This prompt really threw me. I didn’t want to say something that didn’t ring my own bell. I used to have a philosophy toward lighting a fire within students, especially for the battered world of math. I wanted to have students of all ages look at math and say something else besides, “Yeah, that’s really not my thing.”
I needed something more specific than this. It’s hard for me to define my own place in making the world a better place so I had a conversation with my wife.
“What is it that I do. I know I can rock the classroom. I know I can help other teachers. I feel comfortable with tech and current trends… but so does everyone else I associate with in the #MTBoS.”
“You see things differently than others. People don’t think like you do. You think in pictures. You see connections others wouldn’t naturally see”
This got me thinking…in pictures.
First I saw something like this:
I feel like people often find themselves on one side or the other of this bridge. I’m one of those weird ones that hangs out all over the place. I started putting myself into different places within the picture, with wide and narrow fields of view.
The near sided people see a clear local area, but can’t always see another perspective that’s further away. As long as the far side is ignored, we might as well call it a clear, sunny day. This is almost like a naive clarity.
The far sided people are deep in the fog, and have an even more limited view of things, let alone anything off in the distance. The whole world seems foggy for all they know. Foggy visions may actually be the comfort, with too much clarity causing more of an overwhelming experience.
My wife alluded to how I see things from multiple angles, and I’m often looking for the connecting structures between different sides. I attribute most of this skill to growing up in a family with unique personalities, each with a separate style of communication.
When I look at this bridge I don’t usually see the fog, but more often I project what’s beneath the layers of fog. When I think about the world and all its different people, with all the different perspectives, I have to remind myself to keep looking for such underlying structure.
What does this look like?
In the classroom this could be one student not seeing how another understood a concept differently (or how another student doesn’t understand something that seems so clear to them). This was my strength in the classroom; making connections between the students toward perspective(s) that we could share. In leading small group PLCs within the department I helped multiple voices find their place while still maintaining a common vision that puts the students first.
Now that I’m working with teachers across the district as a TOSA, and interacting with more and more people online through blogs and twitter, these connections are growing like fractals.
This idea of making connections for a wider interconnected view has been my vision for transformulas.org for visual understandings in math. Now I want to add that as a part of the vision for this site too.
As I interact with more people and more perspectives, I want to think about making connections. I want to help everyone see the interconnected structures through the fog.
Cue the cliche/abstract conclusion:
A better world is one where we can appreciate one another’s perspectives, find common structures, and learn more in the process of connections. I want to make that happen.
“Why?” asked a student on some day in that one class. The teacher replied, “Because.” Often this conversation goes on without even a word spoken aloud. Teachers develop routines in the classroom, and students learn to follow them. The cliche at home of “Do as I say, not as I do,” doesn’t always fit into the classroom structure of I do, we do, you do (which may not be the best method either). It might have transformed into more of a modeling-focused perspective of “Do as I do [, not as I say].” Words in the classroom can get confusing, leading many teachers to struggle using proper language with students and instead depending on visual aids and demonstrations. These conversations can get even more complicated when the students jump in.
Students are true artists when it comes to words and interpreting directions. They are the best peer-editing service, often exposing any fault or loophole left open in an activity. A skilled teacher can anticipate these attempts for learners to go off script and plan accordingly. An even more skilled teacher can say less with more, only giving a few cleverly designed guidelines that allow students to explore and still arrive at some type of expected outcome. For example, an assignment may have required students to write 1-2 page research paper on the topic of proportional relationships and its applications in scaling up or expanding a business. This guideline is specific but has too many holes. Through various interpretations of format, the students can complete the task without demonstrating any understanding. Some think that more detail in the directions is the remedy for this situation. I’m on the other side, preferring to give directions that would say something like, “In enough words and/or pictures, show me how proportional reasoning can help expand a business.”
Many view math as an objective and direct subject, being so reasonable and having one answer (or at least a best answer). Some also say that one method is the best method and should be the only one that any true mathematician should use. There is a strong movement to have a more open middle lead by dynamic educators such as Dan Meyer. Math still has structure, and such structure should be highlighted. I think it’s just foolish of us to attempt to summarize that structure into discrete, specific statements and expect the statements to transfer the understanding directly and objectively. Math is just as much abstract as it is concrete.
This entire preface is to address one major issue with the most common prompt given in a math activity: “Solve it.” First of all, we might even need clarification on the it that needs to be solved. More importantly what does it mean (in the context of a math activity) to solve. I ask this question to my students every year, sometimes multiple times a year, and their most common responses often include:
- work it out
- break it down
- simplify it
- find the solution
- or everyone’s favorite Nike slogan (yeah, that one you’re thinking of right now)
- and sometimes an unrelated word like sold