
Just teach my kid the math - ColinWright
http://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html
======
mratzloff
When calculating in my head or on paper, I value quick estimations moving to
greater refinement. Common Core math seems somewhat similar to this.

I never subtract, only add up from low to high. If the two numbers have the
same number of differing digits, I move from most significant digit to least:
73-57=10+6. If they cross a round number threshold greater than 10s, I get to
a convenient base first: 2018-1995=5+18; 173-57=43+73=110+6.

For multiplication, I do something similar: 6x57=300+42;
42x23=(42x20=800+40)+(42x3=120+6).

For division in my head, I use a kind of binary search to get a quick estimate
and then refine it. 846/42=42x10? 42x20+6. 20r6. 6/42=1/7\. 0.15x7>1,
0.14x7<1\. 20.14.

From my understanding, the Common Core approach to math is much closer to this
approach I developed intuitively than the traditional methods. I'm sure many
others developed similar approaches. If I want an answer accurate to more than
two decimal places, or if the math gets too complicated to keep in my head, I
just use a calculator.

~~~
meuk
Well, it is super useful do be able to do exact arithmetic. For example, to
not get scammed when you buy anything, or share a bill. I've seen American
university students who don't know how to compute a percentage of a given
amount - so I'm not very impressed by common core math to be honest.

That being said, it's probably a cultural thing too. I noticed that in the USA
(at least in California?) it is customary to exclude the taxes from the price
that is displayed on the price tag. Since the tax rate is different for
different products, it's pretty hard to compute the actual price that you pay,
and in practice you just take whatever you need and don't have an idea what
you pay. In addition, it is not very usual to split the bill (I'm not talking
about simply dividing the price by the number of people, but about actually
computing the price of the stuff you ate, and not paying more than that).

When I go to the grocery store, I usually keep a sum of the price in my head
while I pick products. That way I'll know if something is off at the counter.

~~~
omnius19
The mathematics standards for Common Core were released in June 2010. So
college freshmen this year would have been in 5th grade (seniors in 8th grade)
at the earliest when introduced to Common Core style mathematics. Probably
later, since schools needed time to adapt to the new curriculum and train
teachers in the new methods. Seeing as how Common Core places a heavy emphasis
on developing skills in grades 1-8, I don’t think that current college
students are a good benchmark for the Common Core standards. Talk to some
college students in 5-10 years to get a better idea of how things are
progressing.

~~~
threatofrain
Also I would say that early CA Common Core for math basically just pushes up
the current curriculum up about half a year, a mild improvement; more
importantly it's a cleaner spec for outcomes.

It doesn't really re-order the curriculum, it uses a few new terms, there's
mildly more emphasis on word problems, and there's earlier introduction to
linear sequences. It's just a few touch-ups here and there, presumably to
prepare kids better for Algebra 1. The whole reform is a modest start.

------
noir_lord
I did A-level maths, I've programmed computers for 30 years since I was a kid.

Ive implanted algorithms to calculate solar irradiance varying by orientation,
inclination and latitude.

I don't understand what my 7yo stepsons maths homework is asking him to
do/learn.

It's just weird and I'm not sure he always does either, it teaches the how
(weirdly) but never the why, I've started teaching him how to understand the
practical uses for maths.

We play games now like "how many bricks in the wall" when we are out and
about.

I struggled with maths as a child because I never saw what it was _for_ , once
you realise that it's the language of the universe things click why it is
important, I'm not a mathematician nor do I need to be but I still appreciate
those who are.

~~~
ColinWright
My (very limited) experience of more recent homework is that it makes perfect
sense in the context of what the teachers are trying to teach, but no sense
out of context to people who learned their maths decades ago.

If you'd care to send me a photo of an example of the homework then I can try
to give you some context and understanding. My contact details can be derived
from my HN profile. I might be a little slow to reply at the moment as I'm in
the middle of other things and only surfacing occasionally.

~~~
TheOtherHobbes
And techers are trying to teach how to make change?

I understand “anchoring to fives and tens” but I don’t understand why anyone
thinks it’s a good way to do anything except confuse kids.

Does independent research prove these approaches increase numeracy?

~~~
dragonwriter
> I understand “anchoring to fives and tens” but I don’t understand why anyone
> thinks it’s a good way to do anything except confuse kids.

I found it a huge boost to my ability to do computations without paper or
other tools when I learned it in elementary school; I think it's valuable, but
I'm not certain that the manner in which it is often being taught now is
helpful (which, AFAICT, is not so much a matter of the Common Core standards
as poor curriculum attempting to implement the standards.)

~~~
b1daly
I think the problem with how these new concepts are presented, is that they
are taking these ad hoc methods of doing arithmetic and trying to turn them
into algorithms. My guess is that this is driven by the need children have to
know how to get the “the right answer.”

The traditional algorithms aren’t very intuitive, but they work. Trying to
make an algorithm out of the various ways you can break up a problem, ad hoc,
seems bananas.

------
zaroth
I’ve watched my daughter do her 3rd grade math homework both ways. She’s an
ardent rule-follower at her age (and can’t quite understand why the boys in
her class can’t stay out of trouble) and really enjoys doing her math
homework. Watching her work on the extra credit math assignments and her get
so exited when the multiplication problems extend into 8 digits is a lot of
fun.

Often she will do the problem the “new” way taking up maybe 10 minutes and a
whole sheet of paper which looks more like an art project, and then when she’s
done check her work the “old” way in a few seconds, and then go back and find
the mistake in the drawings.

She’s happy to do it “because that’s the way [my teacher] wants us to” but
she’s faster and better at doing it the traditional way.

My personal opinion is that CC is perhaps better at teaching basic math skills
to the bottom 50% and is less likely to lose students along the way, but at
the cost of holding back the top 50% of students approximately 1 full grade-
level by the time they graduate high school. From my limited sample sized poll
students see the new methods as being just as ridiculous as parents see them.

And parents are generally pretty frustrated about this whole fiasco:
[https://youtu.be/wZEGijN_8R0](https://youtu.be/wZEGijN_8R0)

~~~
OscarCunningham
The amount of time and space needed for her to do the problem on paper are
irrelevant. The only important thing is that she's understanding.

~~~
zaroth
It’s more the incredible amount of time spent drawing it out and ultimately
often arriving at the wrong answer due to drawings becoming so overly complex.

Despite her spending tremendous care at trying to neatly diagram exactly as
she was taught, the methods apparently do not scale well past 3 significant
digits.

It becomes an exercise in frustration which can take up to 10 minutes trying
to solve a multiplication problem which she knows how to do properly in the
blink of an eye.

There’s lots of graphite going on the page, but I’m highly skeptical of any
learning. Certainly any love of math quickly goes out the window during the
process.

------
nitwit005
What seems to happen in practice is the parents end up asking the teachers why
they're teaching that way, and the teachers can't actually explain it.
Obviously, the parents don't walk away impressed.

~~~
sethammons
When I got my teaching credential for high school math, it became apparent and
was openly recognized that many grade school level teachers choose that level
of certification because they are, themselves, afraid of "math expected at the
high school level." We expect many teachers who are math-phobic to lay down
the foundational layers of mathematics with our kids. They cling to whatever
the pre-made material and lessons are in the texts and often don't know why
things are to be taught the way the texts want. Scary stuff.

------
geebee
I don’t have any problem with common core or “new math”. I was a math major
myself and have two kids in public school in SFUSD, and I think it’s valuable
to develop ease and fluency in problem solving. An example in another thread,
2015 - 1985, is a good example. I like the idea that kids learning arithmetic
would see how to solve this without a plug and chug approach.

Here’s why I don’t find it promising: this is mimicry. The US found that other
countries that teach math well don’t rely excessively on plug and chug. But
these countries draw math teachers from the top math students. These teachers
teach this way not because there is a new set of standards to adhere to but
because this is how people who are good at math do math.

Until the US draws math teachers from top math students, the new math will
just be a new set of plug and chug steps. This is why the parent in the blog
entry is frustrated- to them, new path is just more steps than old math. It
may feel that way to the teachers as well, if they aren’t understanding what
they’re doing.

If we want to mimic Finland, we need to start by drawing teachers from the
upper echelons of math students. And once you do this, much of this “new math”
will happen organically. That may in fact be the only way it can happen.

~~~
dorchadas
The problem comes with how elementary schools are structured here (at least
the ones in the district where I teach). If you even have enough teachers for
each teacher to only have one grade (i.e. no split classes), they've got one
teacher teaching each class until 4th or 5th grade. So you have the same
teacher teaching history, science, math and language arts. This person
probably struggled with math and often shuddered at the thought of the math
portion of the Praxis test to become certified. They don't know how to do the
math, but, because of how elementary schools are taught, you can't just hire a
math teacher to teach math to all the students.

Personally, I could easily see the benefits of shifting the students to a
schedule where you went to a math class, taught by someone who knows math
(i.e. the best math students), at the very beginning. It would also help
because you could then make it where someone who is good at teaching, say,
history, doesn't have to worry about passing a math content exam. Or at least
one as in-depth as the math teacher.

But, you also have to attract people to teaching. It's a thankless job, and,
in my state, they're currently under attack on pension reform and pay and
such. Our governor wants to remove mandatory sick days, for instance. And he
wants to guy the pension. Or, he'll keep it all and gut all these other
programs and then blame it on the teachers. Public education in the US as a
whole is under attack, and that's part of the problem of getting the best math
teachers. I'd be willing to bet Finland doesn't have to deal with the issue of
charter schools like is currently happening in the US, either.

------
dahart
> We need to communicate the true goal of given exercises to parents.

This is spot-on, and can't be emphasized enough. The goals also need to be
communicated multiple times, more clearly to the students, in writing in the
homework. So much of the homework asks what seems like trick questions when I
look at it. Whenever they weren't paying 100% attention in class, it seems
like trick questions to them too. The exercises feel like they intentionally
withhold stating the goals clearly for fear that it would give away the answer
or fail to make the students struggle enough on their own.

> Make showing/explaining your work interesting.

This is true, but tough. Not every exercise should be an essay answer or story
problem. The homework my kids get has lots of variations on exactly the
example the author gave, and it doesn't feel like it's helping generate any
appreciation for showing the work or for coming up with alternatives. It
usually just feels like forced busywork.

My real appreciation for showing my work only came in college physics when I
finally realized that I make too many mistakes when I try to think my way
through steps. Writing down every minor step was finally more efficient and
accurate than not doing it.

------
toomanybeersies
This is a really good essay on what's wrong with how we teach mathematics to
children: A Mathematicians Lament
[https://www.maa.org/external_archive/devlin/LockhartsLament....](https://www.maa.org/external_archive/devlin/LockhartsLament.pdf)

It's rather long, at 25 pages, but it's a very good and entertaining read. It
was written in 2002 but it still holds water today.

------
credit_guy
My problem with the "new math" is the lack of volume. Developing a sense for
the numbers is best done by working more with numbers; in the "old math" kids
had to do thousands of additions in the first and second grade, and developed
ten times the sense of numbers compared to kids today.

Theory is theory, but practice is practice. Just get over the addition and
multiplication, please. That's not where the true math is. Don't spend so much
time on finding the true meaning of addition by carry, you won't have time to
teach kids logarithms and integrals later.

~~~
empath75
Learning by rote doesn’t teach you anything.

~~~
credit_guy
Are you sure that it doesn't teach you anything? Somehow the students of "old
math" were able to put a man on the Moon.

~~~
boomboomsubban
So you're advocating the return of the slide rule? As that's what was used for
most calculating, the "old math" method being too cumbersome for such large
problems.

~~~
ghaff
As someone who actually learned to use a slide rule before pocket calculators
became available, that's probably not the best example. Slide rules were good
for getting "[EDITED: precise not accurate] enough" results in various
situations where they could do so more quickly than solving by hand. You still
needed to understand orders of magnitude, precision, and generally having a
feel for numbers to use one.

Note also that a lot of calculations on the Apollo program were actually done
in part by hand by human "computers." There was even a whole movie about it a
couple years ago:
[https://en.wikipedia.org/wiki/Hidden_Figures](https://en.wikipedia.org/wiki/Hidden_Figures)

~~~
boomboomsubban
Those human computers used slide rules, as even with them the problems were so
ridiculously complex they took months. Their were many different slide rules
with varying degrees of precision

[https://www.nasa.gov/audience/forstudents/k-4/home/calculate...](https://www.nasa.gov/audience/forstudents/k-4/home/calculate_feature_k4.html)

------
bfung
Is there a common core method to teach arithmetic in different a different
base, like 8 or 16?

The "old way" algorithm still works with different bases, you just change
extend or truncate the rule for when to carry.

Easy to teach your kid hexadecimal arithmetic using old way, like how my
parents taught me in like grade 4 or 5 - and now I program for a living, haha

~~~
gus_massa
If you ignore the "anchor to 5s" part that is ridiculous, the other parts work
in other bases too.

    
    
      D3-A7 = (D3-B0) + (B0-A7) = (D3-B0) + 9
            = (D3-D0) + (D0-B0) + 9 = (D3-D0) + 20 + 9
            = (D3-D0) + 20 + 9 = 3 + 20 + 9 = 2C
    

(I swear that I didn't cheat to make the calculation and I made it in the
"string" representation of the hexadecimal form, without looking at the
decimal form.)

In hexadecimal can try to anchor to 8s, it should work. Perhaps anchoring to
4s may be better?

[Disclaimer: I don't like it, but the method to do the calculation works in
other bases.]

------
mocopoco
This is like the things you develop yourself as a child although broken down
and over simplified.

Maybe this should just be for the less intelligent children who do not have
the skills to learn their own more efficient method.

I can see this wasting too much of an able pupils time.

Do you have streaming in America where you filter off children by ability like
in Europe?, If so then maybe this is good for the lower streams to gain them
insight into what more able pupils do anyway. (Though maybe not so
convoluted).

------
dictum
> For instance, our standard arithmetic algorithms are somewhat bizarre - they
> are the end result of a human process of codifying arithmetical thinking,
> designed with the extra goal of using as little of precious 17th-century ink
> as possible

I've long thought that this is partly why Mathematics are, paradoxically, at
once terrifying and tedious for students. To learn a second language, you must
immerse in it, using it as much as you can. Math has been attached to a
language that is not used in daily life (except in a few situations, mostly
very basic usage) and where the parallels to real usage feel contrived. If
they weren't contrived, the question "what's the point of learning this" would
get much clearer answers.

When I was a student, I found it curious how I had trouble expressing certain
concepts in that language, but when working with the same concepts in a
programming language, things were much clearer.

I can't offer a solution, but I think learning programming at a young age can
help, though I'm personally against requiring it in classrooms, increasing the
pressure on kids who are already exhausted with the rest of the curriculum.

------
tomxor
> We need to be sure not to insist on one approach when analyzing a problem

It's encouraging to hear from educators out there who understand communicating
the value of problem solving and comprehension is more important than rigid
adherence to methodology and procedure.

I remember the most useful aspect of my secondary school education (12-16yr)
was learning how much I liked problem solving. However I came to this
realisation through solving various simple math homework problems without
following procedure (procedures which I remember finding particularly
irritating for not explaining themselves) only to be lectured on how I had not
followed the rules in spite of arriving at the correct solution and
understanding the problem (albeit not well enough to figure out how the
procedures worked).

My teachers did exactly the opposite of what the above quote is saying - they
insisted on one approach, without explanation, and it totally alienated me
from math at the time. Thankfully I was never a very "good student" and it
didn't dissuade me from enjoying the problem solving aspect, but it did leave
a lasting impression of "i'm not good at math".

~~~
autokad
its my understanding that common core math is of the theology that its more
important to learn how to think than to solve the question.

its also important to understand that if a kid uses 'the old way' to solve a
question, they do not get points for it. remember, this is coming from an
ideology that being taught how to think is priority number one, and priority
number two is to not deviate from that thinking.

it was always frustrating in hs, especially calculus when I would get 0 points
for questions i had right because i used a shortcut, trick, or simply solved
it more efficiently. then I got to college and the professor encouraged that.
on the first major exam I scored a 96, far above anyone else, and the
professor asked to shake my hand, because no one ever solved equations so
efficiently before.

i attack and do problems differently, sometimes out of necessity. dyslexia is
an adversary of mine, and i find it better not to fight it on its home ground.
i also read slow, and take much longer to absorb a problem into my head than
other people. but once i do, i own it. unless people make me do it their way
in the process. its like running 100m hurdles with 30 hurdles.

im sure you love how you solve problems. you can do it fine your way, i cant.
once you start forcing everyone to think one way and evaluating them, your
measuring each animal how well they climb a tree.

------
jonsen
I just asked my stepdaughter "What is 33 minus 18?"

"Because ... 18 plus 18 is 36 ..... it's 18 minus 3 ... 15!"

~~~
bfung
Isn't it suppose to be:

    
    
      18 to 20 is 2
      20 to 30 is 10
      30 to 33 is 3
      2 + 10 + 3 = 15

?

Also, how does she know it's 18, plus an additional 18? Why not 18 + 20? What
happens if it's 33 minus 21? 21 + 21 is 42...

Just curious - but at least she's got her own system that works!

~~~
jonsen
"If it's 33 minus 21, I'd probably do 3 minus 1 and 30 minus 20, because it's
easy numbers."

------
darkkindness
> The 21st-century is not looking for humans who serve as calculating
> machines, but instead it seeks problem-solvers and innovative thinkers.

I distinctly recall how one of my grade school teachers justified learning
maths: "In the future, you aren't going to be walking around with calculators
in your pocket!" Yet today I routinely check even simple calculations with the
calculator in my pocket.

I've found that error-checking is the key to doing 'well' in maths, yet that's
something humans are bad at and something machines are great at. Given this,
I'd love to see a future where learning to do math strongly emphasized
learning how to best leverage computers for error-checking. That's a skill I
wish I had developed earlier...

------
hprotagonist
[https://m.youtube.com/watch?v=UIKGV2cTgqA](https://m.youtube.com/watch?v=UIKGV2cTgqA)

“remember, base 8 is just like base 10, really, if you’re missing two fingers.
Now, anyone who gets this right can stay after class and help clean the
erasers...”

~~~
ghaff
The funny thing is that New Math's considerable focus on non-base 10
arithmetic and boolean logic was an academic exercise largely divorced from
practical application for the vast majority of people at the time. While that
may still be true in terms of the overall population, of course they're highly
relevant to both programming and digital circuits.

~~~
hprotagonist
Indeed. I’m post new math, but I had Boolean logic in 10th grade and it was a
very helpful step up.

------
walshemj
That's <adjective> Arithmetic not Mathematics

------
patja
I thought Hacker News preferred original source material rather than
reblogging.

Or is the original source not preferred in this case for some reason, for
example being hosted on Medium?

Original source: [https://medium.com/q-e-d/just-teach-my-kid-the-expletive-
mat...](https://medium.com/q-e-d/just-teach-my-kid-the-expletive-math-
fb6f495be906)

~~~
sctb
Thanks! We've updated the link from
[http://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html](http://www.solipsys.co.uk/new/JustTeachMyChildTheMaths.html).

~~~
ColinWright
And just for completeness ... now reverted because there is a good reason for
re-hosting the article - Medium is blocked in some countries, and the re-
hosting is to make it more widely available.

------
dazc
The original source you linked to in the article is a lot easier to read.
sorry/

[https://medium.com/q-e-d/just-teach-my-kid-the-expletive-
mat...](https://medium.com/q-e-d/just-teach-my-kid-the-expletive-math-
fb6f495be906)

~~~
ColinWright
That's fine - I'm hosting the copy (with permission) because medium is blocked
from some locations.

Personally, I _hate_ medium's default settings - I just feel like my face is
being pushed through mush. But that's a personal thing, and I've certainly
lost that battle.

<fx: shrug />

~~~
katet
Thank you for that - Medium is blocked in Malaysia, for example, which I can
bypass by using Google DNS on WiFi, but not on 4G...

~~~
zbentley
Interesting. Is it blocked for content reasons (i.e. it hosts political
material that is offensive to the censors of the local internet
infrastructure) or techno-political reasons (Medium-the-hosting company is
banned from providing content in the area due to the company itself)?

------
alphabettsy
Is the issue that parents don’t understand because it’s different from how
they were taught or the teaching method does not work?

------
maximexx
There is a reason why most people hate math.

IMAO the current system of teaching math is ancient and above all deprecated.
We should not punish our kids with it. I mean, what's the point of drilling
stupid sums if you'll hardly ever need it in your life? I think it is totally
stupid and irresponsible if anyone does calculations without a calculator for
almost any application, not excluding: store checkout, health care, aviation,
etc.. The current educational methods are way pre-computer era, it desperately
needs an upgrade.

So why not start teaching kids concepts and let them use the technologies we
create to solve problems that our minds are not wired for? Ever seen a teacher
without a cheat sheet checking the answers? Guess why? Because their own
calculations are too slow and above all not to be trusted! And should I not
use a debugger because theoretically we can write proper code without it? Come
on..

Please stop teaching our kids deprecated workflows. Teach them the best
practice, the best way we know and can do now, because: "As the twig is bent
the tree is inclined".

~~~
dorchadas
You want us to teach them best practice? Then we need to teach them maths,
without relying on calculators. I teach secondary maths (specifically Algebra
II), and they can't understand what I'm supposed to be teaching them because
they have no clue how numbers work. Why don't they know this, if they're
15/16? Because they were given calculators at too young of an age and know
"just push the button". What you're arguing is for a complete removal of
teaching math, period. Also, why would you want to pull out a calculator every
time when it's often quicker to do some mental calculations in your head? For
instance, I've seen my students multiply by _two_ in the calculator. Then be
amazed when I can just say it.

Over-reliance on the calculators is already a huge issue, and we don't need to
make it worse.

~~~
maximexx
> What you're arguing is for a complete removal of teaching math, period.

No. I suggest focussing on explaining concepts, not drilling sums. And explain
them why in ancient times the teacher used to use a cheat sheet because
drilling didn't work because science found out our minds are not wired for
that.

Besides, from over 7 billion people on Earth, how many need Algebra 2? Please
try to be honest and give us here an estimate teacher. In your life Math is
important apparently, but in most lives it's not. Teach it to those interested
please and don't push it through the throat of those not interested.

~~~
ColinWright
> I suggest focussing on explaining concepts, not drilling sums.

The research I've seen suggests that having a bunch of stuff at your finger
tips then makes it easier to have the concepts crystallise. Trying to start
with just the concepts doesn't work.

So what's needed is both, significant practice to help embed the simple
underlying facts, with extensive exploration of the links between the facts to
help the concepts emerge, be identified, and then distilled.

To me, it seems that almost everyone goes full extreme: "Must do this", "Must
do that", whereas, as in game theory, it seems obvious that a mixed strategy
is likely the best option.

