2. Team Work
Magdalene Lampert
Megan Franke
Hala Ghousseini
Heather Beasley
Angela Turrou
Adrian Cunard
Allison Hintz
Megan Kelley-Petersen
Helen Thouless
Lynsey Gibbons
Bryan Street
Teresa Lind
Laura Mah
Anita Lenges
Becca Lewis
Liz Hartmann
Leslie Nielsen
Emily Shahan
Elizabeth Dutro
Morva McDonald
Core Practices Consortium
Ryan Reilly
Jessica Calabrese
Staff at Lakeridge Elementary
School
ECML Colleagues
3. Children have amazing ways of
solving problems. Their often
surprising responses make
teaching fascinating work
Knowing what to do with students’
ideas and teaching children to
meaningfully participate in discussion
can be invigorating and challenging
4. Flow
¤ Principles that support discussion
¤ Different goals, different discussion
¤ Planning and facilitating open and targeted talk
¤ How to learn together to lead productive discussions
5. Principles that support discussion
¤ Students need to be supported to know what to share
and how so their ideas are heard and useful to others
¤ Teachers need to orient students to one another and the
mathematical ideas so that every member of the class is
involved in achieving the mathematical goal
¤ Teachers must communicate that all children are
sensemakers, knowledge generator, invested in school
and wanting to succeed. Our curiosity communicates to
children that their contributions are valued.
6. Intentionally orchestrating discussion
to meet a mathematical goal
¤ Goal acts as your compass
¤ Helps decide what to listen for, which ideas to pursue,
and which to highlight
¤ Distinguishing two types of discussions
¤ Open Strategy Sharing
¤ Targeted Sharing
7. Open Strategy Share
Elicit many different ideas to see the range of possibilities
Generate many different
ideas
Building students’ repertoire
of strategies
Students listen for and
contribute in different ways
to solve the same problem
Move across a
broad terrain of
concepts,
procedures,
representations,
explanations
“Can you explain how you solved?” “Did anybody solve in a different way?”
8. Ms. Lind’s 4th grade classroom
25 X 18
As we read thru this transcript on the following
slides… think about what makes this an open
strategy share?
Open Strategy Share
9. Ms. Lind: OK, Faduma, tell us about what you wrote as you figured
out this solution. I want everyone else to think about whether you
are understanding what Faduma did and if you used a similar or
different strategy.
Faduma: Since I can multiply numbers by 10, I broke up the 18 to a
10 and a 8. I multiplied 25 x 10 and 25 x 8. I got 250 + 200 which is
450.
Ms. Lind: Thank you. I’ve written on the board what I heard Faduma
say. And you’re showing me that many of you did the same
thing. Who can add on to help us explain why we would split the
18 the way Faduma did?
Jordan: Well, it’s like Faduma said, multiplying by 10 can be easier
to do. So since one way of thinking about 25 x 18 is that you
have 25, 18 times, you can first do 25 ten times and then you
have 8 more 25s.
Ms. Lind: Does anyone have any questions for Faduma?
10. Marcus: I do. I kind of solved it the same way but I got a different
answer. Eighteen is close to 20 so I did 20 x 25 to get 500 but then I
subtracted 2 to get to 498. I’m not sure why our answers are different.
Ms. Lind: So you’re really trying to make sense of Faduma’s strategy
through your own way. I’m writing your question up here but before
we take up your question, let’s see if we can put one more strategy
up here and maybe that will help us think about what is going on
here.
Celia: I used what I know about quarters. 4 quarters make a $1.00. So 16
makes 400 and then two more makes 450.
Ms. Lind: What do you think Celia means when she says that quarters
helped her solve the problem? And if you’re not sure, you can ask
her to repeat what she said.
(several students repeat Celia’s idea)
Ms. Lind: We seem to have three different strategies and two different
answers. Could you turn and talk to your elbow partner about which
strategies convince you and what questions you have?
11. Open Strategy Share
Select the problem
Anticipate how students will solve
Pose the problem and monitor students at work
Elicit and discuss a range of solutions
Solution 1
Solution 2 Solution 3
Solution 4
16. Targeted Sharing Discussion Structures
¤ Compare and Connect: to compare similarities and differences
among strategies
¤ Why? Let’s Justify: to generate justifications for why a particular
strategy works
¤ What’s Best and Why?: to determine a best (most efficient) solution
in particular circumstances
¤ Define and Clarify: to define and discuss appropriate ways to use
mathematical models, tools, vocabulary, or notation
¤ Troubleshoot and Revise: to reason through which strategy
produces a correct solution or figuring out where a strategy went
awry
Kazemi & Hintz (2014) Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.
Portland, ME: Stenhouse Publishers.
17. Targeted discussion
Ms. Lind’s 4th grade classroom
Focus on the solution of breaking
apart into tens and ones and justify
with the array – Why? Let’s Justify
OSS 25 X 18
Focus on the solution of rounding one
number and adjusting the product -
Troubleshoot and Revise
18. ¤ How are the targeted discussions different from open strategy
share discussion?
¤ What goal does the teacher seem to be working toward?
19. Why? Let’s Justify
Ms. Lind: Yesterday as we were listening to people solve 25 x 18, I
realized it has been awhile since we worked with arrays. I thought it
would be useful to explain what is happening when we break apart
numbers to make a problem easier and how to make sure we’ve
accounted for 18 groups of 25.
Mark up the array in your journal to show how it matches this numerical
strategy
20. Ms. Lind: Celeste has an idea about the array to offer us, please look
up to the screen at this drawing of the array for 25 x 18. I want you to
see if you can make sense of how she divided up the array.
Celeste: I drew Faduma’s idea. She kept the 25 whole and she broke
the 18 into 10 and 8. So 25 X 18 is the same as 25 X 10 and 25 X 8.
Ms. Lind: Who can use Celeste’s drawing to justify why Faduma’s
strategy works?
21. Troubleshoot & Revise
Marcus: I did 20 x 25 to get 500 and then I subtracted 2 to get 498. I
kind of think it should work because 20 is just two more than 18.
But I’m not sure why I’m not getting the same answer as Faduma.
I think I should be.
Ms. Lind: Marcus had a great way of beginning this problem. By
changing the 18 to 20, he started by making the problem easier
for himself. It might help us to put these numbers into a story. Let’s
imagine Marcus had 25 packs of colored pencils with 18 pencils in
each pack.
Andre: Oh I see, when Marcus changed the numbers to 20 x 25, it
made it like there were 25 packs of pencils with 20 pencils in each
pack. But, we need to have 18 pencils in each pack, not 20!
Ms. Lind: Ok, let’s draw the 25 packs of pencils with 20 pencils in
each pack.
22. Ms. Lind: So, what needs to be removed from each pack to go
back to having 18 pencils in a pack instead of 20?
Ms. Lind: Ok we have worked together to figure out why Marcus’s
answer was different. Who can say again why his answer was
different?
23. Targeted Discussion
Focal
Strategy
What mathematical strategy or idea are we targeting in our discussion?
What is the explanation I want the students to come up with? OR what is the
mathematical confusion we want to bring understanding to?
27. Principles of learning
¤ Teaching is highly complex and relational. It requires us to
communicate to our students that school is a place where
they are known, where they can invest themselves, and
where they belong.
¤ Teaching is intellectual work and requires specialized
knowledge
¤ Teaching is something that can be learned
¤ Learning to do something requires repeated opportunities to
practice
¤ There is value in making teaching public
28. Supporting teachers and students in
your setting
As you think about your own setting
¤ How are you thinking about planning intentionally
¤ Identify a goal
¤ Use planning templates to imagine the orchestration of the talk
¤ When are different types of discussions useful to students?
¤ Open strategy share
¤ Targeted share
29. Collaborative classroom visits
¤ A group of people can get together, create or use a
common plan and think about something they’d like to
try out or learn as a few volunteers initiate the lesson.
31. Visiting classrooms together
¤ When we choose and plan together, “our lesson,” we get to try it
out with our students together.
¤ Often there are insights we gain by listening to children. Or we
have questions or new ideas about questions to ask, or things to
try. During the lesson, we can call “teacher time outs” in order to
pause instruction briefly and chat with each other about a next
step to take, a question to ask, or a way to steer the instruction.
¤ We work together through a learning cycle
32. What are teacher time outs?
Teacher Time Out (TTO) is enacted when
educators co-engineer lessons with students
present, pausing regularly within the lesson to think
aloud, share decision making with one another
and determine where to steer instruction.
Educators signal that they have a question to ask
one another (e.g., “Should I ask x question next or
y?” “Is this a good time to try to represent this
students’ ideas?”) or a question they want to ask
the students (e.g., “Wait, let’s ask students about
…”) or to narrate their instructional decision
making (e.g., “I think I’d like to pursue this
mathematical idea next with students”). We have
found these exchanges open up rich ground for
making sense of practice together in the moment.
33. ¤ Pause
the
lesson
to:
¤ make
sense
of
students’
thinking
¤ make
sugges4ons
to
the
group
for
considera4on
¤ narrate
instruc4onal
decision-‐making
¤ ask
for
help
for
next
move
¤ Jump
in
to
ask
students
a
ques4on
¤ Take
the
pen
¤ Model
the
mathema4cal
idea
being
discussed
34. A starting list of norms for working together
¤ Be willing to take risks with new ideas
¤ Listen actively and generously
¤ Build on others ideas and invite others to participate
¤ Give each other time to think & process ideas
¤ It’s okay to share ideas in progress and revise your thinking
¤ Use specific language to describe what we see students doing,
rather than labeling students. Avoid labels such as “low” and “high.”
¤ Treat the lessons and students that we work on together as “our
lessons” and “our students”
¤ Cultivate joy for teaching & for working together
35. An example of a teacher time out
¤ It’s helpful if the teacher who
volunteers to take the lead
initiates the first teacher time
outs. These are not to be
read as corrections or
evaluations. Remember, we
have designed “our lesson.”
Instead, these time outs are
opportunities to put our
heads together as we try to
bring to life the lesson we
planned.
38. Context: Fair Sharing Problem
3 chocolate bars shared equally
among 4 people
What equations would students
right to connect to these
situation?
Will they write equations that
match the original problem? Or
their solution?
39.
40. 40
Teacher Education by Design: Tools for Learning
Tools for teachers & teacher educations: tedd.org
