

Stop trying to make maths "fun" - lessons also for coding? - RiderOfGiraffes
http://www.yorkshirepost.co.uk/news/debate/columnists/rob_eastaway_fun_subtracts_from_the_real_joy_of_maths_1_3068562

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dkarl
"Making math fun" is fine, but most teachers interpret it as "mixing fun stuff
into math, which is inherently painful and boring," because they're focused on
the kids who aren't doing well. To them, making math fun is the same idea as
bringing a clown into the pediatric burn ward: "Let's make this suck a little
less." That attitude rubs off on the kids.

What those teachers don't get is that math is most fun when you are using
solid, polished skills to explore an area where you're still learning. The
teachers are stuck in the standard educational mindset, which is that getting
enough practice at anything to develop polished skills is "rote" and horrible.
Plus it slows down their curriculum. So they move on and just do some review
now and then, and the mediocre students end up with _no_ solid skills they can
rely on. All their skills are a little iffy, so they can't do _anything_ with
confidence, and everything is stressful.

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hasenj
If I was taught programming in high school the same way I was taught math, I
would've hated it, _deeply_.

Most of math was about number crunching and the application of arbitrary
formulas to arbitrary equations.

I can imagine, 20 years from now, a high school student will have to solve the
following question:

"Write a recursive function in C that finds the minimum number in an array of
integers".

Then imagine the teacher himself/herself has absolutely no interest in
programming what so ever, and is only teaching it because the board of
education decided that children must learn it.

~~~
randrews
That's actually a reasonable question. What's a lot more likely:

"Here are fifteen for loop headers. For each one, write how many times the
loop body will execute."

~~~
hasenj
It's reasonable for us. Most people (who are not into programming) would find
it ridiculous and pointless.

~~~
dkarl
It's a reasonable way (the only way) to develop a skill -- even after you have
a conceptual understanding of how to do something, you still have to practice
a little bit at it. Practice is required first of all to clarify your
understanding, but even then practice is necessary to polish your skill enough
that you can use it to accomplish something. (I.e., you have to be able to
execute the skill and have enough attention left over to understand something
else.)

So many problems in education come from the stigmatization of anything
resembling practice as "rote" and "unstimulating." When you stigmatize
repetition, you make it very hard to develop skills. In effect, students are
expected to develop "understanding" (the fun, easy part) without developing
any skills (the boring, repetitive part.) Unfortunately, working without any
polished, dependable skills is awful. It's anxiety-inducing. You have a little
bit of doubt about every single step, and as you complete step after step,
your confidence in getting the right answer goes down and down. Having a set
of solid skills gives you base of confidence, a security blanket that
reassures you while you tackle new ideas.

~~~
hasenj
I think you missed the point.

Most people find first year of computer science very hard. For me it was easy,
but plenty of people found it hard, and I think many people changed majors
because of that.

Now imagine if it was mandatory in high school. Teachers probably won't
understand it much. The curriculum will probably focus on "formula"-like
things (perhaps, patterns?), syntax maybe, and a whole bunch of boring
details, and ignore the most important part: problem solving.

Students might study (read: memorize) all kinds of functions for doing things.

Grade 8: loops for sorting numbers, loops for finding min and max numbers,
loops for calculating factorials. for-loop synatx in C. for-loop syntax in
python.

Grade 9: recursive functions for sorting (e.g. merge sort), recursive
functions for calculating factorials, recursive functions for finding min/max
numbers in a list.

I only realized this very recently, but math has a lot in common with computer
science. Its core is about problem solving. Unfortunately, that's not how it
gets taught in high school. In high school, math is a set of arbitrary
formulas you have to memorize and use to "solve" arbitrary equations. We were
given a lot of "practice problems"; they were the most boring thing in the
world. They didn't teach you anything; their only purpose is brush up your
muscle memory so that when you see a problem of the form "A B C" you know
which formula to use and how to use it.

~~~
dkarl
Problem solving relies on a lot of muscle memory. Imagine doing a calculus
problem when you have to painstakingly work your way through every algebraic
operation:

    
    
      x^2 + 3x - 3x^2 + 3x + 5
      x^2 - 3x^2 + 3x + 3x + 5
      1x^2 - 3x^2 + 3x + 3x + 5
      (1 - 3)x^2 + 3x + 3x + 5
      -2x^2 + 3x + 3x + 5
      -2x^2 + (3 + 3)x + 5
      -2x^2 + 6x + 5
    

Okay, what problem was I solving again? What does this have to do with what I
was learning? What was I going to do next?

When you have to concentrate on grouping and reducing polynomials, it's next
to impossible to solve any kind of interesting calculus problem, much less
learn anything, because you don't have any time to think about calculus. It's
boring to do math that way, not to mention anxiety-inducing, because you spend
all your time worrying about getting the old stuff right. But that's the way
teachers are supposed to teach math: once the kids can work their way through
one kind of problem somewhat reliably, they are supposed to move on before it
becomes routine. That leads to a pretty sorry state of affairs -- the kids
have to think hard about _everything_ they do. You shouldn't think hard about
algebra while you're doing calculus. When you can do the algebra quickly using
your muscle memory:

    
    
      x^2 + 3x - 3x^2 + 3x + 5
      -2x^2 + 6x + 5
    

Then you get to spend your time actually thinking about calculus, the stuff
you're supposed to be learning and exploring.

The thing about problem solving is that it's just one end on a continuum from
exploration to mastery. When you say "the core of math is problem solving"
you're basically saying all the fun and glory is in exploration. It's true! I
don't disagree at all. All I'm saying is that you can't have exploration
without mastery, because you explore new territory using the tools you've
previously mastered. Trying to learn calculus when you haven't mastered
algebra, when algebra isn't part of your "muscle memory," is backwards and
frustrating.

My favorite example of this is freshman college physics. Different people have
vastly different experiences of freshman physics. For kids who are pretty good
at calculus, freshman physics is amazing. It's a year-long parade of learning
cool, powerful ideas and using them to solve challenging problems. For kids
who haven't mastered calculus, freshman physics is a horrific calculus death
march. They spend ten minutes setting up some equations (the only part that
relates to the fascinating new stuff they learned in class) and then spend an
hour trying to make the answers come out right. They spend ten hours doing the
weekly problem set and wonder why it's so boring and why they're having such a
hard time learning physics. It's because in that ten hours they spent one hour
thinking about physics and nine hours struggling with calculus! When students
spend ten hours working and only get one hour's worth of exposure to the
course material, it's no wonder they struggle in the class. The kids who
_enjoy_ physics are the ones who spend ten minutes setting up the equations
and then five minutes solving them. Those kids get to spend most of their time
thinking about the fun stuff: interesting concepts and problems.

The difference is that the first group of kids "sees a problem of the form 'A
B C'" and just solves it. The second group of kids, when solving the calculus
equations, has to think through the concepts and "problem solve." That would
be great if they were learning calculus, but since they're trying to learn
physics, it's an interruption that detracts from their learning. A skill has
to feel routine, even boring, before it can serve as the basis of learning
another skill. Shaky fundamental skills are like the intrusive noises in
"Harrison Bergeron" -- they make it very hard to maintain a coherent train of
thought about anything else.

So you can't problem-solve and have fun in freshman physics until calculus is
routine. How do calculus computations become routine if, in calculus class,
the teacher is supposed to stop drilling you as soon as you figure out how to
think your way through each problem? If the goal is for the computations to
become routine, then boring practice problems are exactly what you need. (I
suspect in your case, the problem was that you needed less practice than the
other kids, and you had to keep practicing long past the point where it really
would have been appropriate to move on.)

You might say that if some kids are never going to go beyond calculus and will
never do any hard-core science coursework in college, then it's appropriate to
just teach them the concepts of calculus and not worry about their ability to
solve problems. Well, that's fine. But they will have a hell of a time
learning the concepts of calculus if algebra and trigonometry monopolize their
attention. The only class where it is appropriate to shoot for "understanding"
without skills is the last math class a student will ever take.

~~~
hasenj
The details are important, but high school maths focuses _only_ on the
details, and the bigger picture is always lost.

What you're saying is true; practice is important, and muscle memory is
important, but they are details.

I hated high school math because there was never a bigger picture.

I actually liked elementary and junior high math (I didn't study it in North
America, but in the Middle East. Not sure if that's a part of the reason).

Some of the high school math was tolerable, but a lot of it was just details
details details with no bigger picture behind it what so ever.

What I'm saying is, if computer science was taught in high school the same way
math is taught, students won't learn how to program at all. They will just
hate it.

To use your physics example. First year physics in my University was pretty
much the same as high school physics (at least the courses I took). In high
school, I had the privilege of having a really good physics teacher (IIRC he
had a Scottish accent). He focused more on the theories and the ideas. His
teaching style focused more on problem solving than just formulas. I liked his
course and did really well in it.

In contrast, the university physics course was horrible, in the same way that
high school math was horrible. It was boring as hell. I was just so disengaged
that I think I got a D and had to retake the course.

------
wgrover
I feel like math teachers have a fundamentally different task than coding
teachers. Everyone needs at least a low level of proficiency in math - being
able to make change correctly and balance your checkbook. Not everyone needs a
low level of coding proficiency.

If you've reached the level in your education where you _need_ to learn to
code, then you've probably already advanced past the point where everything
has to be presented as "fun" before you'll learn it.

~~~
hasenj
Hey, there was a time when most people could get by just fine without even
knowing how to read and write.

With the proliferation of computers into every aspect of life, it's not
unimaginable for programming to be considered essential knowledge that should
be taught in schools.

~~~
wgrover
I'd agree with you if it weren't for the iPad. Computers have proliferated,
but they're also evolving in a way that makes programming knowledge _less_
important (at least for the majority of people).

~~~
hasenj
Math knowledge beyond 5th grade is not important for the majority of people,
but it still gets taught in schools.

------
bluekeybox
> if you have to tell somebody that something is fun, it means that you have
> lost the argument.

Couldn't agree more.

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gaurav_v
This "Mathematician's Lament" is (by far) the best critique of the modern
mathematics education that I've seen to date:

<http://www.maa.org/devlin/LockhartsLament.pdf>

------
Tycho
Hmm. Finding maths so dull was probably one of the main reasons that I didn't
peruse a degree and CS or physics. Which was a disastrous decision for me
personally. Not that I just couldn't face studying anything unexciting per se,
but that I (wrongly) assumed that if I didn't find something interesting then
i could never be sufficiently good at it. At high school I was 'streamed' into
one of the lower tier math classes, which I resented - result was getting a
higher mark in the end than most of the top-tier students. But perhaps I would
have been better off in a more advanced class where I'd struggle more but at
least find the stuff interesting.

Anyway my point is it's a shame to turn people _away_ from maths by offering
such stale curriculum.

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adnam
Eeee, when I were a lad, maths weren't fun! You did 14 hours down't mine and
only then were you allowed to try yer 'and at partial differential equations.
And if yer got one wrong'un, teacher'd beat you with a wooden pole (etc etc)
(yorkshire post, scnr)

------
Mahh
>But I’m convinced that almost anyone can be drawn into maths if they are
presented with something intriguing or surprising which prompts them to want
to investigate

That's what I used to think when trying to get other students into programming
-- like getting a kid do say 'Holy crap, I just created multiplication'. But
it doesn't seem to work that way.

I've come to be used to the concept that other people think on a completely
different plane than me, so it's pretty hard or often just doesn't work at all
to try to find this 'intriguing or surprising' thing that can get them others
to be interested.

~~~
dwc
I agree with you. But I have to add that there's a big difference between math
anxiety and disinterest in pursuing a graduate degree. There's nothing wrong
with someone choosing to pursue something else even when shown the intrigue
and beauty of math (or programming). But there's _everything_ wrong with the
mind-numbing approach to math taken now.

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mnutt
I have very fond memories from when I was 9 or 10 about a book called I Hate
Mathematics: [http://www.amazon.com/Brown-Paper-School-book-
Mathematics/dp...](http://www.amazon.com/Brown-Paper-School-book-
Mathematics/dp/0316117412)

It was the thing that really made math fun for me. So sure, stop telling kids
that "math is fun", but don't stop trying to make it interesting; it's
definitely possible.

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RiderOfGiraffes
If you like this, you might be interested in these:

<http://news.ycombinator.com/item?id=2209991>

<http://news.ycombinator.com/item?id=2209970>

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chanux
Agree with the argument but the title (on HN) doesn't sound right.

I suggest, _Stop trying to make maths look "fun"_

------
Mz
My oldest son has dyscalculia and just sucks at crunching numbers. He had a
terrible, terrible time with math in public school and really hated and
dreaded the subject by the time we pulled the kids out to homeschool. It was
clear to me he would not be able to memorize his way through math like his mom
had. (I was in my thirties when I discovered some of this stuff had actual
uses. sigh) My top priority for math with this child was to teach him "math is
your friend". He's a science geek (which is tough when math is not something
you are good at) and loves physics. He taught me most of the physics I know
(speaking in little words and repeating himself a lot) when he was 14, which
stood me in very good stead when taking certain college classes later on.

A few things we did:

Chapter books, full of discussion about math and light on formulas.

Let him choose a statistics track over an algebra/geometry/trig track. (We did
some algebra and geometry but not too much.)

Read about halfway through "A tour of the calculus". I dropped out of calculus
my first quarter in college and never wanted to see the subject again, after
having been inducted into Mu Alpha Theta in 11th grade. He would spend an hour
on this with me because it was the only math that made more sense to him than
to me and he was happy to watch me get a headache (which I played for all it
was worth). This book was chosen because he loves physics and calculus is the
math of physics and because calculus really requires you to learn all that
algebra/geometry/trig stuff he wanted nothing to do with. I knew I had won the
battle when he was whining and complaining one day about not wanting to do
math and then got all perked up at the idea of working on reading a couple
more pages of this book with me.

We also did "fun" stuff, like card games and such in place of workbooks and
that did have some value. But reading part of "A tour of the calculus" was the
single biggest thing I did to get him past this mental and emotional block.
Which I guess largely agrees with this article, though perhaps framed a little
differently.

