I am about a month into the school year and, consequently, a month into my action research project. Very briefly, my action research project involves looking at how a classroom that is centered in mathematical habits of mind can support students in realizing (or regaining) a sense of agency/authority. Early on the year, my classes worked on a couple different tasks ("Checkerboard Squares" and "Consecutive Sums"). Along the way, I asked them to be particularly meta-cognitive about the mental actions that were helpful in making sense of each task. They ended up developing this list of the "habits of a mathematician:"

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)

We posted these habits in the room and refer to them often. Last week, I was hoping to get some preliminary/baseline data about how students perceived themselves as mathematicians. I asked them simply, "Do you feel like you have strengths as a mathematician? If yes, what are they? If not, why do you feel this way?" I was expecting many students to respond "no." The results were pretty interesting:

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!


10/22/2012 1:00pm

Hi Bryan,
Thanks for sharing this action research project and the results along the way. I think it's really interesting data that your students are already internalizing habits of mathematicians and seeing them as strengths -- and even extrapolating them to other places.

I've noticed at the Math Forum when I get to read student work that's submitted to our PoWs (I think IMP may have beat us to the phrase by a year or two, but it's close!) that often students from the same class will have some of the same language around their problem-solving process (they refer to "ah-ha" moments or name their strategy or talk about how they made a plan or they share what they noticed and wondered about the problem). They start using that common language in September and October -- it makes me think students pick up on how we hope they will think even more quickly than they pick up on what we want them to do.

I wonder how recognizing that can help us tailor our teaching so that students are getting clear signals about what mathematical thinking is, and get to do it and recognize it a lot!


PS -- I almost forgot to ask! Are the students' blogs public? I would love to read more of their thinking about thinking!


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