Update: Check out these related videos —> Numberphile | Doodling in Math Class | Wrong Turn on the Dragon
It was a beautiful spring day when Usha and Sophie represented CAMI at the 40th anniversary of the New York City Adult Basic Education Conference. Sophie gave a little history of CAMI…
- CAMI was founded in November 2014
- There have been 61 CAMI meetings
- 104 teachers have attended at least 1 meeting
- 15 different teachers have run a meeting
- Average attendance at a meeting is 7.8 teachers
… and introduced the group to our goals and norms.
Mistakes are Valuable - Mistakes grow your brain! It is good to struggle and make mistakes.
Mathematics involves creativity, connections, and making sense - Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss and critique.
Questions are really important - Always ask questions, always respond to questions. Ask yourself: does that make sense? And why does that make sense?
Respect everyone’s views. Remember that you have something to learn from everyone else. Remember that everyone works at a different pace. Take some time to hear another person’s take on a problem.
Teach only if you have to. You may feel tempted to teach others in your group. Fight it! We don’t mean you should ignore people, but don’t step on someone else’s aha moment.
Stop and smell the roses. Getting the correct answer to a question is not a be-all and end-all in this course. How does the question relate to others you’ve encountered? How do others think about this question?
Usha gave an introduction to the Julia Robinson Mathematics Festival, which co-sponsored this workshop:
A Julia Robinson Mathematics Festival offers students thought-provoking mathematics in a social and cooperative atmosphere. Students choose problems to work on for as long as they wish while interacting with other students and a facilitator. They can address any level of student from those struggling to those soaring.
JRMF is seeking facilitators for their mathematics festivals.
CONTACT: jrmfny@gmail.com
And then we jumped into the exploration for the day… folding paper.
Usha took a long strip of paper and showed us how to make the first fold, right hand over to the left hand, and make a crease.
The first fold is right over left, like this:
Then we open the paper to see what it looks like:
Usha called this crease a “valley” because it looks like a V. She then told us to fold the paper back right over left and fold it a second time, right over left.
We then opened up the paper to find the following folds:
We called this pattern: valley, valley and mountain. Notice that the last crease looks different than the first two. We might write this pattern as V, V, A.
Then Usha led us through folding the paper back together and then make one more fold from right to left.
Usha asked us to predict what the creases would look like before we opened the paper.
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Are you surprised at all? We called this pattern: valley, valley, mountain, valley, valley, mountain, mountain or V, V, A, V, V, A, A.
At this point, Usha asked us to brainstorm questions with a partner. Here are some of the questions we asked:
- What is the pattern of folding?
- How many creases (mountains and valleys) are there after each fold?
- How many spaces (or segments) are there in between the creases?
- How can you predict the pattern of valleys and mountains before folding the paper?
- What is the most times you can fold the paper?
Usha then released us to explore whichever question was intriguing to us. In pairs, we each worked on one of these questions or other questions that occurred to us as we were working.
