How to Be Responsive if… · A student solves it one way and can’t think of any other way: · Ask if they can draw a picture that shows the answer. · Ask if they can invent a new way to solve it. · Show them a method that they haven’t used and ask if they can figure out how it works and why. · A student solves the problem multiple ways easily: · Ask why they did what they did. Why do their methods work? Be specific about what you want to know. · See if they can come up with another method that isn’t as easy to find. · Ask the interviewee how their methods are similar and different. Be as specific as possible. · A student solves the problem incorrectly: · Remain neutral. · Ask the interviewee why they did what they did. Why do their methods work? · See if they can solve it a different way. Compare solutions. · Say, “I saw someone else solve it like this….and they got 90.” What would you say to that person? General Strategies for Being Responsive · Ask, “Why?” Why did they do …(be specific about what you want to know)? How do they know it’s mathematically correct? · Be patient. Use lots of wait time, and don’t answer your own questions. · Focus on understanding what they are thinking. · Ask them to make connections. · How is this the same as what you did in the first solution? · How is this different then what you did in the standard algorithm? · Ask them to generalize their strategy. · Will it always work to …? · What if it was … instead? Solution Strategies and Chart for Students Strategy Example Probing Questions Direct Modeling Equal groups Array · How does this represent the problem? · Could you represent it in a different way? · 18 groups of 5 instead of 5 groups of 18 Traditional Algorithm · Why did you put a little 4 on top of the 1? · Why didn’t you put the little 4 on top of the 8? · What does the little 4 represent? Partial Products · How is the 40 represented in the traditional algorithm? · Why is it 50 instead of 5? · How did you know how to line up the 40 and the 50? · Can you apply this method to 32 x 9? Box Method · How did you know where to put the numbers and what to write in the boxes? · Why did you add 50 and 40? Distributive Property a(b+c) = ab + ac 5 x ( 10 + 8) 50 + 40 90 OR 5 x (5 + 5 + 8) 25 + 25 + 40 90 OR 5 x (11 + 7) 55 + 35 90 OR 5 x (20 - 2) 100 - 10 90 · Why did you decide to break 18 into 10 and 8? · You broke the 18 into 10 and 8. If you broke it up differently, would your method still work? · Does the distributive property work with subtraction? Doubling/Halving 5 x 18 Double 5 → 10 Halve 18 → 9 10 x 9 = 90 · Why does this strategy work? What is happening here? Repeated Addition 18 + 18 + 18 + 18 + 18 = 90 OR 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 18 · Is adding 18 five times the same as adding 5 eighteen times? Why? Associative Property 5 x 18 5 x (6 x .

1. How to Be Responsive if…
·
A student solves it one way and can’t think of any other
way:
· Ask if they can draw a picture that shows the answer.
· Ask if they can invent a new way to solve it.
· Show them a method that they haven’t used and ask if they can
figure out how it works and why.
·
A student solves the problem multiple ways easily:
· Ask
why they did what they did. Why do their methods
work? Be specific about what you want to know.
· See if they can come up with another method that isn’t as easy
to find.
· Ask the interviewee how their methods are similar and
different. Be as specific as possible.
·
A student solves the problem incorrectly:
· Remain neutral.
· Ask the interviewee
why they did what they did. Why do their methods
work?
· See if they can solve it a different way. Compare solutions.
· Say, “I saw someone else solve it like this….and they got 90.”
What would you say to that person?
General Strategies for Being Responsive

2. · Ask, “Why?” Why did they do …(be specific about what you
want to know)? How do they know it’s mathematically correct?
· Be patient. Use lots of wait time, and don’t answer your own
questions.
· Focus on understanding what they are thinking.
· Ask them to make connections.
· How is this the same as what you did in the first solution?
· How is this different then what you did in the standard
algorithm?
· Ask them to generalize their strategy.
· Will it always work to …?
· What if it was … instead?
Solution
Strategies and Chart for Students
Strategy
Example
Probing Questions
Direct Modeling
Equal groups
Array

3. · How does this represent the problem?
· Could you represent it in a different way?
· 18 groups of 5 instead of 5 groups of 18
Traditional Algorithm
· Why did you put a little 4 on top of the 1?
· Why didn’t you put the little 4 on top of the 8?
· What does the little 4 represent?
Partial Products
· How is the 40 represented in the traditional algorithm?
· Why is it 50 instead of 5?
· How did you know how to line up the 40 and the 50?
· Can you apply this method to 32 x 9?
Box Method
· How did you know where to put the numbers and what to write
in the boxes?
· Why did you add 50 and 40?
Distributive Property
a(b+c) = ab + ac
5 x ( 10 + 8)
50 + 40

4. 90
OR
5 x (5 + 5 + 8)
25 + 25 + 40
90
OR
5 x (11 + 7)
55 + 35
90
OR
5 x (20 - 2)
100 - 10
90
· Why did you decide to break 18 into 10 and 8?
· You broke the 18 into 10 and 8. If you broke it up differently,
would your method still work?
· Does the distributive property work with subtraction?
Doubling/Halving

5. 5 x 18
Double 5 → 10
Halve 18 → 9
10 x 9 = 90
· Why does this strategy work? What is happening here?
Repeated Addition
18 + 18 + 18 + 18 + 18 = 90
OR
5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5
+ 5 = 18
· Is adding 18 five times the same as adding 5 eighteen times?
Why?
Associative Property
5 x 18
5 x (6 x 3)
(5 x 6) x 3
30 x 3
90
· Why does this work?
· Why did you choose to factor 18 into 6 and 3?

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Template for the Responsive Listening Interview
Performance-Based Assessment #2
Due October 18 11:59 AM
Who did you interview?
How long did the interview last?
Write a paragraph describing how the interview went in general.
Responsive Listening
Responsive Listening 1
Timestamp from your recording.
Transcribe an interaction between you and the interviewee in

7. which you demonstrated responsive listening.
Why was this responsive listening?
How did this interaction support and/or extend the interviewee’s
thinking?
Responsive Listening 2
Timestamp from your recording.
Transcribe another interaction between you and the interviewee
in which you demonstrated responsive listening.
Why was this responsive listening?
How did this interaction support and/or extend the interviewee’s
thinking?
Responsive Listening 3
Timestamp from your recording.
Transcribe another interaction between you and the interviewee
in which you demonstrated responsive listening.

8. Why was this responsive listening?
How did this interaction support and/or extend the interviewee’s
thinking?
Observational or Directive Listening
In this part of the assignment, you need to provide three
examples, each example can be either observational or
directive. So, you might have 1 observational example and two
directive examples.
Observational or Directive Listening 1
Timestamp from your recording.
Transcribe an interaction between you and the interviewee in
which you demonstrated observational or directive listening.
What type of listening was this? Why?
If you could redo this interaction, would you do/say anything
differently? If so, what? If not, why not?
Observational or Directive Listening 2

9. Timestamp from your recording.
Transcribe another interaction between you and the interviewee
in which you demonstrated observational or directive listening.
What type of listening was this? Why?
If you could redo this interaction, would you do/say anything
differently? If so, what? If not, why not?
Observational or Directive Listening 3
Timestamp from your recording.
Transcribe another interaction between you and the interviewee
in which you demonstrated observational or directive listening.
What type of listening was this? Why?
If you could redo this interaction, would you do/say anything
differently? If so, what? If not, why not?

10. Reflection: Complete the
Reflection by answering the following questions.
· How did you feel during and after the interview?
· What are your strengths related to responsive listening?
· What areas do you want to keep working on?
· What challenges do you expect to face related to implementing
responsive listening when you are a teacher?
Self-Assessment:
· After you have completed your interview and the prompts
above, reread your work, and then assess yourself using the
rubric below.
· Show your rating by changing the shading in the section to
indicate a score of (initial, emerging, or proficient) that you
have found your work falls under. To do this in Microsoft
Word, click Table Design, then click Shading.
· Write an explanation for why you gave yourself that rating.
Course Objective # 2: I can engage in responsive listening to
support and extend student thinking.
Initial

11. Emerging
Proficient
A: Type of Listening
I can implement and identify 1 instance of responsive listening.
I can implement and identify 2 instances of responsive
listening.
I can implement and identify 3 instances of responsive
listening.
Explanation:
B: Identifying Types of Listening
I struggle to identify instances of directive, observational, and
responsive listening.
I can usually identify instances of directive, observational, and
responsive listening and I can usually give explanations for why
they are labeled as such.
I can accurately identify instances of directive, observational,
and responsive listening and I can give explanations for why
they are labeled as such.
Explanation:

12. C: Alternatives
I cannot suggest alternative responses to directive and
observational listening.
I can suggest alternative responses to directive and
observational listening.
I can suggest alternatives to directive and observational
listening that move towards responsive listening.
Explanation:
Directions: Responsive Listening Interview
Performance-Based Assessment #2
Due Tuesday, October 18th, 11:59 AM
Course Objective # 2: I can engage in responsive listening to
support and extend student thinking.
Goal:

13. The purpose of this assessment is for you to demonstrate your
ability to use responsive listening to develop a clear
understanding of student thinking and to push and extend their
thinking in new directions.
Overview:
You will interview a student, friend or family member to gain
an understanding about how they think about multiplication.
During the interview, you will practice using responsive
listening as much as possible. You will pose the mathematical
task to your interviewee, listen to their response, and use
responsive listening to develop a clear picture of what they
know.
Instructions
PART ONE: Preparing for the Interview
· Select a student, friend or family member to interview in
person.
· Find a way to
record your interview.

14. · Review the learning activities we have completed related to
responsive listening.
· PowerPoint Assignment Module 5,
· PowerPoint Assignment Module 6,
· Group Activity Module 6
PART TWO: The Interview
At the Beginning of the Interview:
· Give your interviewee a brief overview of what you have
learned in this class so far.
· Explain to your interviewee that the purpose of this interview
is for you to practice
listening to other people talk about math and to practice
how to respond to their thinking. Tell them that you will have
them work on a math problem, but you
will not be explaining to them how to do the problem.
Instead, you will be listening to what they think and asking
them questions to better understand their ideas. Remind them
that you will ask questions regardless of whether they are
answering correctly or not.
During the Interview:

15. · STEP ONE: Begin the interview by asking the interviewee to
solve 5 x 18. Encourage them to solve the problem in their
head.
· Ask them to explain their method.
· Use responsive listening, that is, listen to understand their
thinking, and then, actively work to support or extend their
thinking.
· At this point in the interview, it might be good to focus on
asking them why they did certain things (be specific). (i.e.
“why did you write this 4 here, what does it represent”)
· “What made you say …”
· “How do you know …”
· “Will it always work to do …”
· “Why did you …”
· STEP TWO: Continue by asking the interviewee to solve 5 x
18 in another way.
· As they share their thinking, listen responsively.
· First, you might want to ask for additional thinking about the
current method. Why they did certain things?
· “What made you say …”
· “How do you know …”
· “Will it always work to do …”

16. · “Why did you …”
· Second, you might want to ask them to compare and contrast
the first and second solutions. Try to explore how one idea they
shared relates to another idea they expressed. And, try to be
specific.
· “I see you multiplied 10 x 5 and got 50 in the second solution,
is this represented anywhere in the first solution?”
· “In the first solution you multiplied by 18, but you didn’t do
this in the second solution, why not?”
· STEP THREE: Repeat step two until the person has solved the
problem in as many different ways as possible. Remember that
you need to analyze the interview. If you only talk about two
solutions, you likely will not have enough data to complete the
assessment. Keep asking questions.
· If a student solves it one way and can’t think of any other
way:
· Ask if they can draw a picture that shows the answer.
· Ask if they can invent a new way to solve it.
· Show them a method that they haven’t used and ask if they can
figure out how it works and why.
After the interview:
· Collect the written work.
· If you conducted the interview via video conference, have

17. them take a picture and send it to you.
· Listen to the recording of the interview.
· Think about how the interview went and record examples of
directive, observational, and responsive listening.
PART THREE: Complete the Assignment
·
STEP ONE:
Identify Different Types of Listening
· Use the Template for Responsive Listening Interview
· Identify three examples of responsive listening from your
interview.
· Answer the questions that follow for each example.
· Identify three examples of either directive or observational
listening from your interview.
· Answer the questions that follow for each example.
·
STEP TWO: Complete the
Reflection by answering the following questions.
· How did you feel during and after the interview?
· What are your strengths related to responsive listening?

18. · What areas do you want to keep working on?
· What challenges do you expect to face related to implementing
responsive listening when you are a teacher?
·
STEP THREE:
Self-Assessment
· After you have completed your interview and the prompts
above, reread your work, and then assess yourself using the
rubric below.
· Show your rating by changing the shading in the section to
indicate a score of (initial, emerging, or proficient) that you
have found your work falls under. To do this in Microsoft
Word, click Table Design, then click Shading.
· Write an explanation for why you gave yourself that rating.
· Note: You do not need to turn in your recording of the
interview. Keep it in case you need to go back and revise your
work.
Student Work Example
Identifying Responsive Listening:

19. Below is an excerpt from a student’s assessment. Notice that
this student transcribes more than a single sentence. The back
and forth between the student and their interviewee provides
context that helps demonstrate that the student is listening
responsively. Had the student just wrote “You add zero? Can
you tell me more specifically what you mean?” it would not
have been clear that the interviewer was being responsive to the
interviewee’s ideas.
Student Work Example: First part of Self-Assessment
Course Objective # 2: I can engage in responsive listening to
support and extend student thinking.
Initial
Emerging
Proficient
A: Type of Listening
I can implement and identify one instance of responsive
listening.

20. I can implement and identify two instances of responsive
listening.
I can implement and identify three instances of responsive
listening.
Explanation: I was able to implement responsive listening
throughout the interview. I provided three examples to show
this. I believe each example was correctly identified as
responsive listening showing not only that I can use responsive
listening, but that I can identify it as well.
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