Let’s focus on math, because physics
is hard for the same reasons math is
hard.
Children (and adults) fail at math for
two reasons: (a) because they didn’t
study enough, and (b) because, at
least in the U.S., math is often very
poorly taught.
(a) is self-explanatory. If they study
hard, most students can pass basic
classes. There’s a cultural dimension
here, since some people think math is
an innate skill (“I’m just not a math
person”), but the fact remains: if
they study hard, they should be able
to pass basic classes.
The fact that (b) math is poorly
taught provides one reason for why
students don’t study hard. It also tells
us why, even when they pass basic
classes, they don’t always learn the
math they should have learned.
Here are several ways math is mis-
taught, based on what I experienced
in several public school systems in
the U.S. (note that there are many
exceptions; I’m only referring to the
general gist of the problems in math
education):
To be fair, some things in math do
need to be taught as rote
memorization. This includes addition
and multiplication tables and how to
do long division and multiplication
(while the student is still learning
about division and multiplication). A
student can’t succeed at math without
these. But once a student has
mastered these, much of math can be
taught by helping students to build
intuitions around problems and by
teaching them how to turn those
intuitions into equations using the
formalism of math.
93.1k Views · View Upvoters
Answered Nov 22 · Upvoted by
Amos Shapir, MSc Computer
Science & Mathematics, Hebrew
University of Je… and Max Baroi,
M.A. Mathematics, Claremont
Graduate University (2016)
Sean Gerrish, B.S. in
Math; PhD machine
learning; Quant engineer
at Teza; ex-Google
engineer
1. There is an emphasis on rote
memorization. Children
learn that there is a sequence
of steps they must follow to
“do” math. They’re told to
memorize formulas and to
apply different formulas or
different sequences of steps
for different types of
problems. The problems here
are that, first, math becomes
boring, and, second, the
intuition behind the math is
ignored. When students face
a problem that’s framed
slightly differently from what
they’ve seen before, they’re
unable to figure out how to
frame the problem
mathematically and so
unable to solve it.
2. Subject matter in math is
often not well-motivated
with problems that appeal to
kids. For example: why
should we expect students to
care about sine and cosine?
Trigonometry is insanely
boring if you’re forced to
memorize a bunch of
formulas when you don’t
have a need to use these
formulas. But it suddenly
becomes necessary — and
interesting — once you
realize it can solve certain
types of problems. Trig could
instead be motivated with
problems from computer
graphics or physics (e.g.,
asking kids to estimate the
trajectory of a ball shot from
a Nerf gun). Are the story
problems we see in textbooks
enough? Not when I was a
kid: they were better than
not having story problems,
but they were usually so
simple that they felt
mechanical. And, for some
reason, they came after the
thrust of the chapter.
3. (With some overlap with (2) )
Many topics taught in math
are useful and interesting to
math professors even though
they’re not useful for lay
people. This again makes
math boring, and it
undermines the credibility of
math as being a useful tool
in peoples’ (even adults’)
eyes. In one high school
algebra class, I remember we
had a one-day section on
convex optimization. The
topic is extremely important
to engineers and researchers,
but the treatment in our class
— a single day — was so
superficial that I’m quite
sure it was useless to 99% of
the students. The same is true
of other topics in math. Even
“finding roots of
polynomials” should be re-
framed as “finding where the
value of the polynomial
function equals zero.