classroom Questions in Mathematics

Title I Directors’ Meeting

October 4, 2010

Morgantown

How Could Asking Questions Lead to Higher-Level Thinking?

John Ford, Title I Mathematics Coordinator

What

makes a

question

a good

question?

If there are “good” and “bad” questions, is it better to ask “bad” questions or to ask no questions?

How soon should

you expect an

answer to a

question?

How long is “too

long” to wait for

an answer?

How can a student

learn by being asked

a question? (If she

can answer; she already knows – if

not, why would asking the question

help her learn?)

What does this have to

do with mathematics?

When is the best time to ask a question?

Could a teacher ask too many questions? How many would that be? How would someone know?

What might be the danger in using questioning as an instructional strategy – or is there any?

What does Socrates have to do with all of this?

Wasn’t he forced to drink hemlock?

Isn’t hemlock poisonous? Who wants

to know?

There are 10 types of people in the world.

Those who understand binary and those who don’t.

An exercise in using questioning to teach about the binary number system based on the work of Rick Garlikov.

http://www.garlikov.com/Soc_Meth.html

How can a student

learn by being asked

a question? (If she

can answer; she already knows – if

not, why would asking the question

help her learn?)

What Was Being Asked?

•Content (yes/no) questions – one right answer

“What are words made of?”“How many letters in the English Alphabet?”“How many numerals do we use?”

•Questions with more than one correct answer

“Who can write 10 another way?”“Why do you think we have 10 numerals?”“How can you show ‘55’ with your fingers?”

RECALL{

TH INK ING

OTH RE ER C A T LH LAN

{

Learning begins with Questioning

•Socrates 469 – 369 B.C.E.•Children’s Thinking - David Russell, 1956•Taxonomy of Educational Objectives- Benjamin Bloom, 1956•Classroom Questions: What Kinds?- Norris M. Sanders, 1966•Teaching Strategies and Cognitive Functioning in Elementary School Children - Hilda Taba, 1966 •Teacher Effectiveness Training - Thomas Gordon, 1974•Involving Students in Questioning - Francis P. Huskins, 1976•Improving Classroom Questions- Kenneth R. Chuska, 1995 and 2003

Why ask better questions?

“When teachers master the art of

questioning, . . . they will add

purpose and relevance to learning.”

- Chuska, Improving Classroom Questions,

second edition, 2003, p. 13

Planning Lessons - Planning Questions

• Integral to lesson planning should be question planning

• Questions should be open-ended• Question selection should consider students’ knowledge and allow for personal input

Six Motivation Strategies

• Ask Fewer Questions

Could a teacher ask too many questions? How many would that be? How would someone know?

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers

How soon should

you expect an

answer to a

question?

How long is “too

long” to wait for

an answer?

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers• Pay Attention to the Student

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers• Pay Attention to the Student

• Less Talk

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers• Pay Attention to the Student

• Less Talk• Give Students Time to Write Answers

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers• Pay Attention to the Student

• Less Talk• Give Students Time to Write Answers• Activate Background Knowledge

What might be the danger in using questioning as an instructional strategy – or is there any?

What does Socrates have to do with all of this?

Wasn’t he forced to drink hemlock?

Isn’t hemlock poisonous?

Six Motivation Strategies

• Ask Fewer Questions

• Provide Time for Answers• Pay Attention to the Student

• Less Talk• Give Students Time to Write Answers• Activate Background Knowledge

Components for Effective Questioning

What

makes a

question

a good

question?

Components for Effective Questioning

• An Issue, Problem or Challenge

Components for Effective Questioning

• An Issue, Problem or Challenge• Real-World Reference Points

Rigor /Relevance Framework

C

D

Assimilation

Adaptation

A

B

Acquisition

Application

Components for Effective Questioning

• An Issue, Problem or Challenge• Real-World Reference Points• An Appropriate Approach

Components for Effective Questioning

• An Issue, Problem or Challenge• Real-World Reference Points• An Appropriate Approach• A Reasoning Goal

Designing Questions• What gives rise to the question?

– Origin, Purpose, or Reason

– From what sources does the question arise?

Designing Questions• What gives rise to the question?

• How is the question framed?- How does the teacher determine which

questions and in what order?

- What criteria should the question meet? - How might students approach answering

it?

Designing Questions• What gives rise to the question?

• How is the question framed?

• What answer is anticipated?- What kinds of responses might

students make?- How will the teacher treat the student

responses?- What follow-up questions might the

teacher or students ask?

When Should a Question Be Asked?

When is the best time to ask a question?

When Should a Question Be Asked?

• Before Study Begins To Motivate To Promote Student Goal Setting To Determine Readiness To Stimulate Thinking To Convey Purpose To Create a Positive Learning Atmosphere To Discern Student Interest or Knowledge To Activate Background Knowledge

When Should a Question Be Asked?

• Before Study Begins To Motivate To Promote Student Goal Setting To Determine Readiness To Stimulate Thinking To Convey Purpose To Create a Positive Learning Atmosphere To Discern Student Interest or Knowledge To Activate Background Knowledge

When Should a Question Be Asked?

• Before Study Begins

The “Big Four” Questions

1. What do you know you know about the topic?

2. What do you think you know about the topic?

3. What do you want to know?4. What do you feel or believe about an

issue or problem?

When Should a Question Be Asked?

• Before Study Begins

Timing

- Two to three days prior to the beginning of a unit in the primary grades

- Two to three weeks in advance for grades four and up

When Should a Question Be Asked?

• Before Study Begins

• During the Lessons

- Analyzing and Critiquing

When Should a Question Be Asked?

• Before Study Begins

• During the Lessons

- Analyzing and Critiquing- Anticipating Outcomes

When Should a Question Be Asked?

• Before Study Begins

• During the Lessons

- Analyzing and Critiquing- Anticipating Outcomes- Summarizing

When Should a Question Be Asked?

• Before Study Begins

• During the Lessons

- Analyzing and Critiquing- Anticipating Outcomes- Summarizing- Detecting Bias and Examining

Viewpoints

When Should a Question Be Asked?

• Before Study Begins

• During the Lessons

• After the Lesson- To summarize- To reflect on what was learned- To draw conclusions- To synthesize information with former

learning- To extend students’ learning

One Last QuestionWhat does

this have to do with mathematic

s?

An example from:

“Number Talks: Helping Children Build Mental Math and Computational Strategies” by Sherry Parrish

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?Contact Information:

John Ford Title I Mathematics Coordinator

jford@access.k12.wv.us(304) 558-7805 ext. 53349