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.

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.

Questioning Wise Thinking

When I meet with parents at school functions, they want to talk about what their child is doing in class that’s unique, that’s cutting-edge. So often the question of the purpose of learning mathematics is brought into the public domain. I try to steer the discussion into the creative side of mathematics, how “thwarting” student assumptions and processes can lead to deeper mathematical connections. That message is hard to convey adequately. Most apologists of the historic math curricula give some derivation of the importance of learning logic as a great justification of learning mathematics. It’s a seductive argument, although when analyzed falls apart.

The discussion lacks nuance. Real world applications are tangentially connected to actual problems at best, at worst they’re deceptive to the point of turning knowledge into a set of oppressive devices.

And to flame the argument, when those with bigger platforms than most – the big voices in education –  describe what they think of the purpose of mathematics, I tend to listen. So when the great Ed Burger recently posted his “Truly learning math makes wise thinkers.” my ears shot up. This got some press in the local Austin and Houston papers. Below is my FireJoeMorgan-ification of his piece. Original is in bold and italics.

The question that educators and legislators in Texas should be discussing right now is not whether high school students should be required to take two years of algebra. This is an excellent example of investing time, money and effort to thoughtfully and carefully answer the wrong question.

Man I love Texas politics. Where else can we get a young state senator to filibuster for 8 hours and get a shoe deal out of it?

The right questions for all of us are: What positive and profound lifelong habits of effective thinking are we offering within all of our math classes?

Oh… at first I thought we were getting rid of SeaWorld. But, brother, I hear you. Also, can someone get on that whole “I can use your English state test scores to predict every other test score you take?”

And if the content of the algebra curriculum will be quickly forgotten after the last required exam (or even before), then why bother to offer any algebra?

Well… I’m not sure that doesn’t disqualify Pre-Algebra, Geometry, Algebra 1, Algebra 2, Statistics, Pre-Calculus, Calculus and pretty much every class I’ve taken at the high school level. In fact, If the metric we’re using to evaluate a class’s worth is “Do you remember the content after the last exam”, I don’t know what high school class this wouldn’t disqualify. We’ve changed the discussion from “should we keep Algebra 2 as a class” to “What are we doing with this whole standards and objectives based curriculum?”

Currently, too many of our math classes — as well as other classes — focus on mindless memorization and repetition that is designed to game a system focused on scores on standardized tests that measure the ability to perform a certain act — an act that requires neither deep understanding of the content nor the necessity to make meaning of the material.

Got it, repetition and memorization = bad. Deep understanding and meaning = good. Let’s store these equations for a bit.

Like magic, the moment the final exam is over, poof, the material is forgotten and magically disappears. Think it’s a joke? Math educators know otherwise. The overlap in middle school algebra, Algebra I and Algebra II is conservatively around 60 percent, and more realistically around 75 percent.

This small truth hurts. I understand redundancy when we’re talking about building ships to fly people to outer space. But the redundancy between all the Algebra curriculum reminds me of the painful waste of time when put into an overlap argument.

Our curriculum acknowledges its ineffectiveness at inviting students to make meaning of algebra: Those who study algebra in school are doomed to repeat it.

DOOOOMED I SAY! Also, what?

We need to replace our current math classes with meaningful mathematical experiences that teach students how to think through math rather than simply memorize formulas about math.

Ok Dr. Burger! I’m in. What does that look like? Does it involve teaching kids calculus at 5th grade? Does it involve something playful like sending students to the Desmos carnival?

By thinking through math, I mean understanding the material in a very deep way so that the student can appreciate and (ideally) discover connections between seemingly disparate ideas. Discovering relationships and patterns is not only at the heart of mathematical discovery but also the requisite trait to innovate and create in any space — from big business to the fine arts, from sports to technology, from politics to education.

This paragraph is meaningless drivel. Not once does Burger give any kind of non-jargon examples of what real learning, creating or playing with mathematics looks like.

In mathematics, we need to delve deep into the simplest of ideas until we see how complex they truly are. Only then can we pull back and see the bigger picture more clearly. One of the greatest triumphs of the human mind is that, by intent, we can take our current understanding and challenge ourselves to understand that much deeper—and, of course, that’s at the very core of education. These habits of the mind are what we need to be instilling in our students to enable them to become wise and creative leaders in an ever-changing, multifaceted world.

“Habits of mind” is utter filler and nonsense. “Habits of mind” is a generic approach that give nothing to looking at mathematics as something interesting or creative. “Habits of mind” is a desirable by-product, not the end goal.

Algebra provides a perfect example of this.

Algebra is a set of tools. Learning Algebra has little to do with making wise and creative leaders in an ever-changing multifaceted world. Learning when it’s appropriate to use those tools should be the outcome of mathematics education.

Calculus is one of the most beautiful constructs of humankind (of course, as a mathematician, I’m slightly biased).

Sure Calculus is beautiful. Let’s just start kids with that and then talk about the hyper-specialized cases that arrive in Algebra 2, right?

However, the whole subject revolves around just two basic ideas. So why do masses of students every year struggle with and eventually give up on calculus?

Kids ditch calculus? Or kids never had the chance to take calculus on account of Algebra and pre-calculus being so mind-numbingly boring?

The answer is because they never made meaning of the basic ideas of algebra.

Oh… I guess we agree here.

Even after manipulating the same equations for years in algebra, those students never were exposed to a curriculum that invited them to think through those equations and make them sing in their minds.

Ok Dr. Burger. Here’s where you’re getting me down. You are a textbook writer, the winner of many awards, and you’ve published a ton of material that has been some of the most popular written by a math educator. When you say students were never exposed to an interesting curriculum, this is where you put your money where your mouth is. What’s the interesting curriculum? What gets kids thinking? Where’s your advocacy really going to be powerful?

In my nearly 4,000 online math videos, I have attempted to make those ideas meaningful and, ideally, intuitive.

Awesome! We’re getting somewhere. I don’t really mind plugging your own work if it’s amazing. But then I tracked down a few of the videos where Burger tries to make ideas meaningful and intuitive.

Here’s an example:

“Something x plus something y equals a number.” “Standard form.” “x-intercepts”

Burger simply shows us how to graph the equation. There’s nothing playful here, there’s no higher wisdom to be gained. It is merely a process. It’s a context-less problem. It’s a rote memorization like he railed against at the beginning.

Damn it, I know where someone’s already going with this. Dr. Burger’s videos and general sense of style made him famous. His talks are incredible to go to, hell I’ve been to three in Austin myself. But these videos are dull and lifeless. They’re showing you how to do a hyper-specific process, and I can’t find anywhere where effective thinking comes into play.

This point can be applied to other subjects as well. In music classes, for example, students can simply memorize the finger movements in a piece.

Or watch a video of someone else doing it and try to copy them.

Or they could learn to hear each note and understand the structure of the piece.

Yeah, or that. That’s what the videos are for! Understanding structure.

My real beef is that so many talented minds go into the “let me show you how to do that” field, whether it’s making videos, apps or tutoring. And who can blame them? That’s where the money is at. No one is paying people to scaffold playfulness in math classes. They’re paying teachers to transfer information and skills to students.

In history classes, students can memorize basic facts about the Civil War such as the names of the generals. Or they could try to understand the background, competing forces and evolving social values that ignited the conflict.

Straw man alert! Who is saying history classes should be simply built around rote facts? What happened to the Algebra 2 framework which drew me in?

When teachers give assignments, they should always be asking themselves “What permanent benefit — what habit of thinking — will students get out of this exercise?” Teachers should craft assignments that promote long-term goals such as understanding deeply, learning from mistakes, asking probing questions, and seeing the flow of ideas. In other words, instilling lifelong habits of effective thinking.

Dude! Did you think you came up with that? Why is there no citation to Dewey, Piaget, Vygotsky or anyone else who have been saying the same thing 100 years ago?

And he came dangerously close to shamelessly plugging his book on effective thinking (which is on shelves near you).

Sure, I would be happy to see more students become math majors in college.

Pander to me baby!

But it is even more important to me that they learn to become wise, original and creative thinkers.

This is an empty wish. How exactly do students do so within any context, be it mathematics or somewhere else? I guarantee you, it doesn’t start with curriculum design or choices. It starts with teachers, parents, administrators and students all focusing on empowering students’ thinking. Without that, you could choose the most interesting content in the world, and it’s a lost point.

I’m not here to bash Dr. Burger. Like I said, I’ve cleared my schedule to hear him speak locally. What I’m objecting to is his empty jargon and recommendations around math education without even the slightest mention of what best practices actually look like. As a big voice in education, I dig the memorization = bad equation. But what else are you offering us? What’s your alternative?

End rant.

Thinking Like a Manager, an Economist, and a (sometimes) Mathematician

Every day I have a 20 minute commute, wherein I expect to be entertained! Dodging other commuters has an inherent challenge, but not the level of stimulation I crave.

I love Russ Robert’s weekly podcast series EconTalk. Through his series, I’ve learned how much wine my pregnant wife can drink, how potato chips fly 60 mph over a conveyer belt, and how incentives affect waste policy. His discussions with his guests are playful, inquisitive, and are a nice blend of education and entertainment. I have no training in economics, only Mathematics and education (sometimes at the same time).

I’m always jazzed to hear educators on the podcast… even though I usually have some strong reservations. Doug Lemov of Uncommon Schools and author of “Teach Like a Champion” was recently a guest. The direct link to their podcast is here. Their talk revolved around how to improve performance within schools and of teachers. Lemov framed his background by noticing a strong negative correlation between state-mandated test scores and poverty level (i.e. poverty went up and scores went down). However, there were some schools who systematically scored higher on the standardized tests. His work began by wanting to find the “industry secrets” of those schools.

They go on to discuss successful teacher techniques, systematic culture issues as well as the importance of education in a democratic community. I was incredibly inspired at some of the compassion, care and thought that Lemov had towards kids in the inner city. I don’t teach to that community, I teach at a private school in a fairly affluent community. And as an educator, I have some pretty strong beliefs with regards to mathematics education that I want to highlight no matter the demographics.

Making Teachers Great

Lemov begins by acknowledging that teaching is a performance profession. He mentioned that a good performance one afternoon does nothing to guarantee an equally good performance the next. Teachers are always on the spot. I agree that the discussion in teacher improvement must begin at that point. It gives light to how much preparation must go into every damn day. He offered up a few techniques for teachers. As I was listening, my cynical brain began lighting up. His book has 49 of these techniques, but he covered the following:

1. Call and response

Students are expected to call out certain concepts automatically. No need to invent the wheel here, Christopher Danielson already took care of this critique.

Without getting too philosophical, I still want to mention this: if schooling is a system of memorizing facts, it can easily turn into a tool of systematic oppression. But that’s another rabbit hole for another time.

2. At Bats

The idea of at-bats is simple – kids need to practice skills multiple times. They need to have opportunities to see them in slightly different permutations and practice with feedback, but not an overwhelming amount. This is probably an area where I am admittedly weak. At times I get stuck in the idea that we need to cover so many things that I don’t give students enough straight practice. As I reflect on my last semester, I realize that I selfishly emphasize co-creating concepts; this is a huge time commitment. Sometimes kids gotta practice.

The trap comes when we limit Mathematics to practicing skills. But we’ll come back to this in a moment.

3. Check for Understanding

This is a pretty straightforward technique. Teachers need to gain insight into what their students have learned and haven’t learned. Most educators would call this a formative assessment. It doesn’t have to be a big quiz or test. Lemov describes one way to check by putting up a multiple choice question on the board and having all the students raise their hands at once with their response. It’s feedback for the educator. I’m all for it.


Here’s where I get stuck. We get stuck in thinking of learning outcomes in a very narrow way. To most of those outside of the teaching profession, the only relevant teaching outcome is grades. If a girl is getting an A in Biology and Calculus, she is really doing well. If a girl is getting a C in Biology and Calculus, she is having a difficult time. The nuance of humanity is completely shuttled into a few digestible letters.

Lemov’s desirable outcomes seem to be tied to standardized tests. Forget for a moment that a recent study by Dr. Stroup found that about 10% of the variation in Texas test scores is accounted by previous scores. Forget that standardized tests are “insensitive to instruction.” Hell, forget that Lemov himself said that scores in all domains are highly correlated by students’ ability to read. My question is: what learning goals do we have for kids in math class?

My own most desirable learning outcome is that students think like a Mathematician. My short spiel on thinking like  a Mathematician is someone who can

  • Look at a problem in a novel context
  • Understand the structures of a problem
  • Think in extremes
  • Question assumptions
  • Experiment mentally (no getting our actual hands dirty!)
  • Make logical arguments to convince himself and others of a solution

My list doesn’t have anything to do with computations. I understand where leaders like Lemov come from – they are taking metrics like state-mandated test scores, and try to make his students successful in that way. The only problem is that we conflate doing well on these tests with thinking like a mathematician. In short, here’s an equation:


My heart breaks at one point when Lemov describes how often his kids practice math. He has his children practicing all the time, and he describes his kids at loving. When I think of loving math, my mind doesn’t think of things I can regurgitate facts like multiplication tables, trigonometric ratios or the power rule. I had a terrible experience when it seemed that college math was more memorization. I light up thinking of the time in 4th grade when I created a really strange algorithm for how to test divisibility. I think of my class in Combinatorics when I had to think about sets and functions without any assistance. Math is created, not memorized, and I sincerely hope Lemov’s kids aren’t crushed when they discover that fact.

The reification of those exams would be more interesting if we broke the SAT/ACT tests into: Reading fast, vocabulary, computational fluency and science trivia. So we get this idea that a kid knows how to do Calculus because he gets A’s in his math classes. He gets to higher levels of mathematics, and it’s a shit show. Because when someone is telling you how to find the nth derivative in multivariable Calculus, this beautiful creative process we call Mathematics turns into a chore. I don’t perceive mathematics as someone telling you how.

And I’m making huge assumptions here. Perhaps Lemov doesn’t have his kids “practice” Mathematics by asking them to calculate how to add or subtract repeatedly. Maybe he has them practicing estimation. Maybe he asks them questions where he genuinely doesn’t know the answer. But I’m guessing that most parents don’t view Mathematics in the same way Mathematicians do. They think of it as computations, or a set of rules to follow.

Improving Organizations

When Lemov discussed how he runs schools, I was incredibly impressed. He begins by creating powerful context: “The first obligation of an organization is that it makes its people better.” In all my discussions with administrators of any different organizations, this seems to be an undeniably underserved function. He said that a teacher should be observed every three weeks.


I can tell you that my admin team is pushed to the brink of responsibilities and time already, and I might be observed once or twice in a year. However, priorities are spelled T-I-M-E, and if managers aren’t looking to improve their team, they have to see what’s actually happening in classes. How to promote improvement in the teaching sector is not at all straightforward, but I’’ really appreciate his sentiment.

Listen to the rest of the podcast, there were some great other points when discussing schools as a system: the divide between admin and teachers, how incentives come into play, how autonomy and accountability have to live together.

So while I still have some qualms in Lemov’s approach to what math is, I loved hearing how he views schools as systems. And thanks for the invitation to reflect through writing.

Kick-Ass Parent Meetings and Pancakes

Here’s the situation. You’re in the middle of the school year. You’re checking your email at 10 pm, because at this point you have a terrible, terrible habit. If we lined up all bad habits from biting your fingernails to free basing cocaine, randomly checking your work email would be a solid 7.5. It doesn’t matter if it’s 3 weeks into the year and you’re checking to see if your boss approved the purchase of some rulers or if it’s the middle of October. Spontaneously checking email is a sickness.

So you’re delighting in your vice. You notice emails from your HR rep, a few questions about homework, updates to your favorite websites about kittens… when you notice an email from a parent. You glance at it inquisitively. You scan the email to see what it might be about. You see that your supervisor is cc’d. You see snippets like “crush her confidence”, “discuss this immediately”, and “It sounds like you are setting her up to fail”.

Your reptile brain immediately slips into a few traps. One of two things immediately take over your mindset – “How quickly can I quit this job. Do I still have that emergency resignation letter?” or “How dare they question me. Don’t they know I have a teaching certification??

Slow down. Look away for a moment. Take 5 good breaths. Count them.

I’m not here to solve your twitch-inducing email problem. But I am here to show you a quick how-to on handling your shit in a parent meeting. You might be saying, “Brandon, what do you know about running kick-ass parent meetings?”. Let me give you an analogy I call the General Mutant Pancake Theory (GMPT). Whenever you make pancakes, what happens to the first pancake? The heat on the pan is uneven, the oil is spread evenly, and the first few pancakes are terrible looking. After those first couple, you’re good to churn out some golden, syrup-sponging delights. I am great at parent meetings because I’ve burned so many pancakes and luckily wasn’t fired. My griddle’s hot and I’m here to help you out.

Brandon's mutant pancakes

My first pancakes I ever made

You’re quickly go through the 5 stages of grief.

Denial – this won’t last long. At first, you’ll think “There’s no way this is supposed to be sent to me. You’ll check who sent the email and it won’t take you long to conclude that it’s for you.

Anger – This is where first year teachers will stay before, during, and after the meeting. First year teachers work hard as hell because they basically have no idea what they’re doing. They have all the good intentions in the world. See GMPT.

Somehow, some way, you have to acknowledge you’re in this stage and move forward. There is no having a good meeting with parents if you are here. It is like an anchor that is made up of the opposite of pancakes weighing you down.

Bargaining – read: feeling helpless and vulnerable. No matter how awesome your friends/partners are, even if they are teachers, it’s hard for others how bad you feel when you are called out by a parent. For the lead up to the meeting, you will continually wonder what you could have done.

Depression – quick fix: happy hours.

Acceptance – friends, this is where you should be before the meeting starts. It’s not easy to get here, but it’s the only way you’re going to produce anything positive. You will char the life out of any pancakes you come across if you go into the meeting with anything but acceptance.

The first thing you must accept is that you and the parents have a common interest. Both parties deeply want to serve their child’s needs. There may be some disagreements on how to do so. However, if in your mind, parents are set up as adversaries rather than potential partners, you will fail to find any common ground.

Most of the time, parents want to be heard, deeply and sincerely. They want to share with you all kinds of details that may never surface again – what their kid’s previous education was like, what their social standing is, hell even what they’re allergic to. It is extremely important that you “Hear” what they are saying. I capitalize “Hear” because this must be  reverent act, not just word recognition. When you Hear what they are saying, you are not reacting, not judging (because you’re already past the anger stage, right?).

It is extremely important that you Hear them first, before recommending, prescribing, educating or responding. Hearing does not mean waiting your turn to speak. When it is your turn to speak, you will take what you Heard and feed it back to them. If they begin by talking about their kid getting their confidence challenged, make that something you talk about explicitly. If they talk about their kid not being challenged enough, acknowledge it explicitly. Bring a notebook if your mind has a hard time remembering all their points, don’t be afraid to look vulnerable, especially when you are desperately vulnerable. Make sure you are always framing your responses as a partnership-in-progress rather than defending what you do. Not being defensive is easier said than done. Again, see GMPT.

A few other general points

  • Call the parents by their first names, invite them to do the same for you
  • Sit in a circle
  • If they talk about your lack of experience (especially in front of admin) acknowledge it
  • Let go of your defensiveness
  • Finish with any agreed-upon, reasonable action items. (Note: do not tell parents you will call them every week, unless you are willing to call them every week. You will resent them for the rest of your year)

Look, first year folks. Your first pancake is going to look a little freaky. It can still taste delicious, it might be stackable, heck it might even be the right color. But it’s going to get better. You are a professional and you probably do a good job. Parents love their kids and are crazy and overprotective and over-questioning. It’s the job, but you are going to rock it eventually.

Brandon's good pancakes

Everyone was pumped, GMPT was born

One last bonus tip: within a few days, send a quick follow-up meeting and cc your supervisor. Make it short and sweet – a quick recap of the meeting and any action items. This is professional as hell, and everyone will think you are totally boss.