In this episode, Zac talks with José Vilson about how he shapes his practice in the math classroom, why he hates “wrong answers,” and how education became his life. You can find José at www.thejosevilson.com.
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Pessimist: One who, when he has the choice of two evils, chooses both.
– Oscar Wilde
Part of the beauty of the program of study on which I have embarked is its lack of requirements. Though there are some sorts of courses I need to take to graduate from my particular program, I’ve much latitude in deciding exactly what that looks like. This semester, I’ve chosen to fulfill four of the five requirements.
The idea was to open the spring up to cross-registering courses in the Kennedy School or Harvard’s Business School or School of Public Health.
As I registered at the top of the semester, the freedom of choice I told myself I’d experience in the second half of my time here drove a good deal of the selections I made.
With a certain degree of surprise, my statistics course continues to be the course in which I most feel myself and my understanding of my capabilities growing.
It is also the course in which I know I’m making the most mistakes. I simply don’t know a lot of what we’re learning about. As such, I tend to misuse the language of statistics. It’s like someone who’s fluent in Spanish visiting Paris and recognizing just enough of what’s being said to make the inability to communicate perfectly frustrating.
As I sat in the library tonight compiling a report that referenced t-tests and chi square tests, friends and fellow classrmates happened by. They noticed the sprawl of papers covering my study carrel and commented they were glad they weren’t in the course. One person even said you couldn’t force her to take the class.
It occurred to me then that this might be why I’m enjoying my statistics class so much. No one made me take it. It is a pre-requisite for the next level of stats in the Spring, but I’m not taking that class. None of the millions of possible next jobs after school requires me to have a knowledge of statistical analysis.
I’m enrolled in the class because it seemed like it would be interesting and I didn’t know anything about the subject matter. It is new.
Each time a homework assignment makes me want to disrupt the tranquility of the library with a yelp of, “For the love of all that is holy, someone just tell me the answer,” I remind myself – I chose this. No external, deus-ex-machina force worked to force me into this class. I chose to learn this, to work with material heretofore unknown to me.
Having that choice and agency have made all the difference. I am learning because I chose what to learn. I was curious and free to follow that curiosity.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.
– John Louis von Neumann
The proper iPad app for taking notes in math doesn’t yet exist. I’ve been researching the available options for the last few months. I’ve tried Evernote and PaperDesk. I’ve used Notes and checked out NotesPlus. Still nothing does what I want it to.
For notes in every other class, for study group messages, annotating readings and finding ancillary sources, I’ve a great workflow. Evernote, GoodReader, Google Docs and Safari all get the job done quite nicely.
For math, though, I’m still stuck.
It occurred to me yesterday that the problem might lie in the fact that every app I’ve investigated thus far is imitating rather than innovating. Every one of them wants to be paper — plus a little something extra.
They all start from the paradigm of an actual pad of paper and ask, “What have people always wanted their notebooks and legal pads to do?” From there, each app works to add on. Maybe the additions create a watered down legal pad or maybe the iPad only looks like a notebook. Either way nothing yet strikes me as approaching the problem from a new way.
I saw this video yesterday and thought, “My iPad can’t do that.” I know I can install iMovie and import images, but the kind of free-form playing Vi Hart showcases in her video isn’t possible on my iPad. It should be, though, right?
I, along with any other math student working on an iPad, should have an infinite white board at our disposal with the ability to call up the most complex calculator possible and then copy and paste the order of computations onto the white board so we can annotate what we’ve done. Think an infinite Prezi with the ability to bookmark according to dates and key terms. I want to teraform a white board into a world of mathematics, map it out and then use my iPad as the window through which I visit and manipulate the world. Think of it as Sims meets Presi meets the best parts of Super Mario Bros. 2.
For now, I have a spiral-bound notebook for my math notes. Every other class and meeting is synced to the cloud and the notes and annotated readings from each can be emailed or linked out to friends, classmates and study group members. My math notes will live and die with my notebook — until someone builds something better. No, not better. Different.
It takes half your life before you discover life is a do-it-yourself project.
– Napoleon Hill
I just turned in my second statistics assignment. I should note (and I’m sorry Mr. Curry), when I took statistics during undergrad it became a sad march toward intellectual self-destruction. I hesitate to say intellectual, but the professor certainly attempted to steer my thinking that direction.
More often, my thinking was, “How does this count as math? I know calculus. How is this math?”
It wasn’t pretty.
My current statistics professor came with glowing reviews – from everyone. Everyone.
And he’s fantastic.
A lecture hall can be a stuffy space.
A statistics course can be a stuffy space.
The intersection is potentially numbing.
Not with Terry Tivnan.
In a course explicitly designed with the beginner in mind, Professor Tivnan works to set a pace and climate that has yet to have me feeling out of my depth.
Given the laughter and applause that pepper our classes, I’d say my classmates are in a similar situation.
And then the assignment came.
Now, remember, I have been teaching in an inquiry-driven, project-based school for the last for years and another school for two years before that that was doing those things, but didn’t think to say so. Not only is this learning I believe in, it’s learning I’ve assigned as well.
Until recently, it hadn’t been learning I’d experienced. Seems appropriate I dove into the process in a field for which I’ve less natural predilection.
Without going too deeply into details, our assignment gave us two data sets, some information about national trends regarding that data, and asked us to compare the data and write up a report for a fictional school board regarding our findings.
That’s it. No one outlined steps. No one said this is the information you must report.
“How are these two things related, and what does that mean?” we were asked.
It hurt my brain.
A lot.
Unclear as to how to approach the problems and feeling the wait of my mathematical past, I avoided the assignment for as long as I could.
I worked to help classmates make sense of the work, while avoiding my own.
And then I realized what he had done.
He wanted us to own the process. I’ll get nowhere if I have to look to an authority each time I need to decide when and how to use a “z score” or the importance of a weighted mean. I needed to own it.
The process needed to be mine.
Now, these are things I’ve professed for years. I’ve stood in front of audiences and classrooms and argued the importance of this kind of learning.
Here’s the thing – it’s tough.
As incredibly difficult as shaping a lesson or unit plan for problem-based learning may be, learning that way is incredibly difficult.
From several classmates I heard cries of, “Why won’t he just tell us what he wants or what to do?”
I’d heard that before.
“But how do I do it, Mr. Chase?”
As supportive as I’d meant to be, I never truly understood the difficulty involved in adapting new habits of learning.
I expect it’ll get easier – not quickly – as we’re expected to do more on our own with the knowledge and understandings we’re acquiring.
For this go ‘rough, it was tough. I need to remember that.
I never realized I had that much influence on anyone. I hope you enjoy your teaching career as much as I did mine.
– John Curry
My senior year of high school, I took AP Calculus. In my rural school of fewer than 400 students, 5 of us took the class.
When spring arrived, we sat in the conference room, #2 pencils in hand, and attacked the AP A/B Calculus exam.
Well, 4 of us attacked it.
I held on as long as I could. Through the bubble and grid section, I played it cool.
Arriving at the open answer section, I froze.
My mind was a blank. Not a blank as in something had been their and was erased by anxiety, but blank in the sense that I had no idea what was being asked of me.
I looked around the room and surmised I was the only one. Throughout the room, pencils were scribbling.
In that moment, I wanted to quit even more than I had wanted to quit when my third grade T-Ball team lost every game. Every. Game.
John Curry taught me math each year from eighth through twelfth grade, save one.
He wasn’t looping with my class. It was a small school with two math teachers.
If, on my best days, I am half the teacher Mr. Curry was, I have made something of myself.
He was as traditional and by-the-book a teacher as you’re likely to meet. It is entirely possible our pedagogies are somewhat divergent at this point. We are products of different eras.
Still, I remember he cared.
When a student earned a B or above on a test, Mr. Curry would place a sticker on the paper before handing it back. As we moved to higher math, got our driver’s licenses and first jobs, we continued to treasure those stickers. The covers of our TI-83s were laden with stickers like fighter pilots noting our kills.
For a score of 90% or above, students received certificates congratulating them on showing their ability to master the content of the chapter. Mine hung in my locker.
Perhaps best were the letters. At the close of each unit, after the tests and quizzes were graded, Mr. Curry would send letters to the parents of those students earning Bs or higher, congratulating them on their students’ successes.
I remember seeing the letters as I pulled the mail from the mailbox. It wasn’t the handwriting which gave it away (Mr. Curry was mail merging before it was cool). It was the stationary. Out of his own pocket, Mr. Curry purchased stationary in our school colors watermarked with our mascot. When a Kelly green envelope showed up in the mail, you knew what was inside.
The letters did more than offer congratulations to my parents, they also explained what concepts and material I had shown mastery of. Dinner on letter nights was always interesting, “So, Zachary, explain the slope-intercept formula to me.”
Mr. Curry made me care about math because he showed he cared about me.
Sitting in the conference room, my blank drawn with amazing detail, I knew I could not quit. I could not fail Mr. Curry.
Realizing any attempt at calculus would be a mockery of the mathematics he held so dear, I played to my strengths.
I remember the first lines of the essay I wrote, “If you saw my answers in the previous section of the test, you know I’ve been holding on by a thread. Rather than waste both of our time, let me tell you why I needed to take this test and how great my math teacher is. No matter what you think of my math skills, please, don’t take them as a reflection of his teaching.”
Though I’d struggle if you put a factorial in front of me today, I learned the value of more than I can ever say from Mr. Curry.