
Meet the New Math, Unlike the Old Math - M_Grey
https://www.quantamagazine.org/20161005-commoncore-math-ngss-science-education/
======
lowbloodsugar
FTA: "Traditional math teaches an algorithm. Common Core teaches the concept
of 'proportionality' [over a period of six years]"

My 11 and 13yr olds are dealing with this Common Core bullshit right now. This
article might give an insight into why CC is so bad, yet they think its so
good. Like when we demo a software product that we've all been working on for
six months, and discover that users can't figure out how to make it work: it
only works for us because we've been using it continuously for six months.
Maybe Common Core can teach Proportionality if you sit down with a kid and
give them all six years of it over two days. What happens in reality, is that
my kids (a) don't understand the confusing ways its presented and (b) don't
make the connection between the different expressions of the same underlying
concept. Its not useful. Its actually immensely frustrating for everyone.

I think they have it exactly backwards. Teach the algorithm. Rote practice.
Then teach the concept.

I'm reminded of my first year thermodynamics lecture at Imperial: "We're going
to teach this to you every year. The first year you wont understand it. The
second year you'll think you understand it. The final year you'll realize you
never really understood it, but at least you'll be able to use it."

~~~
wvenable
My daughter went through this in Canada; same basic concept and she did not
like it and neither of us could make sense of a lot of it.

My theory is that this version of Math is designed by people who hate Math
(English teachers). It's all about estimation and fuzzy thinking. Everything
that I personally liked about Math as a kid seems to have been stripped away.
In my opinion, children who want to become computer programmers, scientists,
and engineers are probably not well serviced by this type of teaching.

I'm not saying the old method was perfect either; mostly because if you're
just teaching algorithms then there isn't much understanding about why they
actually work.

~~~
candiodari
One of the things machine learning has taught me that for many complex
algorithms, I don't know how they work, and ... no-one does, and here's the
great insight : it's not important, it is in fact a very good thing that I
don't know what they're doing. It wouldn't make any difference if I did, and
it would in fact be more limiting than not knowing. Having the ability to
execute and design them is all that's important.

The issue is that machine learning, at least in the modelling domain, is
exceeding the maximum complexity the human mind can contain. Attempting to
analyze neural networks is fun, and it's what you do as a researcher. But no
amount of study is going to tell you what more than 10 neurons are doing to
any reasonable amount of detail, no matter how smart you are. Machine learning
algorithms suck at explaining what they're doing mostly because what they're
doing is far more complex than what we do. And yes, I can build toy examples
like a 100 bit binary adder where I do know, I'm talking about non-obvious
cases.

Therefore: rote is all that matters. You should be able to execute these
things, forwards and backwards and take it's code apart and put it back
together again. That's all there is to it. And if machine learning does indeed
conquer the world, that's all there will be to anything.

~~~
johncolanduoni
That may apply to machine learning, but not to anything you'd get in a grade
school math education. Or a graduate one for that matter. Moving from rote
implementation of something else came up with to figuring out how to approach
problems where the steps aren't already laid out for you is a big speed bump
in university education for mathematics majors.

Also, unless our current machine learning algorithms just need bigger
computers to take over the world, _somebody_ is going to have to develop more.
If some kind of guiding intuition isn't a part of that process, the universe
will hit heat death before we build an AGI.

------
ivan_ah
> “[Teachers] are woefully unprepared [for] engaging in inquiry driven
> lessons. [...] instructional changes entailed by NGSS are too big to
> internalize in isolated chunks of professional development.

I think this is currently the main obstacle with the CCSSM and NGSS. The
structure and logic of the news standards are good, but they're new so it will
take some time for teachers to adjust. We need better course plans, better
textbooks for teachers, better textbooks for students, and better exercise
frameworks.

We can't look to mainstream publishers to provide this, because they're large,
slow, and extractive organizations. Therefore, this seismic shift in the
structure and material taught represents a tremendous opportunity for OER to
come in and eat the big publishers lunch, e.g. [1].

Our company (Minireference Co.) is currently focussed on university-level
textbooks so we can't "attack" the high-school market, but we're happy to
share technology and insights with anyone out there who is working on OER for
primary/middle/high school.

[1] State-sponsored content push to create common-core-aligned textbooks for
high schools:
[http://k12oercollaborative.org/](http://k12oercollaborative.org/)

~~~
Spivak
> but they're new so it will take some time for teachers to adjust

It's actually much worse than this, the only math teachers that actually
understand how to teach this material are math teacher teachers and their
newly graduated students who have gone through their curriculum. It's going to
take a literal lifetime to actually meaningfully execute the new methods even
if you manage to get the textbooks in every classroom.

I really truly hope the kinds of resources you're developing can help existing
teachers transition, because as it currently stands the outlook is bleak.

------
hondo77
My daughter is a senior in high school. She used to love math. Then they
switched to Common Core. Now she hates it. Having looked at her textbooks, I
don't blame her. Confusing concepts presented quickly, with no depth, and it's
unclear how those concepts solve the problems presented. Say what you will
about the old way to solve for "b", at least you learned how to do it.

~~~
mjevans
If she mostly learned the old way, get her old books your self and finish the
job?

------
helthanatos
Experimenting with education is what broke the system in the first place. We
can't very well go back to how anything was in the 1960s because times have
changed, but that's not to say those methods are completely broken. Common
core is a hideous atrocity that has been proven to hurt young children's minds
and cause them to do things in redundant or roundabout ways. I've been
experimented on throughout my school career - some of it good most of it bad.
Taking education out of its broken state is important, but breaking it more
helps no one. Proceed carefully and think things through before possibly
ruining the education and, by extension, their lives. Education is seriously
important. It takes a lot of work to rewrite your brain after being taught
wrong.

~~~
ThrustVectoring
No, what broke education is a fundamental misalignment in motives between the
folks advocating for, paying for, and running education, and the actual
children who go through with it. The things the decision makers are optimizing
for are so very far removed from the actual experience of children. Like, how
exactly does administering a multi-day standardized test help children? It's
clear how it helps parents - they get to send their children to "better"
schools. It's clear how it helps administrators - it gives them political
cover for the decisions they make. But the actual children involved? Pretty
damn near pointless, and the test is just the tip of the iceberg really.

I don't have high hopes for education reform movements, either. The direction
education needs to go to get better is simply "less", and there's no
incentives for doing so. (After all, how can you get credit for "helping
children" if you're not actively doing anything?).

~~~
candiodari
In my experience, what Common Core is really doing is allowing (and giving
cover for) teachers who don't know the subject they're teaching. They cheat,
because the only alternative is to actually become decent and fast in the
subjects themselves, and that requires more knowledge and work than they'll
ever put in. My kids math teacher tried to defend for >20 minutes to me that
you cannot ever differentiate an equation with matrices instead of numbers.
Well ... I made sure my kids double check with me if something sounds odd, and
I'm forcing them to go through khan academy exercises.

This is probably exactly what administrators want, though. Cheap teachers, and
damn the consequences.

~~~
throwaway729
_> This is probably exactly what administrators want, though. Cheap teachers,
and damn the consequences._

Are you kidding? Administrators live or die on test scores, and the non-brain-
dead ones realize that good teachers are the best way to get those test
scores.

They don't really have a choice, though -- they work with what they're given
in tax money and in many states don't even have any autonomy in compensation
(NEA).

IMO the problem is way earlier in the pipeline, anyways. Even if
administrators deeply cared about quality, they'd find a shallow pool. As a
good rule of thumb, people who are good at mathematics _don 't become
teachers_. They become engineers or go into finance and consulting or write
software.

And it's all about pay and quality of work environment. I'd teach high school
math in a heart beat if the working conditions were more reasonable and it
paid even half as well as my other options.

------
empath75
I have a son now, and I was sort of considering trying to introduce him to
abstract algebra and category theory kind of early, because it seems like
something that might be easier to understand if you know less about math than
if you know more about it.

~~~
throwaway729
Abstract algebra seems doable at a young age for a typical child (say,
somewhere b/w late middle school and late high school depending on the kid).
I've done bits of group theory with kids in that age group before. It usually
gets pretty well, but we never get past the first chapter or two. Basic
proofs, but it's a good introduction to what "real" math is like.

IMO category theory would be a waste of time without first going through a
mathematics undergraduate course of study.

Getting past the preface of a reasonable book on category theory requires
internalizing the idea of a natural transformation. If you can't get that far,
you won't get anything non-superficial out of studying category theory.

Understanding what a natural transformation is requires at least one example
you can relate to. Understanding why it'd be useful to abstract away from that
particular example requires knowing enough about at least one other example.

And to do anything even moderately interesting in category theory you need a
fair bit of mathematical maturity, which means being able to write and read
proofs together with a bit of knowledge about modern logic, analysis and
algebra. Without that, a lot of the motivation for category theory is kind of
lost (and probably most of the available exercise aren't even comprehensible.
And learning math without exercises is close to impossible.).

~~~
mathgenius
There's quite alot you can do with _finite_ categories. Along the lines of "a
group is a category with one object". etc. I'm pretty sure a sharp 12 year-old
could get this.

~~~
throwaway729
Yeah, I suppose that's true.

You'd have to pick your topics carefully and probably reformulate a lot of
definitions. And you'd need the student to think it was cool for its own sake.
But I could see this working out.

------
adamnemecek
Unless you remove the concept of a teacher and replace it with a person who
helps you with your school work when you get stuck, schools won't be fixed.

~~~
sethammons
I like the idea of reciprocal teaching. You view well made lectures from home,
and practice at school, where an expert can help you when you stumble.

------
platz
Tom Lehrer: New Math
[https://www.youtube.com/watch?v=DfCJgC2zezw](https://www.youtube.com/watch?v=DfCJgC2zezw)

~~~
slavik81
I enjoy this song, but it is rather dated. The new and confusing way of doing
math he describes is the way I learned it in the 90s. It's mostly confusing in
the song because it's done quickly and the visualizations added in this
version are intentionally obtuse.

The song is occasionally used as an argument for going back to the old way,
but it seems somewhat contradictory when parents of school-aged children
aren't old enough to have experienced the old style of math instruction he
advocated for. New math was a trend from the 1960s, so you'd have to be
pushing 70 to have experienced elementary school math before it.

~~~
ghaff
What the "New Math" was about as I remember/understand it--I suppose that's
what I went through we also did plenty of arithmetic drill--was a lot of
emphasis on simple set theory, doing arithmetic in different bases, etc. As he
jokes in the song, the focus was on certain types of mathematical theory as
opposed to being able to add, multiple, divide, and subtract.

Of course, this sort of tension is present in a lot of academics. Focus too
much on the theory and students can't actually do anything useful; and many
will be completely lost. Focus too much on the rote learning and the students
don't actually understand any underlying principles (and, in the case of
arithmetic, can't actually do anything a $5 calculator can't today).

~~~
WalterBright
If you don't understand arithmetic, a $5 calculator will inevitably produce
the wrong answer for you.

Sometimes people question the value of teaching math to kids. But I can say
anecdotally that the people I've met who did not understand arithmetic
correlated strongly with people who were disasters with their personal
financial affairs.

~~~
ghaff
Oh I fully agree. For Example, I can still remember having an argument with
someone who just couldn't understand that it wasn't some banking conspiracy
that you paid mostly interest at the beginning of a loan. I also tutored for
an economics class and the lack of understanding of really basic mathematical
concepts was frightening.

~~~
WalterBright
College econ textbooks also dumb down the math for their audience. Makes you
wonder about the quality of the economists' work.

------
ch4s3
I just read this National Review article [1] criticizing common core, but it
all kind of makes sense to me. I get that when you have 6 of soemthing and
visually move 4 away, two things remain. IS there something more insidious I'm
missing here? Is the idea that 82 is 0 hundreds, 8 tens, and 2 ones all the
crazy? I kind of like it. But, I don't have kids and the only thing I ever
taught kids was how to tie knots and sharpen an ax at summer camp, so what do
I know.

[1] [http://www.nationalreview.com/article/373840/ten-dumbest-
com...](http://www.nationalreview.com/article/373840/ten-dumbest-common-core-
problems-alec-torres)

~~~
maus42
Some of that is just bad material (#3, shapes that should be shaded are not
shaded). Others try to explain how at least I do arithmetic mentally (the
particular example 7 + 7 feels silly because the answer was drilled to my
brain in primary school, but the idea of decomposing number to parts that
easier to sum together is sound -- and it feels like nice intuition to
algebraic way of thinking). On the other hand, insisting in drawing graphical
representations might be boring and feel silly if you already got it.

In other words, the Common Core seems to get flak because some of the material
is simply bad and sometimes seems not to have good idea how to convey the
Common Core ideas.

~~~
ch4s3
That's my read on it as well. Funny that you mention 7 + 7 which I've always
visualized as 5 + 5 + 2 + 2, or reduced to 10+4 in my head. Whenever I add 7
to anything that doesn't end in 3, I quickly add 5 and 2 instead of 7. With
respect to base 10 math, 7 is awkward.

------
jcoffland
It seems like a lot of parents these days are appalled when schools actually
make their kids do work. Sure it's not fun at first, especially when you're
not used to having anyone tell you what to do, but once you get the hang of
it, work is fun. It's not about an oppressive system making you in to another
drone. Kids should be encouraged to think for themselves but the humans that
came before us have a lot of beneficial knlowedge to share. Teach your kids to
not take advantage if this and to play all day at their peril.

------
sopooneo
How about this for a "reform": small, incremental improvement to the system
year be year. Because we have one of these "revolutions" in education
approximately 1.8 times per decade since 1970. And no matter how noble the
ideas, they almost always turn to nonsense by the time the hit the classroom.

------
sporkologist
Meanwhile in Finland.....

