How Python Can Help

Sorry it’s been awhile. I love being a dad and giving an attempt at that while going to graduate school is not an easy combination. But I’m still a heavy consumer of all the great Mathematics posts I see on Twitter. Usually when I see a post that catches my eye, I’m able to contemplate how I respond… but then immediately get sucked into preparing food or trying to set up a new gadget or just making faces at the kiddo.

But this one really got into my brain. I thought: what the hell kind of mutant number always contains the digit 1? I’m pretty good at simply multiplying numbers in my head, so I thought I could solve this fairly quickly.

First I tried some simple ones. 11? Nah, we can see that it has no 1 when multiplied by… like anything. 21… 31… 41… all lose their ‘oneness’ when multiplied by anything. Time to think bigger…

How about 379? Dude that doesn’t even have a 1 right now.

Ok, let’s get crazy. How about the number 123,456,789? Surely when you multiply it by anything a magical one pops into view… Gotta bust out a calculator for that one. Ok, type it in, multiply by 2 and I get 246,913,578. Aha, a 1! Clearly I’ve solved this problem, let’s just check once more to prove to myself how AWESOME I am at solving math puzzles. So we type in 123,456,789, multiply by 3 and… 370,370,367… No 1 in sight.

Clearly this is my cup of tea: simple-on-the-face, but can’t be solved without effort. What I want to show here is another way to think about problems like this. How can computers, and more specifically Python can help solve this.

I’ve been studying programming in the business sense for the last semester (see the zero posts I’ve made in last 6 months). But I want to show you how easy it is to get started with a language like Python – a free, open source programming language that is a breeze to install and use. Python has tutorials all over the place if you want to try on your own, but here’s a starter package.

First, we need a function to test whether a number actually has a 1 in it or not. That might seem unnecessary at first blush, after all can’t we just look at the number? Well… I guess it’s possible, but then it can’t be automated. The purpose of setting up programming is to let the computer do all the heavy lifting.

This program can be pretty simple, we can even get it a badass name like “The MF’ing One Extractor”, or maybe “one_tester” for short. Now Python functions are just like algebraic functions – you pass some stuff in and get something out. In this case, we’re going to pass a number in and get either True or False (stored as ‘flag’) out based on whether it contains a 1 (and yes the capitalization matters, Python is a little finicky about punctuation). Here’s our script:

def one_tester(word):
if ‘1’ in str(word):
flag = True
flag = False
return flag

Now the main thing I’ve learned is that when we test programs like this, we need to try some weird inputs to see if our script holds up. Let’s try a few inputs: 435909; 000000001111100000000, and just for kicks, let’s throw in ‘brandon1rules’.


Perfect, we could keep testing, but seems like that part is working. Now that we have a function for testing for ones, we can do something a little more advanced. For a given candidate number to the solution of the puzzle, here is what we would like to do:

  • Test if the candidate contains a ‘1’
  • If it does not, stop the script and send a message to the user
  • If it does, try multiplying by 2
  • Go back to the first step and continue the process

Essentially we’re trying to do the opposite of the puzzle: find a multiple of the user’s chosen number that doesn’t have a ‘1’.


def number_tester(num):
flag = False
multiplier = 1
while (flag == False):
if (one_tester(multiplier * num) == True):
multiplier = multiplier + 1
print str(num) + ” does not have a 1 when multiplied by ” + str(multiplier)
flag = True

Now, is this script the best we can do? Absolutely not. But it really gives the user the power to do something really simple and easy, rather than manually trying to find a multiple of a candidate that doesn’t contain a 1. In fact this program is so poor that if we actually found a candidate whose multiples always contain a 1, it would be caught in an infinite loop. But this is the kind of beginning that takes the burden of getting started off of the puzzle solver. I can start plugging in numbers quickly and try to find patterns.

Say you have a hunch that the number 574,381 is the one to solve this problem. Instead of trying to multiply over by one and manually checking for a ‘1’, you can simply execute the script:


Now we’ve been freed up from manually checking numbers and can move our brainpower to looking for patterns of numbers.

Over the last couple of years, I’ve really been converted. I think that we have to prioritize computer literacy, not how to format generic powerpoints about solar systems, but rather being able to have computers take the burden of certain tasks . We have super computers in our pockets and on our laps, and they can be used so much more powerfully than glorified word processors.

Guest Post: Music Teaching, UIL, and the Problem with Skills

Editor’s note: Although I’ve been thinking of you during my time away from the blog, grad school + new baby make it terribly difficult to sit down and write. Lucky for me (and now you) the astounding Marshall Escamilla has agreed to share some thoughts on teaching music. Visit his twitter and say hello!

    In order to understand what goes in the world of music education–particularly at the secondary level–you have to understand the world of competitions. In Texas, we have something called UIL, which is an organization that mostly takes care of competitive sports, but that also happens to deal with competitive music. As someone who spent most of my life playing music, I found the idea of competitive music to be extremely strange when I first moved here and started teaching. But that’s neither here nor there.

If you watch the following video, you can get a pretty good idea of the kinds of things that happen at a music competition:

If you don’t care to spend 10 minutes watching this video, or don’t understand what’s going on in it, let me elaborate a little bit. This is a middle school band at a sight reading competition. They’ve been given a piece of sheet music that they’ve neither heard nor seen before, and for the first 7 minutes (or so) of the video, their director is instructing them on how to go about learning this piece of music. After that, they play a scale to warm up, and then have one shot to play through the piece. That set of tables off to the right of the screen is a group of judges, who are listening carefully to their performance and, ultimately, giving them a score on it. The sight reading contest is one part of the bigger picture of the UIL competition, as bands are also evaluated on individual pieces that they’ve prepared all semester–or, sometimes, all year.

In most typical programs, UIL competitions are really the centerpiece event. Directors are judged primarily by how their kids perform at contest–both by their peers and their employers. In other words, it’s a really, really big deal.

Now, I think it’s actually fun to watch a group of middle schoolers that are so thoroughly trained go through an activity that then comes together so beautifully into actual music. It’s also fun to watch an excellent teacher at work. She clearly enjoys what she does and is obviously terrific at it.

And that’s all great.

But then, you should also watch this:

Most of the tunes the Carter Family learned when they were young probably they learned in church. I’d be willing to bet that most of their learning came from singing together in a communal setting. Even those songs they learned from songbooks might have looked more like this than anything like traditional music notation. The bottom line is that as much of a storied career as the Carter Family enjoyed, they would not have succeeded at a UIL competition.

Of course, the Carter Family isn’t alone in this regard. In my years playing around Austin, I’ve met scores of professional musicians–including some very successful ones–who can’t sight read worth a damn. There’s no shortage of successful professional musicians who know next to nothing about music theory. In fact, I would say that at this point most people making their living in music don’t know anything about theory or sight reading.

So what gives? Why is it that this set of skills that are so highly valued in school music programs are so non-essential in the “real world” that most professionals in the field don’t even have a basic proficiency at them, let alone anything close to the mastery displayed by the 8th graders in that first video? There is no equivalent to this phenomenon in any other professional field. I suppose you can imagine a successful engineer who hasn’t fully mastered multivariate calculus (maybe?), but to find one who can’t add or subtract?

The only possible explanation is that there must be a set of skills that most professionals do have that are more important for predicting success in the field than their ability to read or understand music theory., I’d also be willing to bet that the skills that June Carter gained by singing with her family in church–namely, a thorough knowledge of repertoire, an ability to learn by ear, and an intuitive understanding of how music works–are probably much more important.

I don’t want to knock the very, very hard work of any of my colleagues in the field of music education, but when I see stuff like that I can’t help but wonder what’s missing from that picture. Have the kids in this ensemble ever once been asked to play music without a chart in front of them? Have they ever–once–improvised a melody or a solo?

The answer to both of those questions is almost certainly no. With the intense emphasis on preparing for contest, pretty much any other form of music learning outside of the “traditional” Western-art music approach has been crowded out. And to tell the truth, based on my experience at music education conferences, there’s precious little interest in pursuing those forms in any serious way.

And the thing is that those non-traditional forms of learning music are, actually, a whole lot more traditional than the model that depends on sight-reading. It’s really only in the last 150 years or so that any form of music making has existed that didn’t rely heavily on playing by ear and improvisation. Outside of the realm of Western Art music (e.g., folk music, jazz, rock and pop, “world” music), those two skills are of foremost importance.

The thing about non-Western Art music skills is that they are a hell of a lot harder to assess at a contest. Sight reading is great in that way. You can give an adjudicator a chart; they listen to the students play; they mark it up when they hear anything that differs from what’s written on the page.

Though music competitions may seem to a layperson like any other kind of school competition–you know, like football, or debate team–what they really are is a kind of standardized test. They function as a way to measure whether a music teacher is effective at his or her job, and when overemphasized they have a similar effect on learning that overemphasis on testing does. It causes educators to narrow their focus into a tiny realm of types of learning that are deemed acceptable; it causes educators to emphasize rigor and precision over joy and motivation; it crowds out student interests that won’t (can’t?) be assessed.

Marshall Escamilla started the music program at the Khabele School, where he’s been teaching music for the past 11 years. You can read his other random musings at

Guest Post: The Common Core and a Right Brained Math Approach to Math

Editor’s note: Although I’ve been thinking of you during my time away from the blog, grad school + new baby make it terribly difficult to sit down and write. Lucky for me (and now you) Thomas Burwell has reached out and offered to write a guest post. Hopefully I’ll rope him in to continue posting.

The term “right-brained” has become almost synonymous with creativity over the past few decades. To what extent this usage is scientifically backed requires some qualification. As Kara Federmeier rightly observes, “One problem with answering this question is that we would first have to agree on what ‘logical’ and ‘creative’ even mean.” What has been established is that the left-brain typically handles mental functions that are routine and predictable, whereas the right-brain handles events that follow a non-predictable pattern. A perhaps more appropriate description is to refer to left-brain processes as “inside-the-box” and right-brain as “outside-the-box” thinking.

Properly learning any subject requires a BALANCE of left and right-brained thinking. You need to be able to deal with both the routine and the unpredictable aspects of the field. The reason why I like “right-brain” label for math education is because the standard approach to teaching math in schools today is overwhelmingly left-brained. An emphasis of right-brained thinking is needed to create a balance.

For any individual problem, both parts of the brains are almost always working to different degrees, so we should be careful when using the left-brain and right-brain labels. That being said, a proper diagnosis of a student’s thinking approach can reap real benefits to the student and the class as a whole if that student becomes a more active participant.

A student who answers “positive” to the question “what happens when we add two negatives?” is displaying a typical left-brained strategy. They are giving a “correct” answer but to the wrong question. Your left-brain hemisphere seeks to differentiate new information from your day-to-day winning strategies. When presented with a new situation, the left-brained approach is to try out one of your go-to strategies, and then (hopefully) check to see if that result is good.

On the other hand, a right-brain response to the same question might be to draw a number line and count backwards. The right-brain handles the (mathematically more complex) task of “lumping” knowledge, which means to look for connections. Your right-brain hemisphere seeks to store new information for future reference. Even if it is never useful to you personally, it could be useful to someone else someday! A right-brained approach asks “what strategy that I have encountered at some point in my life feels like the right approach here?” Unfortunately, mathematics, being entirely symbolic, has very few surface-level connections to be found. In mathematics, the useful connections are almost always on the deeper, structural level, such as the logic that dictates that the distance formula can be derived from applying the Pythagorean Theorem on an X-Y axis or that the Quadratic Formula can be derived by completing the square from the standard form quadratic equation.

The Common Core addresses the problem with the overly left-brained, approach to teaching mathematics, stating:
“Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts.”

As the Common Core points out, mathematics is incomplete without attention to these structural-level connections. “[It] is not a list of disconnected topics.” Understanding mathematics on some level MEANS understanding the underlying patterns. Fortunately for math teachers, students who possess this deeper understanding of math will also perform better on assessments.

How can teachers use knowledge of the left-brain vs. right-brain approaches in their classrooms? One strategy is to try to appeal to both thinking styles within lessons. For example, a right-brain approach to the topic of, say, quadratics for instance, is to start with a concrete experience such as dropping a ball from the ceiling, or showing a video of a car accelerating at a constant rate. An equally good, but left-brained, approach would be to draw upon students prior knowledge of rectangles, by presenting the following problem:

Displaying rectangle quadratic.jpg

A not-as-good, left-brained approach is to start the lesson with a powerpoint slide titled “QUADRATIC EQUATIONS.” Instead of seamlessly activating the correct prior knowledge, students now must use a lot of their brain real-estate deciding where in their existing math schema to put “quadratics,” which is still nothing but an empty label for them at this point. It’s much easier to just copy the words down in a notebook, and not think about it at all, which is what most students will do.

As the following table outlines, the left-brained approach starts with language, next explains the procedure being taught, and lastly discusses what situation to use it. The right-brained approach is the opposite order, starting with the problem, next encouraging students to figure out a procedure to solve it, and only at the end applying a label, such as “the quadratic equation” to what has been covered. The left-brained approach is preferable when students have a lot of prior knowledge with a similar topic (like the rectangle problem when introducing quadratics), whereas the right-brained approach is preferable when prior knowledge is not so easily activated.

Left-Brained Right-Brained
Label-> Procedure -> Situation Situation -> Procedure -> Label
Results-oriented Process-oriented
“Does this procedure always work?” “Is this the only procedure that works?”

Tom is a math educator in Greensboro, NC. His interests include the history of physics and the study of psychology as the discipline of interiority. He believes math should be taught as “the pleasure of figuring things out”, using Dan Meyer’s approach of starting each class with a concrete problem, and also exploring the etymology and historical context of math symbols.

Furthering Education: Signal or Human Capital?

Apologies for leaving on a somewhat shaky note…. Although I seemed dissatisfied with teaching in general (partially true), I overstated my case as a means of emotionally disconnecting from something I really loved – similar to how novice chicken farmers deal with slaughtering their pseudo-pets.

As the world-famous Justin Lanier noted, no matter what I do next, I’ll still have that teacher hat on. Education is the lens that I’ll always analyze larger events. And while I’m still in school now, I most likely will not be working within a school next year.


I came (back) to the University of Texas at a strange time. There is a power play surfacing, where the President of the University has been forced out. The beginnings of the ouster still seem very unclear. It either had to something with the football team’s poor performance (*snicker*) or perhaps less realistically: the tension between what education has been and what it could be.

Education in America resides in a strange, directionless space: oscillating somewhere between creating good citizens and useful worker bees. Being wrapped in a capitalist country of wealth imbalance that guarantees its citizens a free education makes this tension grows louder and louder.

The local schools have gone the route of being more and more relevant to industry, while still stuck to an outdated curriculum (Biology, Algebra, World History) mandated by the state. The bureaucracy around changing state requirements in the internet age seems antiquated at best, and at worst it seems like a counterproductive borne of backdoor deals between powers that be. Here in Texas, the graduation requirements don’t require a single computer class. So while today’s students take equivalent courses as their counterparts in the early 20th century, it seems strange how we still actively avoid teaching kids how to use current technologies.

This is a seemingly disconnected way to ask my real question: at the post-high school level, should the purpose of schools be to create signals or human capital? Diplomas are signals, they tell others that a student has reached some particular milestone, gained some kind of talent, or at the very least they added to the amount of alcohol sales in the region. Human capital is the skills and talents we gain or discover through experiences (i.e. they know how to create some kind of monetary value. Here are some examples outside of the realm of education of one without the other.

Signals without Value

Value without Signals

Cargo shorts with 58 pockets – half of which could never be filled without ripping the cloth apart. Those secret pockets inside of jackets where you keep your knock-off Raybans
BMW stickers applied to a beat up Honda Civic Dropping a BMW engine in a beat up Honda Civic
This sweatshirt for $129 This shirt for free

Schools strive to create both by making kids go to class and giving them a piece of paper at the end.Most educators would like to think they create human capital and that it will show up for the students at some point in their lives. But the incentive to gain that signal is extremely strong – hell it’s spawned an entire industry dedicated to faking degrees and created scandal for more than a few. The push for more and more signals has driven up the price of tuitions and deflated the value of degrees, especially at the higher end. That goes doubly for a high school degree which is essential if one wishes to earn any income over the poverty line.

Which brings me back to thinking about the signal of college degrees. Recently on Econtalker, author Bryan Caplan described his research where he tried to disentangle the affects of signals and human capital on future earnings. His results were somewhat shocking. If getting a college degree indeed built human capital, you would expect that for every year complete, the percent of your future earnings should be somewhat linear. That is, if the school environment helps students build skills and experience that translate to higher earnings, every year would give you a fraction (around one-fourth) of that.

However, Caplan looked at the data and saw the exact opposite. As a percent of what they could earn, those who finished one year only earned a net benefit of 5 – 10%. With two years, another 5 – 10%. People who finished three years earned essentially no more than those who finished two years. Those who finished all four years earned the remaining 80 – 90%. Listen to the rest of the podcast if you want to know more.

But my question really goes even further: do traditional colleges even care about building human capital? To me, college professors in general utilize the worst form of pedagogy: direct lecture. They employ all kinds of tricks to pretend that they aren’t employing the same arcane practices as their medieval counterparts. To wit here are a few common “best practices” of professors:

Ask a question to class, answer it to yourself.

“Last time we discussed..” when we didn’t discuss anything.

Ask class entire class question; get one correct response; infer that everyone else gets it.

Stand up and read from their notes.

Proof by example.

I’m sure you can think of your own favorites. And I get it, teaching a class where you’re not in control of 100% of the movements is intimidating and scary and oh-my-god-what-if-we-don’t-get-to-that-one-important-point. Maybe they prefer the silence of their audience, like performers in a local musical? Perhaps they want to show their own intellectual prowess?

So I’m left with this question of how universities feel about building human capital. And for all of that, I obviously chose to come back to school. I don’t think I’ll ever be on board as someone who promotes college as a preparation for the job market (here’s one response to a “market-driven” university). Yet there’s no greater concentration of great minds (besides bars, which are also plentiful in college towns). But it’s really strange to expect professors to build human capital by teaching.

Are today’s colleges places to network? Learn interesting material? Or are they still places where you get that paper so you can get more papers? I’m not sure entirely. But if students are taking out huge loans to get some kind of return, their timing could kill the whole process.

But I’ll leave with one of my favorite images. image

This is a college student’s notes from Dartmouth in the late 18th century. It shows he was working on long division, surely a novel algorithm at the time. Knowledge keeps pushing downwards. Students are learning more and more at an earlier level, just ask any 12 year old how to change the wifi settings in your phone. My one desire is that we could let go of the canonical K-12 experience and find skills and experiences that local communities agree upon. In Austin Texas, where Samsung, Dell, Apple, Google and Facebook have large presences, my position is that learning to code is much more useful than learning Algebra 2. And even if you don’t agree with that premise or it’s not possible politically, let’s at least remove the barriers of the movement downwards, maybe get the kids to Calculus in middle school…

Breaking Up with Teaching v2

This is an attempt for me to understand my own motivations of leaving the field of teaching. For an explanation, see part one here.

Suspect 4: Opportunities

“The difference between an escape and an exit is really just context.” – Andy Greenwald, author who does awesome recaps of Game of Thrones

I think about motives a lot. My M.O. is to make decisions and then try to understand them after the fact. So I’ve made a decision and now I’m thinking: am I running away or am I running towards? I think the latter more than the former, even though the tone might not seem like it.

I’ve been working as a teacher for five years. As I began to entertain the idea of trying something else, I realize how pigeon-holed I had become. This is my fault, I work at a private school that doesn’t put any emphasis on student performance on standardized tests, the lifeblood of funding for other schools. I’ve spent five years trying to build up my skills in the techniques of holding mathematical discussions (namely the “Modified Moore Method”).  I became so specialized that it’s hard for others to see how my skill set would fit into various jobs I’ve applied for.

I experienced a moment (read: months) of claustrophobia. I never intended to teach my whole life. Again, I’m accepting total accountability here. Teachers basically have one-year contracts, and until I started looking for something else, I couldn’t see further than that one year.

When I discussed leaving the profession, friends of mine reacted strangely. Forgive the strawmen here, but when someone decides to sell real estate after working as a corporate salesman, no one really blinks an eye. If a truck driver settles down and decides to get an office job, who objects? When a teacher decides to leave teaching, there’s genuine shock. It’s part guilt and part where’s-your-sense-of-duty. There’s “Oh but the kids will miss you”, “We’re losing a good one.” and my personal favorite, “But you get summmmmmmmmers offfffff.”

People will say these things if you’re the worst teacher in the world and students throw a party as you walk out the door. Why? Because they’re merely pleasantries and people are nice. In reality, most people think that teachers are pretty interchangeable (or even totally replaceable).

Seen from I-35 Highways

What does that ad tell you? That with a couple of weeks of training you can be as good as the other teachers. That perception matches up with reality because your pay is pretty much the same.

The first step as I thought about exiting was: ok, what else is there? I tried to gain some traction with some of the bigger education agencies out there as a teacher trainer or working in policy, but couldn’t really get my foot in the door. I am convinced that my skill set just wasn’t marketable enough. I needed to improve in some area in order to create opportunities for myself.

Suspect 5: Value and Advancement

Most of our strengths and weaknesses as a nation – our ingenuity and our industriousness, our arrogance and our impatience – stem from our unshakeable belief in the idea that we choose our own course. – Nate silver

This suspect is really an accomplice (so to speak) of time and pay. What value do teachers actually create? Will the movement towards automation of learning continue? I honestly don’t know, but I don’t see the valuation of teachers increasing very quickly over time. There’s a supply problem – too many people going into teaching (with merit or not).

Last year I read Silver’s The Signal and the Noise. I was genuinely moved. I hadn’t read a book that had the holy triumvirate of good story-telling, super clear mathematical analysis, and new approaches old problems. I wanted to be more like Nate.

Let me digress a bit. When I was a kid, I had numbers on the brain all the time. When I learned about factoring integers, I played this really cool game by myself called “factor all the license plates.” My mom’s license plate started with 403. I still remember the day that I figured out it 403 = 31 x 13. (I walked home by myself a lot obviously). As I continued through middle school, my math classes got pretty dull.

I enrolled in college as a Physics major because Physics problems were much more enjoyable to analyze. The bulk of my math classes during freshmen and sophomore year were super tedious Calculus classes – symbol manipulation, memorization of esoteric proofs, and bland instruction. Then I took a class that was inquiry-based, and I was back forever. No Physics class on earth can stand up to the pure joy that radiates through my soul when I tackle interesting mathematical problems.

Flash forward, and over the last four years I regularly attended Math Teacher’s Circle meetings. MTC’s are professional development meet-ups for math teachers where we hear from speakers who show us what kinds of Mathematics they use. Usually they bring us problems to solve that are clever and novel and have nothing to do with state standards; they’re just fun. It was a way for me to continue taking psuedo-math classes while being fed (!!!) for free.

One speaker described what he did at the Department of Transportation. Admittedly, I would not have predicted many interesting math problems living in that space. He told us the story of creating a good system to determine when to replace DoT vehicles. The main constraints were that new cars cost a lot, and repairs of older vehicles cost a lot. But the best system anyone had come up with at that point was to replace the whole fleet every ten years. No analysis, just someone’s best guess. Based on some assumptions and after a few quick calculations, we had come up with an entirely new system for replacing the vehicles that saved millions of dollars for the state

I was completely smitten. I asked the presenter to lunch and he described other tools that I had never seen in my abstract mathematics classes: optimization, linear programming, risk analysis, forecasting, multi-criteria decision making, and spreadsheet engineering.

I love solving problems. I love using creative means to solve them. I’m not a salesman, I’m not a manager. I’m a problem solver at heart. But teaching is like middle management without the incentives like hitting sales goals. Teaching allowed me to build up interpersonal skills more than anything else, which is great but hard to communicate. I’m itching to do math again. I decided to see if I could hop on this analysis train.

Suspect 6: Comfort

Rocky: He took his best shot at becoming champ. What shot did you ever take? Bartender: Hey, Rocky, if you’re not happy with your life, that’s nice. But I got a business goin’. I don’t have to take no shots. Rocky: (gives stink eye to bartender, throws down crumpled bills) Stick that up your business. Bartender: You want me to take a shot? All right, I’ll take a shot! (drinks) – Rocky (1977)

I’m at a point now where continuing being a teacher is not really an option.

Staying means comfort. It means I’ve taught this class before and I know everything.

Comfort means stagnation. Why make new stuff, I’ve got all this old stuff, let’s just run that back – it worked last time, right? (And there’s not really an incentive to do new stuff other than avoiding boredom).

Stagnation means misery. Some people love doing the same thing day after day, but I need new problems. I need mathematical problems to solve, not managerial ones.

It’s time for me to get uncomfortable, because that’s where growth comes from. Here’s my shot.

I found a graduate school program that offers the kinds of skills I would like to have, and it’s right down the street from me. It’s terrifying to be a novice again. It’s exhilarating because who gets to do this at 30 years old? It’s oh-my-god-I’m-not-going-to-get-a-paycheck for a year. It’s heart-wrenching because saying goodbye to kids and my support group (colleagues) is hard (most of the time). It’s ego-checking because I’m going to school again as all my friends continue their normal jobs, and why can’t I just be happy at work?

Like I said in the beginning, I think I’m running towards something that’s new and fresh and better suited for me now. I loved that I taught. I don’t think of it like a military service where everyone does their part, but I think it’s what I needed at the time. Now I have to see what other adventures lie beyond the immediacy before me.

Breaking Up with Teaching v1

Note: The timeline below gets a little wonky. I’ve been writing this off and on for the last month, with a newborn baby occupying most of my mental space. Also, I teach in a private school. There are different perks and costs to doing business there. I doubt I would have even made it the five years I did if it wasn’t for my wonderful colleagues at the Khabele School. At times, I overstated my case, because that’s what you have to do when you break up.

Recently, the question “Why do you blog?” made its rounds through the math-twitter-blogosphere. When I thought about my own reasons, I couldn’t come up with a complete answer. It was some parts self-promotion, reflection, and connecting with brilliant people. Today, I have a very clear reason to post. I would like to use this space to reflect on why I’m leaving teaching.

After a brilliant class yesterday, I’m stuck in the silence of my room, prepping for tomorrow. It’s deafening. I’m not crying, but tears are coming down my face. I don’t really know what the difference is, but I’m slowly disconnecting from this profession.

When I began telling my brilliant colleagues and students about my decision, I really struggled. It’s no easy feat to say “I don’t want to be a part of this anymore. I want to move on.” The first part of that sentence, the running away, isn’t really true, but it feels like it.

In the movie “Who Killed the Electric Car”, the directors helped us understand which factors were at play behind the first electric cars being essentially outlawed. With Tesla, Leafs, and hybrids dominating new car sales it seems strange to think about. But, the narrative stayed with me. It was driven by putting seven or so “suspects” on trial. A similar structure might help me understand for myself why I’m moving on, so I employed it below. This first post deals with the movement away from teaching, and the second part deals with what I’m moving towards.

Suspect 1A: Pay

“If people aren’t paying you for what you do, they don’t value you.” – Steven Levitt, author of Freakonomics

Every time I’ve talked to colleagues, parents or friends about moving on from teaching, salary is the first thing to come up. Let’s face it, the only way for a teacher to advance and get paid is to stop teaching. Whether it’s running PD conferences, or becoming an administrator or any other occupation tangentially related to being in the classroom, this is a top heavy environment.

Teachers obviously know what they’re getting in to. Payscales are completely transparent. Here’s what pay raises looks like for a teacher in Austin ISD during their first ten years.

–, 0.00%, 0.00%, 0.00%, 0.24%, 0.24%, 0.24%, 0.24%, 0.47%, 0.00%, 0.70%,

Well, that’s ok, right? I’ve heard before the teachers in their latter years make BANK. Let’s check out raises from years 11-20.

0.70%, 0.69%, 1.38%, 1.36%, 1.34%, 1.32%, 1.31%, 1.29%, 1.27%, 1.26%

Not one time in twenty years of service will a teacher at AISD get a raise of 2%. Typical cost of living increases is estimated around 3% per year, probably higher in bigger cities. When we talk about the average tenure of K-12 teachers, we should start with those numbers.

I realize that merit pay is a really uncomfortable proposition. But in the salary schedule above, the only variable that controls a salary is how long you didn’t get fired. I don’t even want to link to it, but look at google “curriculum specialist”, “high school basketball coach”, or any administrative role and compare them to teachers’ salaries. Clearly, we value the two quite differently. It sucks.

For me, there’s this secondary biological component. When I found out my wife and I were going to have a child, it began changing how I view my own role. I’m perfectly fine with my salary now; I agreed to the terms. But looking forward, after all the obsession with getting better, with advancing my craft, after giving so much of myself, it becomes more disheartening to realize that the only way to get paid as a good teacher is to stop teaching. I realize that education doesn’t fit nicely in the capitalist mindset, but it wrecks me to think that the value I’m creating is not honored in a monetary way.

Suspect 1B: Time Commitment

“To me, there are only five real jobs in America: police officers, teachers, firefighters, doctors, and those in the military service” – Charles Barkley, former NBA player

Time goes hand in hand with pay. There’s two sides to thinking about how much time teachers work. The first is both very primitive and totally legitimate: teachers get summers and major holidays off. The second is that teachers rarely leave their work at work. A colleague of mine once said that he actively avoided calculating his hourly salary rate – the idea is that it would be too damning a number.

Over the last two years, I’ve tried to get a handle on my time commitments at the school. I stopped coaching basketball, I took over the math department and taught one less class, and I made myself available for office hours on a more limited basis. I didn’t do a great job, I wound up taking over NHS and teaching four different types of classes (preps). I’m not great at saying no to taking on extra work.

I had a moment where I was confronted with hours and my commitment. It went something like, “As math team lead, work on this project. Since it counts as one of your accountabilities, this should be worked on about 3 hours per week.” This is one of the fucked up assumptions of non-teachers, even (especially?) those who work near them – that the amount of time spent on each class is predictable and linear.

Because each class is a performance, I see the breakdown as something like this:

Class time + Preparation = Total time spent on class

Preparation eases a little bit if I have two sections of Geometry, and not every class has the same workload. Our classes are either 1 or 1.5 hours long, two or three times per week. I usually put about 1 – 1.5 hours outside of the classroom, whether that’s giving kids feedback or finding cool stuff for them to do, making copies, etc. So for the five class periods I taught, let’s say I was directly involved 7 hours each. I’m already at 35 hours.

This doesn’t include communicating with parents via email and phone, office hours, school assemblies, filling out paperwork, going to meetings, going to special events, answering more emails, eating food fit for human beings or general health maintenance. All of that time will vary, but if I stayed on a super strict schedule and never looked at my phone, chatted with colleagues or did things like “go to the dentist”, I’m hitting around 40 hours minimum. That’s normal, but it doesn’t include the huge swings in time from week to week. I tried my damndest to avoid taking work home with me this year, and the pull is just too strong – especially in an environment with outstanding other teachers where I feel the need to compete. This leads directly to the grind, but before that…

Suspect 2: The False Environment

“Don’t let school get in the way of your education” – Mark Twain

After my few years as a teacher, my philosophy is that knowledge is socially constructed. Knowledge is not linear, it’s not value-neutral. So how do I balance those basic tenets with a state-mandated curriculum or standards? How am I supposed to say “You should learn Geometry because _______”?

I find myself in the middle of a statistics class thinking, “All this p-value stuff is crap, there are huge incentives for researchers to keep sampling until they find results they want.” But that doesn’t come up on the AP test. And even though my kids were trained assassins as far as skepticism, they’re trying to show they have this knowledge of inference or bias or whatever while trying to keep in their head the inherent flaws of statistical methods.  And the kids have huge incentives and pressures to do well on that AP test, so where does that lead us?

There’s too many inner conflicts I find myself battling. And the longer I do this, the more and more I feel like a charlatan.

Suspect 3: The Grind

“You pay me for Monday through Saturday, but Sundays, you get for free” – Ray Lewis, NFL linebacker

The biggest hindrance to individuals staying in the profession is the grind. I love working hard. I think I inspire my kids to really do the same. Being in a classroom is easy for me (now that is), the hardest thing in the world is not being in the classroom when my kids are.

Before this year, I hadn’t taken more than two days off in an entire year, not because I’m awesome, it’s because subs are death. Being a classroom is a performance; it’s a result of tons of preparation and practice. It’s anticipatory, it’s carefully crafted. What would Cirque du Solei look like if they tried to find an acrobat the night before?

Subs are like the worst babysitter in the world – they’ll give kid whatever sugary substance is available as long as they just stop making noise. That’s why every time I see sub lesson plans they begin with “Put the movie into the dvd player….” Even on days where I have to go to a wedding or NBA games went on too late or (looking forward) I might have to take care of a child, the prospect of calling nine people just to find someone who can go to youtube and find something valuable for the class to do is the worst.

Just as damaging as finding subs is email. I don’t think there has been a worse creation for teachers than email. Email’s role ideally would be a non-intrusive way for people to schedule times to speak with one another. In reality, email counterproductively gives a forum for people to give contextless feedback; gives other people work to do; or is sent to an ungodly amount of people who have no actual interest in the content of the message, thus wasting precious seconds of the recipient by actually opening them.

At our school where we had a policy that email was not a mode of instant communication. But it’s just too close, because it’s delivered pretty close to instantly. And because new work was given through email, it gave me an incentive to check it all the time. And checking work email sucks.

Also, there’s meetings. I don’t have a lot to say except fuck regularly scheduled meetings. They’re like an opportunity to fill up someone else’s time by making shit up as you go…

Ok, let’s pump the brakes. Seems like I’m getting derailed in the details. It really comes down to my premise that teaching is a crafted performance. Over the last two years, I lost sight of why I should improve my craft, which magnifies all the other flaws of being in a school. I don’t hate schools, I’m just ground up. So I’m leaving. In the next post, I will reflect on where I’m going, rather than why I’m leaving.

Talking Circles and Math

Strange things happen when you go into a classroom and talk about something of which you’re very passionate. Sometimes, people take away something you had no intention of discussing. The same principle applies when giving a talk at a convention apparently.

When I was at NCTM talking about what I tried in my stats class, one of the slides I showed became an instant hit. It was posted on Twitter I think 5 times, making it one of the most popular tweets of all time.

So Geoff at Emergent Math asked me for a follow up explanation of tracking conversations. He flattered me, and I’ll oblige.

Last year around this time, I began to read Nate Silver’s The Signal and the Noise. As I read, I became more and more convinced that the narrative behind the book could drive my AP Statistics class. I set an intention to integrate the learning objectives of the stats class by reading parts of the the Signal and the Noise. For example, instead of introducing confidence intervals with a definition or an example, I really wanted to take the story of a flood plain in North Dakota to introduce the idea. This idea is what I presented at NCTM.

When I decided that I would assign actual reading to my class, I had an idea of how it would go. I would assign a reading, then at the next class I would begin a class with a simple question, “What did you LEARRRRNNNNN?” all mystical like, as if I was in one of those hoity-toity movies about … reading or whatever.

It turns out that when I framed the discussion this way, I didn’t exactly get the result that I was looking for. But, hey, this is coming from the guy who invented General Mutant Pancake Theory – no problem. I’ll just walk down the hall to my friends in the English and History departments and steal all of their ideas. One idea they had for me was tracking conversations.

The basic structure is this: Before class starts, I have students read and I give them some leading questions. Questions like:

  • What are the differences between an observation and an experiment?
  • How were correlation and causation discussed?
  • What is a lurking variable that came up?
  • How do we “prove” causation?

During class, students sit in a circle. We put up all the names on the board. Either a student or I are in charge of “tracking the conversation”. My job is to listen and ask questions. Their job is to make the conversation awesome.

In the diagram below, A(dam) makes a point about how causation can be confused with correlation, then D(enise) follows up with something she heard on NPR that relates to the pregnancy study. F(reddie) asks how one can prove causation and then A(dam) reminds him of a problem in which we talked about proving causation. C(eara) asks another questions about how this relates to confidence intervals, and the conversation continues.


We don’t really need arrow heads for any of these lines, we just need to see who’s involved and to what degree. G(reg), E(than) and B(etsy) haven’t chimed in yet, but everyone sees that, and at times I might direct the conversation at one of them if they still have no lines connecting them to the rest of the conversation. But usually, another student will call them out, which I think is super empowering.

What makes this work? First, no matter how advanced the students are, they are still amateurs in the subject area. Even though they may be great symbol manipulators or really understand what we’ve done so far, I intentionally gave them material that is new and just outside of their knowledge base.

Second, by taking myself out of the circle and being a guide, it takes the sense of agency away from me and gives it to them – again, then idea that I’m trying to empower them. I rarely correct any incorrect interpretation, but if it seems to pervade the conversation, I might ask some clarifying questions.

Caveat: this system probably isn’t working if you have a class of 30. I have only tried it with ~15. However, it’s totally possible to break the kids into smaller subgroups and do the same kind of thing.

I’ve been interested in Socratic-seminar-like conversations in math class for a long period of time. All knowledge is socially constructed, so when I see students being active agents in that process, it models what learning outside of the false environment of school looks like. Not to get all Vygotsky on you, but constructing a situation like this makes different neurons fire in young brains than just having them work independently.

Takeaways from #NCTM14

Nothing is rejuvenating like spending a few days with like-minded people. I feel incredibly fortunate that I was able to speak with many innovative, passionate, and engaging math educators.

And… there’s more to it than that. Obviously, the people who are able to attend NCTM either have districts who are willing to foot part of the bill, received some kind of grant, or paid their own way. That is, the attendees are not representative of the larger math education population. But it seemed that I talked to two kinds of people: those who were content being there and those who were super hungry to connect.

I teach at a super small private school. We have about 220 kids in 6th – 12th grade. I don’t hear bullshit acronyms like “KWLM” – literally “kids we love the most” when talking about children who have not had success at school. I don’t hear kids being called “low” or “high.” I don’t hear these false classifications of children that have nothing to do with how they learn. Even a casual label like “lazy” is describing a behavior, not a person. I encourage you, if you hear a child being called by a label, call them on their shit. It can be awkward, but it can’t be a practice that continues or ignored.

End rant. Here’s a collection of takeaways I had.

The sessions by Christopher Danielson and Michael Serra respectively were the only two where I actually had to think mathematically. I think that it’s such a rich experience for math teachers to be able to be back in a learning environment with novel material. Students do it every day.

What I loved about Danielson’s presentation is that he didn’t know where it would lead: when students come up with their own classification system of hexagons, he doesn’t have a pre-defined notion of what we would create (unless he’s already come up with every possible way to classify his set of 14 or so hexagons.)

Michael Serra had created inquiry based materials which can be found here. We worked together in groups on some of his pre-created materials. I highly endorse the donut polygon problem set.

Recurring theme: Few people have a clear vision of what to do with technology in the classroom. I heard so many stories of computers, iPads, smart boards and other gadgets being stuck in storage because they were being used improperly or didn’t foster student learning (or both).

This was the first year I went to a talk on math and social justice. Rochelle Gutierrez’s sessions focused on the “unearned privilege” that those who can do math have in society. Math typically is heralded as the highest form of intelligence, and presents a high barrier to some. I really dug her point that “math needs people” as a converse to the traditional “everyone needs math.”

People I met put up with a lot of pressing questions. I don’t know how no one told me to shut the hell up all weekend. When asked about your craft, you people are much less defensive than I think I would be.

Steven Leinwand gave the sermon of the week. Among other items, he mentioned the “devastating impact of teacher isolation”; how standards and assessments are the bookends – necessary but not sufficient; and plugged the new Practice to Action text. I’m still confused why Practice to Action isn’t a free text, supported by NCTM, the Dept of Ed or some other professional organization. If the document is so important, why not put it in the hands of everyone? Maybe I’m naïve here.

“Don’t read off your slides. Don’t read off your slides. Stop it. Don’t read off your slides.” – me talking to myself and about half of the presenters.

Dan Meyer had a great presentation on lessons we can take from how video games are structured. He’s got a summary here. But what I really took away was a line at the end of his presentation. He pointed out that so many people are vying for kids’ attention: video game developers, shoe creators, wanna-be teen celebrities, musicians, etc. etc. etc. But what teachers are given (by law no less) is a captive audience. Students are “forced” to be with us for 180 days out of the year, and it’s a time that should be treasured and honored. It’s a time to innovate and connect kids with mathematical thinking instead of mechanical procedures.

I couldn’t have been more grateful for everyone who stopped by for my presentation. I was literally in the hallway grabbing anyone who looked at my sign in an act of shameless self-promotion. It was my first one, and I didn’t really feel nervous – it seemed like all who attended really wanted me to succeed.

I think that’s the vibe that should be supported by NCTM: we want you to be a badass and you can do that here at our conferences. Other than that, I’m still not sure why people come.

NCTM 2014 Slides

I embedded my slides from my talk about using non-traditional texts in my AP Statistics class. They might not be clear if you missed it. Feel free to hit me up on Twitter if you have any questions.

(I tried to embed this about 10 different times, but the heights were all wrong. Forgive the extra click)

Bringing the (Signal and the) Noise

Thinking quickly

I’m going to ask you a question about pizza, but I’m going to trust that you won’t look below until you agree not to do any calculations. By calculations, I mean on paper, in your head, or on a machine.

So don’t break our circle of trust.

Seriously, just move on if you’re tempted to cheat.

Ok, got the stragglers out of here. Without calculating, answer the following question

The largest pizza at East Side Pies has is fairly big. It’s 18 inches across. What is the area of the pizza?

a. About 254 sq inches
b. About 1017 sq inches
c. About 56.5 sq inches
d. About 740 sq inches

I…. couldn’t resist doing the mental estimation. It didn’t come to me naturally.

Now the rest is of this post is obviously speculation. I imagine that the rate of correct responses is somewhere in the 25-33% range, that is you might be able to rule out one of these questions pretty quickly. However, I don’t think there would be much difference if you asked a 4th grader or a high school junior.

If I have no real intuition about many, many little squares of pizzas, what does that say about my ability to “do” mathematics? To me, it shows how being able to calculate an area of some generic shape is a lower level of skill. If we made a Bloom’s taxonomy for math classes, I think calculation should be like level 2.