Thursday-Saturday morning sessions

TMC15

Claremont, CA

Presenters: Alex Overwijk and Mary Bourassa

Present picture of tree: write all the questions you have about this tree

Groups of three share questions and pick their best three; write each on separate papers with a reason why it's theirs best; rotate to read other groups and vote on their best and why; groups return and read feedback, then write their overall best question on the board and why they chose that.

Each group makes a poster of the criteria that makes a good question. Then groups do a gallery walk of the posters and as a class we decide what the criteria is for a good question.

Criteria for Good Questions

-generates discussion

-invokes curiosity

- unanticipated layers, extends, drives further questions

-element of surprise, a "wow" moment

-simply stated, concise wording

-low entry, accessible

-not straightforward calculation

-multiple perspectives

-gives choice to the person asking questions

-offers multiple pathways

-has closure

-does not feel contrived

This activity builds to the summative district assessment which gives students pictures where they have to asks questions and then answers them. Students have to ask quality questions in order to show the math they've learned.

Don't be afraid to revisits activities to see growth or extend to new content.

Co-create criteria for good questions, communication, and problem solving.

Alex unloads the course over the first six weeks by doing an activity that introduce the big ideas of the course. Direct instruction as needed. Some activities are designed toward specific skills.

Criteria for Good Math Activities

-low ceiling, high entry

-authentic questions

-evokes curiosity or questions,

-students do the heavy lifting

-challenging

-promotes discussion

Classes are semester class of 75 minutes = full year

26 Squares Activity introduce linear relations, quadratic relations, triangle inequality theorem, four families of Pythagorean triples, Pythagorean theorem "sum of squares", similar triangles, right triangle trig,

Interleaving has better results even though teachers and students feel that it's messy and doesn't work and they prefer blocking.

Ebbinghaus Forgetting Curve shows that forgetting and relearning material four times has the best retention.

Read 20 words and have students write as many as they can remember. Graph results in Desmos and do a quadratic regression (serial position curve). Desmos uses ~ in place of = to do regressions. What questions would students ask?

"What would flip this curve upside down? Why is the a-value so small? Would you expect a positive or negative b-value? What does the y-intercept represent? If we did it again, would the r-value be similar? Would students graph of the same activity resemble ours? What does the model say compared to what actually happened?"

We repeated the experiment but at the end Alex shouted "Oh no, I messed it up. I'm sorry, go ahead and write." That burned our short term memory and we shared strategies to remember so our results looked totally different than the first time.

If you're not ready to fully give up units and do activity based teaching you can still incorporate activities into your units.

bit.ly/MTBoSbank A searchable database of activities sorted by grade level and topic. Share your activity by submitting it at bit.ly/MTBoSactivity

And sometimes we just watch Alex, the circle drawing champion of the world, draw a perfect circle.

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