
Math teachers should be more like football coaches - mjirv
https://www.nytimes.com/2019/05/11/opinion/sunday/math-teaching-football.html
======
yodsanklai
I used to teach maths (undergraduate level) and I was also a snowboarding
coach. These two roles aren't really comparable.

\- In my snowboarding groups, there were usually about five students, no more
than ten. We would spend a full day together, and I had time to spend quite a
lot of time with each student individually. In my math "exercise" classes,
there were up to 25 students. I would see them 3 hours a week (they had other
teachers as well).

\- Unlike math students, snowboarding students were all very motivated. Nobody
forced them to be there.

\- Snowboarding students have usually quite similar level of abilities. Of
course, some learn faster than others but nobody improves 10 times faster than
someone else (which happens in maths). If a student is better, she/he can move
to another group the following week (something impossible in my math class).

\- As a math teacher, I'm also the one who evaluates them, and who stands
between them and their degree. As a snowboarding coach, I'm the one who helps
them achieving their goal. Different dynamic.

\- I'm confident that anyone without disability can learn to be a decent
snowboarder after a few weeks of training. But I think that a lot of students
don't have what it takes to learn the mathematics curriculum they signed up
for, no matter how you teach them.

~~~
jacobolus
> _nobody improves 10 times faster than someone else (which happens in
> maths)._

This does not happen in math either. What does happen is some students have
significantly more preparation than others (including, for example,
introspecting more while doing their homework for several years, playing board
games, solving logic puzzles, building with construction toys, ...) and do
more or better focused practice during a course.

Better-prepared students already know a significant part of the material being
presented in a course, have extensively thought about ideas which are similar,
or have improved their generic problem-solving skills. They end up stuck
behind fewer blocking misconceptions.

~~~
jasode
_> This does not happen in math either. What does happen is some students have
significantly more preparation than others _

Are you saying people don't have inherent different abilities in mathematics?
That's hard to believe based on real-world examples.

On the low end of abilities scale, you have people suffering from
_dyscalculia_ [1]. You could repeatedly attempt to teach some of them algebra
and calculus for _years_ and they'd never be able to master it. It doesn't
mean they're stupid; It's just that math in particular is very difficult for
them. There are 20-year olds in college that have been subjected to math
education for _decades_ that still can't pass a remedial algebra class.

In contrast, on the high end, you have prodigies like Terrence Tao[2] that
learned calculus at age 7. His brain literally burns less calories and
requires less study time than most others to learn calculus.

[1]
[https://en.wikipedia.org/wiki/Dyscalculia#Common_symptoms](https://en.wikipedia.org/wiki/Dyscalculia#Common_symptoms)

[2]
[https://en.wikipedia.org/wiki/Terence_Tao](https://en.wikipedia.org/wiki/Terence_Tao)

~~~
TallGuyShort
I think the vast majority of math students don't fit the extremes you've
mentioned. Personally I find it hard to blame anything but the system, at
least in US schools. I began school in 2 Commonwealth countries and was a very
average student, underperforming compared to my siblings. I moved to the US in
7th grade and was considered a genius, always getting in "gifted programs",
etc. I was in possession of math books from my siblings high school and
enjoyed them - ultimately finding that my bachelor's degree from an
engineering school still didn't require math classes that got close to those
books. So I have a hard time saying it's inherent ability holding math classes
back.

~~~
andrewem
What are some topics which were covered in your siblings' high school math
textbooks which weren't required for your degree from a university? (You say
"from an engineering school", but it's not clear if it was an engineering
degree.)

~~~
TallGuyShort
Degree was computer engineering - less calculus than mechanical engineering,
but all degrees from that department had a base standard of some 200-level
courses from the math dept. for science & engineering majors. Linear algebra
was probably most lacking - as it only covered system of equations and basic
matrix operations and properties. Eigenvectors, subspaces, etc. I've had to
learn all that myself. Calculus never actually exceeded AP calculus as taught
in a US high school. Statistics included a pretty similar set of concepts,
though the problems were much simpler (fewer layers of conditional
probability) and didn't cover quite as many example of tests & methods, etc.

------
majos
For those debating reading the piece -- do it! John Urschel wrote it, and he's
probably the most qualified to do so.

I think his point is broadly correct: the way we teach football, and the way
talented football players get mentored in high school, often puts mathematics
to shame. Two responses come to mind:

1\. The incentive structures are different for high school math teachers and
high school football coaches. If a high school football coach produces an
elite college (or pro!) prospect then colleges will pay more attention to the
coach. Get enough attention and the high school coach might become a college
assistant, a college head coach, etc. There is a very real personal incentive
for high school coaches to produce good players.

In contrast, a high school math teacher who produces great math undergrads
will probably get student appreciation and little else. Maybe they'll get to
work with the math olympiads or something, but it's not like a college will
recruit them as tenure-track faculty. Most great high school math teachers are
doing it for pretty pure reasons. Admirable, but hard to expect from rational
people.

2\. Another big problem is that there are _very_ few high school math teachers
who have a good idea of what mathematicians do, or have strong math
backgrounds in general. Makes sense given that most people with strong math
abilities can make much more money doing something that's not teaching. Plus,
based on almost a decade around people who study, research, and teach math,
it's a pretty small fraction of them who get excited about teaching math to
people who, for the most part, aren't into it anyway. In contrast, outside of
very small schools, most high school football coaches love football, even if
they didn't necessarily play at a high level.

These factors combine to make math teachers not like football coaches.

I don't have a great solution to either problem. I do wish there was some
better, more organized way for bored and retired math people to help teach
middle and high schoolers. I think for many such people the desire is there,
but they're not going to start a whole organization and overcome a bunch of
administrative hurdles (which, apparently, are particularly offensive to many
people who like math) to do it.

~~~
ken
> or have strong math backgrounds in general. Makes sense given that most
> people with strong math abilities can make much more money doing something
> that's not teaching.

That argument supposes that high school teachers ended up with that career by
looking at all job prospects and picking the one with the best economic
prospects. Based on my experience, exactly none of them did that, in any
field. My sophomore English teacher used to work at an aerospace company, and
my biology teacher studied to be a physician, for example.

> Most great high school math teachers are doing it for pretty pure reasons.
> Admirable, but hard to expect from rational people.

Exactly so. Until we can reliably identify success in a field (like football
wins), and then make the economic incentives align to promote that success, we
can't hope to increase the number of great people in a field by economic
metrics.

~~~
sturgill
My dream is to be independently wealthy and become a high school math teacher.
I love math, I enjoy teaching, and I’m pretty good at it (I spend a good deal
of time tutoring various youth in our church group).

Why am I not a math teacher? Because I make 5x what a teacher makes. And I
don’t want to raise three kids on a teacher’s salary.

But I dream of being a teacher. Help kids out for nine months and spend three
months hiking and camping with the family. But until then, I’ll just make a
very comfortable living doing quant marketing and building out Bayesian
models...

I enjoy my work enough that the opportunity cost is not worth the forgone
revenue to teach. Not yet, any way...

------
omixi
The key difference that's being overlooked between math teachers and football
coaches are the populations they are working with. Football teams consist of
competitive kids that WANT to play the sport and perform well (win). On the
other hand most math classrooms consist of kids that HAVE to be there against
their will, regardless of their interest in math.

~~~
mmsimanga
I have to confess I haven't read the article. My first thought though was this
would work only if the participants in Maths lessons are as keen as football
players. Football(rugby in my case) is fun, even now as a middle-aged man I
have vivid memories of playing rugby but hardly any memories cracking hard
maths problems. I was motivated to play sport, it was fun. Maths was fun but
not to the same level as a sport.

~~~
humanrebar
Casual phone games have more mathematics involved than people appreciate. Even
if that involves figuring out that you will die before completing the game
unless you pay for it.

But, regardless of their merits, casual games are insanely popular for various
reasons.

And not just casual games. All sorts of games involve mathematics.

That may not be your case, but a lot of people have fond memories playing
SimCity or min-maxing their paladin.

~~~
momofarm
I wonder what's the relationship with Simcity with Math? It's just a game with
building keep growing and some random disaster.

~~~
humanrebar
Budgeting. Tax rates. Growth rates. Density. Efficiency. Geometry in the
planning.

Most can intuitively guess and check to some success, but there is a ton of
math involved even if most players don't bother to formalize it.

------
acjohnson55
Former math teacher here and basketball coach. I agree with the article. My
training as a teacher emphasized fostering investment from students just as
much as it did lesson planning. All of these things are are really important.

But one of the toughest problems in teaching math is that, unlike sports, a
student doesn't get a whole lot of feedback on their success and improvement
in the short-term, besides grades. And grades have some major cons when it
comes to motivation. Also, most of us don't use the exact skills from math
class in life outside of class. What we use is the mindset of finding first
principles, of abstraction, of modeling, and of problem solving. It's quite
difficult to connect these skills to the mentality of kids and adolescents.

This is where extracurriculars come in, in my opinion. They teach the meta-
skills of improvement mindset, coachability, and work ethic. I saw first-hand
how my players came to class with a different mindset when sports were in
season.

I have to say, it sounds like Mr. Urschel benefited from having good sports
coaches, while having math teachers that maybe weren't so good at the
motivational part. A lot of folks have the opposite mix. So I wouldn't say
there's necessarily an underlying thread that generalizes to all of American
education.

------
j7ake
The workload of a football coach is probably much higher than that of a
mathematics teacher. They are up and ready for morning practice early and stay
late after school for more practice. They review videotapes of games, create
strategy , and travel with students.

I doubt there are many mathematics teachers that have the same dedication for
the success of their cohort as football occurs , on average.

~~~
maxxxxx
Football coaches also don’t have to deal with players that don’t want to be in
the team. It’s much more rewarding. You can’t compare The two.

~~~
_qhtn
They can also cut players.

The closest a math teacher can do is give the minimum necessary grade for the
student to move on to the next class at the end of the year.

~~~
6gvONxR4sf7o
Failing a student _should_ be possible.

------
naveen99
Math teams are a thing. They even have a coach just like football. Also
football gets played in regular physical education also, with much less
individual attention to students.

~~~
vitaflo
Yup, I was on the math team at my HS and we won state my senior year.
Certainly not as rah-rah as football (which I was also in) but it was
competitive and we all took it pretty seriously (obviously). Winning the state
competition was just as satisfying than any playoff victory I had in football
(perhaps more so).

------
alexashka
Football coaches are helping students achieve their dreams.

Math teachers are living out hell - teaching a broken curriculum to students
who don't understand why they have to suffer through it.

Name 5 superstar athletes. Name 5 superstar scientists. Fix that first, the
rest will follow.

------
dragonwriter
You mean, they should only have to deal with people who are motivated enough
to volunteer to spend extra, non-mandated time at school and who are supported
enough that someone is paying extra money for them to participate, in an
activity that while not mandatory produces broader social approbation for
success than math?

Football coaches aren't generally better at motivating people than math
teachers (heck, they are sometimes the exact same person.) They are just
operating in a context that favors having more motivated people to start with
and accepts them further weeding out the unmotivated.

------
cjohnson318
I agree with the general idea that coaches are able to provide a much more
personal and thorough training than the traditional teacher, but that's not a
good thing for students and society in general. The reason is because students
should have a right and an expectation to equal access to education. The
reason we see very little diversity in the history of mathematics and science
is because of this unequal access to mentors in particular, and education in
general. (Most of the outstanding non-white and/or non-male mathematicians had
white male mentors or sponsors that helped them get into the Old Boys Club.)
When you have a monoculture in a field, then people tend to follow societal
and cultural norms. This tendency impedes progress at best, and can cause
disastrous blindspots at worst. The current American educational systems is an
imperfect attempt at providing all students with equal opportunites. If we'd
like to improve upon this, then let us improve the teacher to student ratio,
rather than leaving it up to new hybrid teacher-coaches to try to identify
MVPs at a young age, potentially allowing late-bloomers and marginalized
groups to slip through the cracks.

~~~
impendia
I'm a math professor, a white male, I was something of a child prodigy, and I
was _enormously_ blessed with math coaches who went far out of their way to
help me.

I agree wholeheartedly that opportunities need to be made more available to
everyone:

\- Roughly 80-85% of those who get their Ph.D.s in math are male. That's a
depressing statistic, and we need to do better.

\- Nearly all Americans who get their Ph.D.s in math are white. African-
Americans and Latino/a Americans are underrepresented. Moreover, perhaps
surprisingly, so are Asian-Americans. (There are many Asians in math, but
usually they grew up in Asia and only came to the US for university or grad
school.) Here, too, we must do better.

That said, your comment strikes me as rather nihilistic. Because opportunities
aren't equally available to everyone, they shouldn't be made available to
anyone?

Most people aren't like Urschel: most students won't go on to love math or
excel in it, no matter how many opportunities they have. But some people will.
Those people are spread across ethnicities, across genders, across
socioeconomic groups, all over the world. We need to do a better job of
finding and nurturing talent from diverse sources. And we need to make
individual mentoring more widely available, not less.

Have I misunderstood you? Am I saying things you disagree with?

~~~
cjohnson318
I really only disagree with your characterization of my point: "Because
opportunities aren't equally available to everyone, they shouldn't be made
available to anyone?"

I'm not saying opportunities shouldn't be made available to anyone, just that
a stronger mentorship system than we already have in scientific higher-
education is likely to reinforce the trend of white-male dominance that we
already have, rather than temper it.

------
parsamzand
I think the fundamental difference here is that football is inherently
competitive while math is not. While it's true that football coaches have
incentives to produce great players that will eventually play in
college/professionally, the most immediate incentive is to have players that
will win games. Math teachers have no similar competitive incentives. The
"passion" that Urschel mentions here is probably largely a product of the
desire football coaches have to win every Friday/Saturday night, and this is
reflected in the way that they develop kids. Additionally, Math teachers have
to both teach kids AND grade them. This limits how much a teacher can really
be "on your team" because they need to retain the ability to give you a bad
grade. This is true with football coaches as well, but with football there is
always a bigger "bad guy" (other teams/players) so a good coach is always more
aligned with and close to the players.

------
bjornlouser
“... it didn’t stop my coaches from encouraging me to believe I could reach my
goal, and preparing and pushing me to work for it. When they told me I had
potential but would have to work hard, I listened. I heard their voices in my
ear when I dragged myself out of bed for predawn weightlifting sessions ...”

How many adults can clearly communicate the incentives for predawn calculus
sessions?

“You’ll do better in college!”

~~~
thisrod
"You'll have a chance at landing the dream job of the richest person on
Earth"? (Bill Gates, member of the technical staff at Bell Labs in the late
1940s.)

~~~
bjornlouser
"You might play in the NFL one day!"

------
avip
"Mr. Urschel is a Ph.D. candidate in mathematics and former professional
football player".

That is, in essence, the only line you should read. I also have many opinions
about how others should do their work. They are doing it all wrong.

------
stephencanon
A plurality of the math teachers in my high school had degrees in PE, and two
of them _were_ the football coaches, so, uh ....

------
naveen99
If advertisers can individualize teaching consumers about their products,
maybe we just need an advertiser to start teaching math.

~~~
ThrustVectoring
As someone who works in the field of digital advertising, please god no.
Advertisers have zero idea what they're doing.

------
zaphirplane
Like shouting and motivational.

Coach: you will put in 110%

Student: 100% is the max

Coach: you are cut off the team. Who else thinks 100% is the maximum?

------
microtherion
I'm sure math teachers would love to get a million dollar salary. Not quite
sure whether they would be willing to leave their students with irreversible
brain damage for the sake of their career, though.

[https://careertrend.com/much-average-division-football-
coach...](https://careertrend.com/much-average-division-football-coach-
earn-28837.html)
[https://en.wikipedia.org/wiki/Chronic_traumatic_encephalopat...](https://en.wikipedia.org/wiki/Chronic_traumatic_encephalopathy_in_sports)

------
jasonhansel
Math teachers should be just like football coaches: well-paid, especially when
they work at prestigious universities.

------
olliej
Is this saying that they should be paid huge amounts of money?

------
User23
My high school calculus teacher was the football coach.

------
Torwald
Students should be more like jocks: giving a dam.

~~~
daveFNbuck
That probably has a lot to do with it. It's hard to maintain enthusiasm over
the years if it isn't being returned. I think the lack of passion from the
students is more about the voluntary nature of the football team than anything
inherent to the jocks.

~~~
papeda
The rewards are different, too. There is no level of mathematical achievement
that will get the kind of broad (but typically local) social status and public
approval of being a starting high school quarterback. Math just doesn't tap
into anything near as easy and primal.

~~~
daveFNbuck
That's true, but I've seen years where an enthusiastic professor gets a packed
room for a normally undersubscribed elective course like computational
complexity theory or advanced algorithms.

~~~
majos
True, but there's a heavy selection going on there. A packed complexity class
might mean 50? enthusiastic undergrads out of several hundred math/cs students
at a university.

A dedicated and charismatic professor might be instrumental in turning an
interested computer science student into a raging algorithmist (indeed, I
actually think a lot of computer science grad students study what they study
because somebody appropriately passionate introduced it to them), but
converting a just-here-for-the-requirement high schooler is a different story.

~~~
daveFNbuck
The football team also has a heavy selection bias.

Personally, I got into CS because there was a required intro class at my
undergrad. A dedicated and charismatic professor noticed my aptitude and
encouraged me to take the next course and consider a CS major. This could
easily have happened in high school if my high school had a required CS
course.

------
madengr
Hell, my math teachers in high school were the coaches.

Geometry - Volleyball

Algebra II- Football

Trigonometry-Track

I wish I had a math teachers who taught math as a main function, not a
secondary.

At least my daughters middle school math teacher has a BA in math.

------
devoply
Perform brain imaging, split students into those with a strong math co-
processor brain and those without. For those without, teach them math using
logic rather than rote learning which is obvious to those with a strong math
brain.

~~~
scoopdewoop
What an absurd, elitist, reductive, sci-fi response. Brains don't have ALUs in
them, btw. Nor can we image for different skills. Nor should we subject people
to this kind of dystopian hierarchy of faulty biological determinism.

