Look for Patterns and Regularity
Experiment and Play
Be Confident and Persistent
Conjecture and Test
Solve a Simpler/Related Problem
Be Systematic and Organized
Justify and Support
Create a Rule (Generalize)
Out of the 68 students polled:
54 replied yes
10 replied no
4 replied yes and no
BUT, of the 54 students that said yes, HALF of them cited one or more of the habits as their mathematical strengths and they used the exact verbiage of that/those particular habit(s). These habits are new to them this year, so I was surprised to see that so many of them are already internalizing them as part of their mathematical identity. I'm optimistic to see where this leads because I plan on having all students do a "snapshot of a mathematician" soon where they identify personal strengths and weaknesses based around these habits.
Each student has a blog where they post weekly about one piece of work that they are proud of and how it is representative of one (or more) of these habits. There have also been some interesting things happening on their blogs:
One student wrote about how she finds herself "experimenting and playing" in singing:
"This is an important step for any singer, weather they know they are doing it or not. The more a tune is played with, the more original it will be, even if it has been sung 1,000 times before. A song can be sped up, slowed down, the pitch can be changed, the melody can be altered...there are endless possibilities, but progress can't be made without trying new ideas, even if they aren't all golden."
One student wrote about how she used "systematic organization" in rearranging her bookshelf:
"When I was organizing my bookshelves, I needed to find a system that would work for the books."
One student wrote about how he "looked for patterns and regularities" in the stock market (not an assignment):
"The task at hand was to search for trends and patterns within the graphs of the DOW Jones industrial that I had made. Essentially I was looking for ways to predict stock market behavior and how to ensure some safe investment."
One student took a task about group norms that we did and turned it into a task about systematic list making by "experimenting and playing:"
"The interesting part came when my group member tried to pair them into couples. We had an interesting discussion as to whether monogamy was possible in a closed environment such as this one. I didn't think so, and my group member insisted it was. So, I attempted to create a genetic graph."
The really interesting thing to me about all of this is that students are taking mathematical ways of thinking and recognizing these same mental actions in other parts of their daily lives. I am excited to see where this leads!