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AMA online

Productive Struggle

Getting our students to do more

For further information on PLD or MoE funding and applications contact

Sonja He-Steen at she@cognitioneducation.com

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Tūtawa mai i runga

Tūtawa mai i raro

Tūtawa mai i roto

Tūtawa mai i waho

Kia tau ai te mauri tū,

Te mauri ora ki te katoa

Hāumi e, hui e, tāiki e

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Are any of your students…

The one and done

– one answer, question is done, move on.

The sit back and wait

– waits for others to answer or to think for them.

The dominators

– dominates the discussion during turn and talks.

How can we get our ākonga to engage equitably in productive struggle at maths time?

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Consider ...

... what's something that you learned to do but you weren’t very good at initially?

How did you improve?

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So, what is productive struggle?

Consider what this might look like in your classroom.

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Students who hide, �hide because...

Doesn’t identify as a maths person

Remove the challenge because we don’t want them to hate maths

Over simplified task

Doesn’t engage

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Develop strong maths norms

Everyone is a mathmatician
Mistakes are valuable and we learn from them
Respectful discourse
Equitable Participation
No one left behind

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Let’s engage in some productive struggle

Consider:

In this lesson

How does this task enable productive struggle?
What is the role of the teacher?
What is the role of the student?

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Warm up: What do you notice? Wonder?

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Break out rooms

https://jamboard.google.com/d/1fxzR0OkZbpDpVkH_moMdMFArjoO1UmX3_LZ0XekQt6I/edit?usp=sharing

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The Reveal

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Thinking about productive struggle

Consider:

In this lesson

How did this task enable productive struggle?
What is the role of the teacher?
What is the role of the student?

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Talk Time

70

30

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Why 70:30?

More opportunities for feedback
It limits the amount of teaching teachers do
It promotes fluency
A more satisfied student (my teacher talks to much!)
Creates a student centered classroom

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What actions can we take?

I don’t get it

I don’t know what to do

I know the answer, I just don’t know how to explain it

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The Rain Barrel Problem�Suppose we have a 48 gallon rain barrel containing 24 gallons of water and a 5 gallon water jug containing 3 gallons of water. Which container is said to be fuller? ��If we drain a gallon of water from each container, does this change your answer about which container is fuller? Explain. ��Source: McCabe, Warshauer, and Warshauer (2009)

Sandy: I don’t know what to do.

Teacher: OK. How can we compare the

amounts in the barrel to the jug?

Sandy: I’m not sure.

Teacher: Well, you have part and the

whole for each, don’t you?

Sandy: Yeah.

Teacher: What kind of numbers can

we make with part and a whole?

Sandy: Fractions?

Teacher: Bingo! So, what do your

fractions look like?

Sandy: Um . . . 24/48 and 3/5 . . .

but. . . .

Teacher: Good. Now what do we do

with fractions when they have

different denominators?

Sandy: Get common denominators?

Oh, OK. I think I can do that.

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Teacher actions

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The Rain Barrel Problem�Suppose we have a 48 gallon rain barrel containing 24 gallons of water and a 5 gallon water jug containing 3 gallons of water. Which container is said to be fuller? ��If we drain a gallon of water from each container, does this change your answer about which container is fuller? Explain. ��Source: McCabe, Warshauer, and Warshauer (2009)

Sandy: I don’t know what to do.

Teacher: OK. How can we compare the

amounts in the barrel to the jug?

Sandy: I’m not sure.

Teacher: Well, you have part and the

whole for each, don’t you?

Sandy: Yeah.

Teacher: What kind of numbers can

we make with part and a whole?

Sandy: Fractions?

Teacher: Bingo! So, what do your

fractions look like?

Sandy: Um . . . 24/48 and 3/5 . . .

but. . . .

Teacher: Good. Now what do we do

with fractions when they have

different denominators?

Sandy: Get common denominators?

Oh, OK. I think I can do that.

Can you show me how this might look as a picture

What can we do to compare the two barrels?

What do you notice about the problem now?

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Teacher Actions

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Practice your Switzerland face

Be neutral.

Be interested.

“Interesting.” “ Tell me more.” “Why do you think that?”

“Hold onto that thought, let’s come back to that.”

Do they know the answer or are they reading my face?

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The Rain Barrel Problem�Suppose we have a 48 gallon rain barrel containing 24 gallons of water and a 5 gallon water jug containing 3 gallons of water. Which container is said to be fuller? ��If we drain a gallon of water from each container, does this change your answer about which container is fuller? Explain. ��Source: McCabe, Warshauer, and Warshauer (2009)

Drew: 2/5 . . . but isn’t that fuller

now? [Looking up at the teacher

questioningly]

Teacher: Hmmmm, why would that

one be fuller now, do you think?

Drew: Because the other one isn’t a

half.

Teacher: OK, it’s not half. That means

it’s not fuller?

Drew: It’s more than 0.5 now.

Teacher: Tell me that one more time.

What do you think?

Tell me more

Why do you think that?

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Teacher Actions

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The Rain Barrel Problem�Suppose we have a 48 gallon rain barrel containing 24 gallons of water and a 5 gallon water jug containing 3 gallons of water. Which container is said to be fuller? ��If we drain a gallon of water from each container, does this change your answer about which container is fuller? Explain. ��Source: McCabe, Warshauer, and Warshauer (2009)

Drew: I said it’s more than 0.5 now.

Because this one is no longer 0.5 because

[squints and thinks]

you have to subtract; you have taken away a gallon.

Teacher: OK.

Drew: And this one is no longer 0.6

because you have taken a gallon.

And this one would no longer

be a half. . . . I know what I’m saying.

Teacher: Be patient [gives Drew time

and listens intently].

Drew: [Prepares to compute long

division of his fractions that he has

on his paper]

Teacher: Get your percents and call me

back over. Keep working.

Spray and walk away

Gives time

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Teacher Actions

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"Taking the pencil out of their hand"
Breaking down the task too much
Guiding students step by step
Lowering the cognitive demand of the task
Not having the time or opportunity to make sense of the mathematics

What actions shut down productive struggle?

We perceive frustration or lack of success as our own failing.

We rescue.

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Patai?

Start

Stop

Consider

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Kia wātea ao te ara

Kia turuki whakataha ai

Hāumi e, hui e, tāiki e