Productive Struggle in Math
Prepares Students for Success
Schema
Jorge and Alicia both have containers.
They use markers to mark tenths on their containers and fill each of them to seven-tenths full with orange juice.
How can Jorge have more orange juice than Alicia?
Adapted from Q40 of 40 from my daughter's fractions unit final test
What is wrong with this question?
How do we teach?
How do we learn?
STUDENT
DISCOURSE
bit.ly/PatternMachine
Creative
DISEQUILIBRIUM
Reasoning
ORIGINAL THINKING
Rank these questions in order of difficulty for students
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B
Rank these questions in order of difficulty for an AI
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B
A
Rank these questions in order of difficulty for an AI
A
B
Characteristics of questions that drive productive struggle
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No obvious solution path
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Maybe multiple solutions
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Possible very visual
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Low floor but high ceiling
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Invites "doing"
"Why can't we just teach math the way I learned it?"
The volume of work often necessitates computers who can perform the routine machine operations with great speed, but who need not have much logical insight into what the results should be...
Memo: "Computing Group Organizations and Practices at NACA" April 24th 1942
The old way of teaching math was to make you do it like a machine...
The new way is to understand it so you can build the machines!
To ensure that all students are mathematically equipped to solve the world's most challenging problems.
OUR MISSION:
