# An Automathography

This writing is an assignment for Justin Lanier’s Math is Personal smOOC. The first prompt was to “start writing an account of the story that you tell to yourself about what your mathematical experiences have been.”

This is a difficult thing for me to write about (which is the reason I was interested in the course in the first place). It is difficult because I don’t feel that I am the ordinary math teacher who grew up loving math and having a passion for it. Nor am I the ordinary math teacher who grew up struggling with math and decided to teach in order to help others who struggle. (At least those are the two most ordinary stories I hear…particularly during interviews).

My story is different than those. I excelled in math classes. Actually I excelled in everything, but math stood out because fewer people excelled. But I certainly didn’t love it. I didn’t have a passion for it. But I also had *no idea* what mathematics was. I was never exposed to finding patterns or structure. I was never exposed to *posing* problems. I was never exposed to figuring out something mathematical on my own. Heck, I was never (really) exposed to anything remotely “real-world”. In other words, I was never exposed to mathematics. And that, quite frankly, *pisses me off*.

It makes me angry for two reasons. First, I paid a price for this lack of exposure. In my junior and senior engineering courses, I lacked the ability to apply much of the math that I had been taught. (Yes, even my college math courses taught very procedurally – here’s how you do it, now do it). I can recall several times in those engineering courses, and even at my actual engineering jobs, being embarrassed by my inability to apply math to novel situations. (This is why Shawn Cornally’s “Confessions of an AP Scholar” hit home with me).

Second, I didn’t know that I actually had a passion for mathematics. You would think if you pretty much aced every math class through Calc 4, you might at some point find that you liked math. But alas, this did not happen. In fact, this didn’t truly happen until a couple of years ago when I read Paul Lockhart’s “A Mathematician’s Lament”. That spurred me to read more and as it turns out, I really do like mathematics.

I think the saddest part of all of this is that I taught for a good four years before this realization. That means that I had four years of students who learned math (the same way I was taught) from a teacher who lacked passion. If I could find them, I’d apologize to each and every one of them. And it’s these kinds of thoughts and recollections that drive my teaching presently.

Jeff,

So much of what you describe resonates with my own mathematical experience—both the frustration with my own math education as being too procedural and hiding the beauty from me, and the revelation that Lockhart gave me as to what math can be. But I’ll add another frustration—reading Lockhart and being relatively new to teaching math has also opened my eyes up to so many of my own failings as a math teacher—as much as I love the ideas Lockhart presents in both Measurement and Lament, I find myself stuggling to find a way to apply this approach or mindset to the lesson I have to teach tomorrow on topic 1204 in the Algebra II syllabus.

Thanks John,

When I first finished reading Lament, I definitely had those kinds of feelings…he’s very persuasive. But I also try to remember that I am tasked with teaching the standards, and “understand the beauty of mathematics” is unfortunately not a standard (at least not directly). So I think I’m finding a pretty decent balance between teaching math in ways that will be meaningful and applicable, while also letting my passion bleed through and helping students see the beauty in math whenever possible. (If I’m being honest, though, I spend much more time trying to improve my pedagogy than I do trying to find ways to instill passion…and I think I’m OK with that).

Hi Jeff,

First off, great post! The AP scholar post hit pretty close to home for me as well.

I feel that one of the great but frustrating things about math is that you can feel like you describe each time your understanding “jumps a level.” I definitely felt all through high school and college like I was getting the best possible math education (proofs, sustained and genuine problem solving, problem posing, etc) and then sometimes think back to how little I actually remember from math lectures, no matter how interesting or engaging they were at the time. Kind of a random thought, but it’s what came to mind.

As for Lockhart, I agree he can be tough to reconcile with a lot of teaching situations, since if we’re asked to teach a particular topic, it can be hard to make it inspiring, and fake enthusiasm seems to a be a good way to get kids to distrust you as fast as possible. While there are definitely some duds in the standards, it seems that part of improving pedagogy should be using your knowledge and passion for math to do your best to turn standards into engaging problem-solving situations. Easier said than done of course (this describes the teacher I’d like to be in 10 years or so), but I just mean that “understand the beauty of math” and “teach certain standards” are not necessarily at odds.

Thanks David.

“…part of improving pedagogy should be using your knowledge and passion for math to do your best to turn standards into engaging problem-solving situations.” –Agreed, and this is where I have placed much of my improvement efforts.

“…’understand the beauty of math’ and ‘teach certain standards” are not necessarily at odds.” –Not necessarily…but often. I present as evidence: factoring polynomials. Or pretty much everything here: http://christopherdanielson.wordpress.com/2013/04/21/the-goods-nctmdenver/

That is the perfect one-link example of how “teaching for later” is not the best idea. Ok, now that I went and read that, I know that the old NY state standards have lots of junk like this, and while the Common Core is far from perfect, it seems like an improvement on that front.

As for the factoring polynomials example, I maintain that there are many aspects of factoring polynomials that fall under “the beauty of math,” it’s just that (knowing all the different little mundane techniques and being able to apply them flawlessly in a timed situation) does not fulfill that criterion. I see what you mean though about the standards themselves often mangling the nicest parts of mathematical concepts to the point where they are at odds with having fun with the mathematics.

Great start, Jeff!

I feel like we have some experiences in common—especially the part about being a stand-out in math more because other people had trouble with it than anything else. I’m looking forward to chatting about that with you.

How much do you feel like your insufficient/shallow experiences in school were specific to math, or how much of your anger/disappointment is directed at your schooling experiences in general?

I look forward to reading and hearing more about your math experiences in your engineering jobs, as well as about some of the ways that you’ve connected with and enjoyed math these past few years. Keep it up!

Thanks Justin. To answer your question, I’m guessing that my disappointment is in response to my education in general. Now that I teach math and am exposed to it daily, I’m sure the shortcomings are just more visible to me than in other subject areas. I think (hope) if I went to the school I now teach at, I’d have been much more satisfied.

Jeff – thanks for sharing! I’m still digesting all the links in this post (reading Mathematician’s Lament is making me simultaneously frustrated about student teaching geometry last year and excited about trying to figure out how to prepare next year’s course). How/when did you decide to do engineering/become a math teacher?

Thanks Nicholas,

After a few years of engineering, it was clear that I wasn’t enjoying it (something strongly foreshadowed yet ignored in college). It was also clear that I wanted to be a teacher, pretty much since middle school. I got into education with an eye on reform – to do things differently than what I experienced. That’s part of the reason I jumped at the opportunity to help start a school.

Great post! I’m curious, what you doing different in your classes than the ones you had in high school? I ask because I don’t think I do things different. Yes I make fun foldables and I think my students see my passion, (I see the looks they give each other about the crazy math teacher). But I don’t think I’ve made it more authentic nor allowed them to experience it in a way that could develop a passion and love for math in them. There are still too many worksheets in my classroom :( I would love to hear some things you have done in the classroom that have worked well and that connected with the students.

Hi Mary,

I don’t want to exaggerate things, but I think the simplest way for me to answer the question of how my class is different from the ones I took in high school is…everything. That, of course, is not fully true, but unless I can clearly see the benefit for my learners, I question any method that was used in those classes. For instance, the day after a practice assignment, we don’t just “go over it” in class. I’ll certainly answer questions, but we’ll run a protocol for discussion or – better yet – play the Whiteboard Mistakes Game (see http://kellyoshea.wordpress.com/2012/07/05/whiteboarding-mistake-game-a-guide/).

The big picture difference, though, is that my school is a Project- and Problem-based Learning environment. 100% of our instruction is done through projects or problems. This alone makes my classroom vastly different than those I attended.

Good news! I nominated you for a Liebster Award!

Bad news. I nominated you for a Liebster Award.

http://brennemath.blogspot.com/2013/07/huh-what-where.html

Jeff, at first this post frustrated me. I really aced Algebra and Geometry, and enjoyed it. And they were taught by a pretty rigid instructor who daily took his cue from a notebook that looked older than us students.

But then I thought to college, when we as physics majors learned most of the math concepts six months to a year before we “learned” them in the math classes. To the extent there was any like or dislike (‘grind through it’ was the only mode), I supposed I liked the physics better. The formulaic math classes seemed strange.

Either way, when I later “used” math building and simulating the US’ premier warfighting aircraft, it all seemed to work.

I’m still dubious that one can cram as much in doing project-based as can be learned by practicing problems. At least on the high end. Hopefully there will be data.

But it’s exciting to see teachers everywhere exploring how to reach more students, in new ways. Good luck!

Hi Ed,

Thanks so much for your comment, I appreciate your thoughts. I agree with just about everything you’ve said. I would never say that I didn’t learn in my math classes…just that I didn’t learn as much as I feel I should have (both in terms of depth of understanding, and application to novel problems). And I agree with you that there are simply too many standards to attempt a solely project-based approach. In fact, I almost never do “projects” (depending on the definition), instead focusing on problem-based learning in which we can “cram” much more. Another thing I don’t think I’ve been clear about is that my learners do practice problems. The most important thing to me is that the practice problems are always being done within the context of the larger problem – the reason/purpose for practicing them in the first place.

Thanks again for your insights.