Eric and Mark did a workshop at the 2017 COABE Conference in Orlando called Mathematical Modeling: Questions from a Math Teachers’ Circle. A few weeks later at the NYC ABE Conference, Brian took the lead and together with Mark and Eric did a similar workshop called 3-Act Math Tasks: Let Students Build the Problem.
At the heart of both workshops was the Pyramid of Pennies, which was the first three-act math task we explored in CAMI back in May 2015.
- We started both sessions by asking participants to get into small groups and talk about what real-world math meant to them.
- Then we shared an answer that came out of that May meeting, before diving into the problem.
“Real-world math is the creative process – the creation of the problem is the math, rather than relying on what others have told you”
After we did the problem in 3-acts (the bulk of both workshops), we put another version of the problem up and asked participants how their experience would have been different if we’d simply given out a handout that said:
A pyramid is made out of layers of stacks of pennies. Each stack contains 13 pennies. The base layer is a square with 40 stacks on each side. The next layer has 39 stacks on each side. The top layer has 1 stack. How many pennies are in the pyramid?
Finally we shared a section from Mathematical Mindsets by Jo Boaler
According to Conrad Wolfram, working on mathematics has four stages:
- Posing a question.
- Going from the real world to a mathematical model.
- Performing a calculation.
- Going from the model back to the real world, to see if the original question was answered.
Students spend most of their time on step 3. What if we changed that?
The url link above will take you to a folder with all the materials for the workshops, including out presentation slides and facilitator notes.