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.

Outcomes

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:

MATH != COMPUTATION

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.