The Productive Struggle.
"Struggling" is a vital part of learning something new, similar to riding a bike for the first time.
We try and try different ideas, fail and fail again, but learn through the process.
Without a productive "struggle," something easily learned is as easily forgotten.
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Challenges students to reach a HIGHER LEVEL of cognitive thinking.
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Students enjoy mathematics for the challenges it poses, not for it's simplicity.
How does it apply to this problem?
1) Understand a trapezoid can be constructed with triangles.
Has learned how to apply the trapezoid formula.
2) The height is unknown. Struggle!
Assign a few problems like these to get the gears turning!
3) Has prior knowledge of finding the area of a triangle.
4) A problem done in 3 minutes, is forgotten in 3 minutes.
Foster patience and the enjoyment of problem-solving!
5) Make mistakes and have fun :)
