“The happiest people I know are
dedicated to dealing with the most
difficult problems”
Rosabeth Moss Kanter in the Harvard Business Review
Turning ‘I don’t know’ into ‘Yes, I can’:
Supporting Productive Struggle
TLQP Workshop
Binghamton University, December 19, 2015
Dr. Rachel Bachman
“Effective teaching of mathematics consistently
provides students, individually and collectively,
with opportunities and support to engage in
productive struggle as they grapple with
mathematical ideas and relationships”
What does Productive
Struggle look like in
classrooms?
Beyond my ability right now
Productive Struggle
What I can do
now
EXAMPLE 1: Ali and Samy had an
equal amount of money each. After
Samy gave $15 to Ali, the ratio of Ali’s
money to Samy’s money was 7 : 5.
How much money did each boy have
at first?
Why encourage
students to
productively struggle?
Why productively struggle?
What prevents
productive struggle in
our classrooms?
Preventing Productive Struggle
Think: What prevents productive struggle
from happening in our math classrooms?
End
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
So how can we
support productive
struggle?
Supporting Productive Struggle
Think: How do you support productive
struggle in your class?
End
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Supporting Productive Struggle
Think: How do you support productive
struggle in your class?
5 minutes
Pair: Take turns sharing strategies you use
in your classes
End
Supporting Productive Struggle
Think: How do you support productive
struggle in your class?
Pair: Take turns sharing strategies you use
in your classes
Share: Report back on the interesting
ideas from your partner
Supporting Productive Struggle
 Set up classroom norms
 Normalize mistakes
 Write what you know
 Hurdle interviews
 Thinking Aloud in Pairs for Problem Solving (TAPPS)
 Pose Problems of Interest
Setting up Class Norms
Strategy #1
Cooking Lesson for Making chicken mole
1. Remove items from package
2. Place inside the microwave oven
3. Cook on high for 3 minutes*
*for a 950 watt microwave
4. Let stand 1 minute before serving
For those that didn’t know what chicken mole is…
What is chicken mole?
Name one ingredient in the dish besides chicken.
Did we do any of the things a chef would do when
preparing chicken mole?
Do you have a better appreciation for the process of
making chicken mole?
How long would you remember this exact procedure?
 8 ancho chiles
 1 cinnamon stick
 2 poblano chiles
 6 cloves of garlic, peeled
 ¼ cup lard
 1 onion, sliced
 ¼ cup whole almonds
 1 plantain, cut into chunks
 ¼ cup hazelnuts
 2 corn tortillas, toasted
 ¼ cup pecans
 4 cups of chicken broth
 ¼ cup sesame seeds
 ¼ cup Mexican chocolate
 ¼ cup raisins
 1 tablespoon sugar
 ½ teaspoon anise seeds
 Salt and black pepper
 ½ teaspoon cumin seeds
 Roasted, grilled or poached chicken
 ½ teaspoon peppercorns
 3 whole cloves
For the chile paste: Toast the ancho chiles by opening them and pressing them flat in a hot
skillet for a few seconds on each side. Soak the chiles in hot water until they are very soft,
about 30 minutes. Drain and pour into a blender with the roasted poblanos and chicken
broth. Pulse until pureed. Season with salt and set aside.
For the mole: Heat the lard in a large skillet over medium heat. Add the almonds, hazelnuts,
pecans, and sesame seeds and cook, stirring until lightly toasted, about 3 minutes. Remove
the nuts with a slotted spoon to a food processor or blender. Add the raisins to the same
skillet and stir for a minute as they puff. Put them in with the nuts. Add the anise seeds,
cumin seeds, peppercorns, cloves and cinnamon stick to the skillet and cook until fragrant,
about 1 minute. Transfer to the food processor. Add the garlic and onions to the skillet and
cook until browned, about 10 minutes. Remove to the food processor with the nuts and
raisins. Then, fry the plantains and add to the food processor with the tortillas. Add 1 cup of
chicken broth and blend to a smooth paste.
In a large skillet, heat some more lard over medium heat and pour in the mole. Add the
ancho chile paste, chocolate, sugar, and remaining chicken broth. Season with salt and
pepper and continue cooking on low heat about 1 hour. Serve the mole with roasted, grilled,
or poached chicken.
Toast
Remove
Press
Transfer
Soak
Fry
Drain
Blend
Pour
Puree
Season
Heat
Add
For those that didn’t know what chicken mole is…
What is chicken mole?
Name one ingredient in the dish besides chicken.
Did we do any of the things a chef would do when
preparing chicken mole?
Do you have a better appreciation for the process of
making chicken mole?
How long would you remember this exact procedure?
Let’s compare
Microwavable Math
Real Math
 Step-by-step instructions exist
 Active thinking is needed to find answer
 Answer is the focus
 Process is the focus
 Mistakes are a symptom of something
wrong
 Mistakes are normal
 Everything is solvable in a few minutes
 Sometimes answers take awhile to find
 Outcome is the same every time
 Possible to find creative, more efficient
ways of solving
 Done independently
 Collaboration is important
 Involves mostly numbers and symbols
 Involves pictures, words, debates
Normalizing Mistakes
Strategy #2
Dealing with mistakes…
 Mathematical Mindsets by Jo Boaler
“When I told teachers that mistakes cause your brain
to spark and grow, they have said, ‘Surely this
happens only if students correct their mistake and go
on to solve the problem.’ But this is not the case…the
brain sparks and grows when we made a mistake,
even if we are not aware of it, because it is a time of
struggle; the brain is challenged, and this is the time
when the brain grows the most” (p. 11-12)
My Favorite No…
https://www.teachingchannel.org/videos/class-warm-up-routine
Setting class norms and normalizing
mistakes
EXAMPLE 2: The Chocolate Milk Problem
Write What You Know
Strategy #3
Strategy #3 – Write what you know
 EXAMPLE 3: If the lengths of every side of the
rectangular prism are doubled, how many times
larger will the volume of the new box be?
Strategy #3 – Write what you know
EXAMPLE 4: Determine, by eliminating
possibilities, the number multiplied by itself
three times that gives 68,921.
Hurdle Interviews
Strategy #4
Strategy #4 – Hurdle interviews
 EXAMPLE 5: Decide which of the following is true and be prepared to
defend your answer.
 Figure 1 has the most area not black
 Figure 2 has the most area not black
 Figure 3 has the most area not black
 All three figures have the same amount of area not black
Think Aloud in Pairs for
Problem Solving
Strategy #5
Strategy #5 – Think Aloud in Pairs for
Problem Solving (TAPPS)
The Problem Solver
The Listener
Strategy #5 – Think Aloud in Pairs for
Problem Solving (TAPPS)
EXAMPLE 6: A dart board allows players to score
either 5 or 7 points each time they throw a dart.
What is the largest score that cannot be
5 minutes
earned in this game?
End
Strategy #5 – Think Aloud in Pairs for
Problem Solving (TAPPS)
EXAMPLE 7: You have $1000 in one-dollar bills.
You have ten envelopes. How can you
distribute the bills so that for any purchase for
any dollar amount of money, some
combination of the envelopes will add up to
the purchase price? (You may use an
envelope only once.)
5 minutes
End
Pose Problems of
Interest
Strategy #6
Pose Problems of Interest
 https://www.ted.com/talks/dan_meyer_math_curriculum_makeov
er?language=en
 http://threeacts.mrmeyer.com/watertank/
What information do you need to
solve?
Pose Problems of Interest
 EXAMPLE 9: My brother is building fence for our cows for the
summer. He has a piece of pasture that basically looks like an
isosceles right triangle. He wants to make six equal size lots that cut
across the triangle from one leg to the hypotenuse. How should be
build the lots?