
How our 1,000-year-old math curriculum cheats America's kids - chrisgd
http://www.latimes.com/opinion/commentary/la-oe-adv-frenkel-why-study-math-20140302,0,5177338.story#ixzz2uosSUJh4
======
bane
I was a _terrible_ math student in school.

Looking back, it wasn't because the material was hard, or boring, but because
it was completely unmotivated. They may as well have been asking me to
organize piles of toothpicks or count ceiling tiles to fill up the class
periods. There was simply no sense to it.

I think this is partially understood, and the attempted solution is to try to
find applications for the math you're learning. Except that once you hit even
basic algebra, you quickly run out of applications a young student can relate
to. So they go home, ask their parents "what do _you_ use Algebra for?" and
get "I don't." and that's that.

I think, along with application concepts, the history of these maths...why
were they created, about the creators who came up with the concepts, what were
they trying to solve, let's solve the same problems with these new techniques,
etc. This would have grabbed me and pulled me in. Instead you sometimes get a
little box in the reading quickly going over all this (if you are lucky)
before a hundred problems are dumped on you to drill through. It's rarely
talked about in class, and if it is, it's by a teacher who doesn't know or
appreciate the value of this history at all.

By doing this you show applicability to entire fields, even if the child
doesn't understand what's involved in the field. Those kids that say "when I
grow up I want to be a biologist" will encounter stories about people who
learned to apply logic or math or fractions or whatever to solve difficult
problems in biology or whatever, and then relive those moments as they try to
solve the same or similar problem using the tools they were just given.

~~~
Pxtl
The problem is that if you _don 't_ fill the period with busywork? The
students don't build up the intuitive, gut-level skills they need to handle
the higher-level stuff.

Math requires building _muscles_ in your head, and _muscles_ take reps. Lots
of reps. Let's look at the elementary level: it's not enough to simply
introduce BEDMAS or least-common-denominator and write a few problems that get
the student to check off "okay, I know that" from the list of stuff they know.

The student has to be so practiced at these concepts that they could do it
while trying to juggle 9 other extremely complicated brand-new concepts in
their head because _that 's what you need to do_ when you build calculus upon
factoring upon algebra upon fractions upon arithmetic.

If you fail to do this, you get kids walking into grade 9 math class who've
forgotten everything they were supposed to know about fractions and teachers
have too much new material to cover to re-teach fractions (my wife is a math
teacher. This happens way, way too much - too many students enter her class
missing necessary prerequisite skills). Students struggling with applying the
basics cannot properly grasp the new material - so the basics have to be _rock
solid_.

~~~
katbyte
personally, busy work just never sticks for me, i don't remember almost any of
the math i did in HS and uni that was just "do these problems over and over
till you remember it" because it just wasn't all that interesting, and this
goes for any subject.

However some concepts, limits, derivatives and integrals i remember perfectly
well (5+ years later) because my math teacher explained how the all fit
together, what they represented wrt the real world and how they can be useful
and that actually got me interested.

Yea you need to know the basics, but i daresay busy work isn't the best way to
teach them.

~~~
Pxtl
It's the difference between skills and knowledge. Limits/derivatives/integrals
are interesting knowledge so you can discuss them verbally, even if you don't
have extensive practice in using them.

The basic, core stuff is the opposite. Fractions, bedmas, etc. you don't care
enough to talk about, but if I handed a problem that used those concepts you
could do it in your head, because they're _skills_ that have been developed
down to an instinctive level.

Common factoring is dull. There's nothing to say about common factoring. But
if I show you an equation where you can apply it, you'll spot it instinctively
because you've had common factoring ground into your reptilian brain.

~~~
j2kun
There is quite a lot to say about 'common factoring.'

For example, nobody knows whether there is an efficient algorithm to factor
integers (where efficient depends on the number of digits in the integer).
However, there is an efficient algorithm to factor polynomials, and you can
write all irreducible polynomials of a certain degree as factors of one mother
polynomial.

Moreover, being able to factor integers efficiently would allow you to break a
lot of encryption schemes.

------
jerf
Focusing on the age is probably the wrong approach. Math true then is still
true now. The problem is that the curriculum is now held sacred (and I mean
that _fully_ as nastily as possible), and it is being held there by people who
are now the blind-leading-the-blind unto the sixth or seventh generation. I've
gotten around in the math world a lot since primary school, and what I was
taught vs. any actual modern mathematical practice, across the entire spectrum
from utterly practical to the utterly theoretical, bears surprisingly little
resemblance to what I wasted my time with in school. The current curriculum is
bizarrely overfocused on real analysis to the near exclusion of all else (a
few other disciplines will be introduced, generally poorly motivated either
practically or theoretically, fiddled with for a couple of weeks, then
dismissed; matrix math, for instance... in primary school nobody ever gave me
a clue why we cared about this, and once you're done solving polynomial sets
of equations ( _itself_ an unmotivated activity), you're pretty much done),
and even if we grant that real analysis really is worth crowding out
everything else, it still comes with a very 19th century flavor to the whole
thing, too, wasting time on some dead-ends and missing some things that would
be both mathematically and practically useful, too. (For instance, numerical
approximations methods are usually covered as "Newton' Method For Finding
Roots", and that's it. There's several things I'd trade away in favor of more
of this, and it's easy to motivate why this is useful stuff.)

I'm pretty pessimistic in the short term about any efforts to reformulate math
curricula, though, due to the aforementioned blind-leading-the-blind unto the
seventh generation problem; math educators aren't even aware how bad the
problems are, let alone in any position to fix them themselves, or aware
enough to ask for help.

~~~
gus_massa
The curriculum changed. For example, logarithm tables were a standard topic. I
don't know haw many hours in a year were use to explain it. Now that subject
luckily has disappeared because it's not necessary.

Note: There are some tables that are very similar, for example the voltage of
a thermocouple.

~~~
j2kun
And yet, we somehow think that being able to draw an accurate picture of an
ellipse given its equation is useful, along with knowing the derivative of
every inverse trig function, and countless other things.

~~~
gus_massa
I agree that the exact form of an ellipse is not useful, but some general idea
is.

Other example is the method for long multiplication. I think that it's not
1000 years old, but I can't find a source. One of the formed methods was to
use square tables and the identity xy = ( (x+y)^2 - (x-y)^2) )/4\. It guesses
it was explained in schools, but now it's almost a curiosity. To use it, you
must have a book with the tables of the squares, and the last edition of those
books is from 1888:
[http://en.wikipedia.org/wiki/Multiplication_algorithm#Quarte...](http://en.wikipedia.org/wiki/Multiplication_algorithm#Quarter_square_multiplication)

------
sn41
As a person who does some math, I disagree with this article. I agree with the
author that mathematics is the language of abstraction, but do not think that
school mathematics should put abstract before the concrete. One would think
that the failure of "New Math" of the 1960s would have been enough:

[http://www.youtube.com/watch?v=8wHDn8LDks8](http://www.youtube.com/watch?v=8wHDn8LDks8)
[Tom Lehrer, "New Math"]

Just because something is abstract and more general does not necessarily imply
that it is more insightful than concrete calculations. I feel that abstract
mathematics should be confined to higher education. A good antidote to such
articles are these by legendary mathematicians:

[http://pauli.uni-muenster.de/~munsteg/arnold.html](http://pauli.uni-
muenster.de/~munsteg/arnold.html) [V. I. Arnold]

[http://ega-math.narod.ru/LSP/ch1.htm](http://ega-math.narod.ru/LSP/ch1.htm)
[L. S. Pontryagin]

------
bhixon
This is like learning art history instead of how to draw. How does the
"majestic harmony of Platonic solids" help a middle schooler actually do some
math? Why should the average sixth grade class learn about Riemann surfaces
when most of them haven't even learned what an exponent is yet?

An occasional lecture on a 'fun' topic (or even better, an assigned reading
and short essay -- expository writing should be practiced in every subject
starting in middle school or earlier) could be motivational. But the author
wants to spend "20% of class time opening students' eyes to the power and
exquisite harmony of modern math," which he expects would "feed their natural
curiosity, motivate them to study more and inspire them to engage math beyond
the basic requirements." That's fantasy land. The author sounds like what he
is, a UC Berkeley mathematics professor. If students are going to succeed in
his college-level courses then they need the basics down cold, which means
memorization, repetition, and application to concrete problems. That is, the
"stale and boring" stuff.

~~~
kaitai
I've taught a lot of enrichment seminars on Saturdays. They involve "clock
arithmetic," or Fermat's little theorem and the basics of RSA encryption for
older students, or fractals and ways of computing fractal dimension (and
exploring polynomials and iteration and Newton's method), or the differences
between geometry on a beach ball, a paper towel center tube, and a piece of
paper, or even a bit of Mill and Frege's ideas on how to define a number...
Kids love this stuff and they get really excited and they start asking
questions about infinity and making connections with their other learning.
They have fun, but the topics aren't fun -- they are important and useful!
Learning about solids has applications (if that's what you value) to proteins
and polymers and all sorts of funky stuff. Check out
[http://phys.org/news/2014-02-years-mathematicians-class-
soli...](http://phys.org/news/2014-02-years-mathematicians-class-solid.html)
for some new solids mathematicians have just discovered, inspired by
biological research.

Seems better than just learning to hate math. Our current system is certainly
not effective in teaching young people to add fractions, which I see as the
single greatest indicator for competence in college mathematics (sigh).

Ok, after another moment's thought your argument seems similar to "Why should
kids read stories and books? To succeed in writing dissertations they need
grammar. All that extra reading of literature should be confined to the
side..."

------
Steuard
I'm very much a math person, but I think this author is being rather naive. In
the current political climate surrounding education, it seems like madness to
say, "Teach math more like we teach art!" After all, art classes in the US are
pretty much first on the chopping block for the many, many people who think
education should be all about test scores and checklists.

I would _love_ to see more kids exposed to "real math" somehow. But there's a
valid question of how to make sure they wind up with practical, applicable
skills in the process, and I found the arguments here about "the value of
abstract thinking" too vague to feel convincing (at least to folks who aren't
already immersed in real math). I don't know the answers to those questions,
but I certainly hope we can find them.

~~~
jcampbell1
Not to mention, "The curriculum is 1000 years old" is a terrible argument from
a logical perspective. I have no idea if that means math is timeless or dated.

There are other funny gems.

"A mathematical statement is either true or false"

~~~
arbitrage
Gödel might have something to say about that. Then again, he might not.

------
geebee
I read that article over the weekend. I agree completely, but it's downstream
of a bigger problem. Think of it this way - when we file the bug fix, the
report will reference a different bug fix that solved this one downstream.

We need to draw math teachers from the top tier of math majors (or physics,
stats, etc). And if we do that, it's very likely that people with real insight
into math will teach it very effectively but less mechanically.

One thing I've noticed is that the US system loves a "plan". This might be a
result of the career ladder - a teacher is on the bottom rung, whereas someone
who sets the curriculum for all teachers has moved beyond that lowly spot. But
what we really need is an armada of accomplished math majors in actual
teaching positions.

Without that, the plan won't really matter. With it, the plan? It matters,
sure, but I'd personally be inclined to give quite a bit of latitude and
autonomy to people who were in the top tier of their class and majored in math
and who are inclined to teach.

~~~
DerpDerpDerp
> We need to draw math teachers from the top tier of math majors (or physics,
> stats, etc). And if we do that, it's very likely that people with real
> insight into math will teach it very effectively but less mechanically.

Then don't pay me 25%-33% of what I'd make working in industry.

------
Spooky23
I don't think that you can appreciate this stuff until you actually have the
mechanical background in math.

Unlike most subjects in K-12, you can't BS math. You're right or wrong.
There's no subjectivity in evaluation, and no opportunity for lazy students
like me to BS a tired teacher with flowery prose that doesn't say much.

Why not make math accessible in easier or more practical ways? My trigonometry
teacher walked us out into the schoolyard and gave teams of students
assignments to measure the heights of various objects. It was a simple thing,
but it made the not-so-interesting mechanics of looking up sine/cosine/tangent
in some table real.

~~~
j2kun
This is the viewpoint of an engineer. The salient difference in thought is
that the goal is rarely to be right (initially), but to get insight about
mathematical stuff.

Mathematicians do (and students should) focus on proofs over computations, and
there is an extreme amount of subjectivity there. If you produce a false
proof, it can nevertheless be beautiful and yield fantastic insights.
Likewise, a correct proof can be unsatisfying and ugly. Your goal then is to
revise it (or completely rewrite it) to make it more beautiful and insightful.

Here is an example: the 7 Bridges of Konigsberg problem is one of the most
famous (solved) problems in all of mathematics. One can easily give a proof by
exhaustion, but that is wholly unsatisfying and perhaps the ugliest possible
proof. A much better proof involves some insight into graph theory, and a
satisfying and elegant proof would give you a characterization of these kinds
of trails in graphs.

You don't need a mechanical background to start trying to solve such puzzles
(I know because I've taught it that way), and you don't need any mathematical
background to appreciate the very elementary proof. But as you let students
flounder with puzzles like these, you can slowly introduce technical matter.
The point is that it has a context they care about (people like working on
puzzles!).

~~~
ghaff
I guess I have an engineering viewpoint as well--which may not be surprising
because I, well, was one. I never especially connected to geometry with its
proofs in high school. What I did learn was lots of basic trig and algebra and
the beginnings of calculus (which I took more of in college). The result is
that while I've never had much of an interest or flair for advanced math, I
did develop most of the math skills I needed both for school and, more
importantly, through career and life.

I've had stats as well. As I was just discussing with someone in a different
context, I think stats, accounting, and similar applied math would be far more
useful to most students than either most calculus (past simple differentiation
which is used in a lot of contexts), proofs, or set/group theory. And,
arguably, could be linked a lot better to real-world applications.

~~~
j2kun
The question is what are you trying to develop in your students: factual
knowledge or mathematical thinking skills? I think it's the latter, and if
that's the case then proofs are by far the best way to do it.

And do you really think students would be any more motivated to learn about
accounting than they are about current math? I mean, come on, nobody wants to
do that stuff. It's a chore even for adults.

------
dabrowski
This reminds me of Lockhart's Lament, which I highly recommend reading
[http://www.maa.org/sites/default/files/pdf/devlin/LockhartsL...](http://www.maa.org/sites/default/files/pdf/devlin/LockhartsLament.pdf)

~~~
chrisBob
That was a fun read, but no one can teach that way. You can't become a teacher
by studying math, physics, chemistry, biology, literature, french,
programming, history, geography or english. You become a teacher in the US by
getting a teaching degree. I believe that is the biggest problem we have in
the US education system.

Teachers only need minimal knowledge of their subject, and if someone
discovers that they don't actually like teaching then they just keep doing it
anyway because they got a teaching degree, and can't do much else with it.

~~~
DerpDerpDerp
I know a number of math teachers who have undergraduate degrees in math, and
then attended a 2 year masters program to get their degree in teaching.

I also know a number who came from a humanities background, and "learned
enough math" in the single, poorly taught math-for-teaching class they had in
getting a masters.

One of these groups makes better teachers (and likely has a wider career path,
because of the undergraduate degree).

~~~
chrisBob
I also know some smart teachers that started with something else and ended up
teaching high school. I have more examples of people who got a degree in
something else and wanted to teach, but then found out how hard and expensive
that transition is.

------
drakaal
Ok. First I'm not taking lessons from anyone who plagiarizes. This is a re-
write of:

[http://j2kun.svbtle.com/you-never-did-math-in-high-
school](http://j2kun.svbtle.com/you-never-did-math-in-high-school)

Which may also be someone's work, but it was one I read recently.

Second, I learned some Calculus in school, how about you? That is not a
subject a 1000 years old. So we haven't been teaching it that way for 1000
years.

Third, did this guy not have story problems? Applied Math is basically what
this author is claiming we don't have.

Fourth, Graphing is pretty new. We didn't use to visualize plots because we
didn't have the resources, I can't tell you when that became part of algebra,
but it was in the past 100 years.

I can't believe LA Times ran such a poorly informed piece.

------
gus_massa
Math is like knitting. It's not useful to read about it. You must do it.

When reading an advanced math book for the fist time, I can spend 1 hour per
page, because I must copy the proof, try a few "improvements" that are dead
ends, do some exercise, and understand what is the main idea of that part.

It's very difficult to mixing some modern subjects without calculation. Most
of the time, the idea is to just hide the technical details so now it's
totally unintelligible and the only possible way to learn it is by
memorization. It's possible to teach magic and religion in the same way.

I like to add some comments about applications in my classes, but they are
marked as off topic, and they are short because usually there is no time to
spare.

Some of the proposed subjects are plausible to teach, for example module
arithmetic. I'd like to see a discussion in school about the module 2, 9 and
10 arithmetic. (2 is almost intuitive, 10 is easy to see, and 9 is the base
for the "rule of nines" test, that is usually teached without proof)

But, for example, Riemannian geometry is difficult. It's possible to pick a
sphere surface and show that the geodesic intersects in two points. Explain
the sum of the angles in a triangle? And then what? I don't have any intuition
about hyperbolic geometry. It's difficult to students to see what is happening
with the geometry in a plane in spite it's easy to draw, and we have paper
everywhere to tray.

> _I recently visited students in fourth, fifth and sixth grades at a school
> in New York to talk about the ideas of modern math, ideas they had never
> heard of before. [...] I used a Rubik 's Cube to explain symmetry groups:
> Every rotation of the cube is a "symmetry," and these combine into what
> mathematicians call a group. I saw students' eyes light up when they
> realized that when they were solving the puzzle, they were simply discerning
> the structure of this group._

It's an interesting topic, but the problem is not how much you can explain but
how much the students understand. Did he make any test to measure it? Can the
students solve the Rubik's Cube?

I'd like to see a test for this idea. Pick 10 classes and divide them in two
groups. Give 5 of them the traditional education and 5 of them the "modern
topics" proposal. Pick the classes at random. Pick the teachers at random!!!
Don't compare one class with a standard underpaid "traditional" teacher with
30 students and a class with a specially selected for the experiment teacher
with 10 students. And compare them with multiple choice exercise, not teacher
opinion or self report interest.

~~~
kaitai
Since you mentioned knitting (and I agree with your analogy), check out the
great intuition you can get about hyperbolic geometry via crochet and
knitting.

See how "parallel" lines act and the angle sums of triangles end up smaller
than 180 degrees:
[http://theiff.org/oexhibits/oe1e.html](http://theiff.org/oexhibits/oe1e.html)

A TED lecture is linked: [http://geknitics.com/2010/11/sunday-knitting-
science-hyperbo...](http://geknitics.com/2010/11/sunday-knitting-science-
hyperbolic-geometry/)

Hyperbolic baby pants also convertible into a 2-holed torus (not while on baby
I guess), with added note that on 2-holed tori you can make maps that require
8 colors instead of just 4 like maps on the plane or sphere:
[http://www.ravelry.com/projects/smbelcas/hyperbolic-
pants-2](http://www.ravelry.com/projects/smbelcas/hyperbolic-pants-2)

Geometry, topology, map-coloring theorems, crafts: all things many kids never
get to do anymore.

~~~
sitkack
This is absolutely beautiful.

------
w1ntermute
The biggest problem in education isn't the curriculum or method of teaching or
the teachers, it's how motivated the student is (which is usually a product of
their home environment). Trying to solve this social issue with "technical"
fixes is not going to succeed.

~~~
drcube
Try motivating art students to paint fences. And never show them any "art"
except different colored fences. That's what this article is about. If you
teach _real_ math, you can actually motivate people to want to learn it.

------
j2kun
> By hiding math's great masterpieces from students' view, we deny them the
> beauty of the subject.

The problem is that math's great masterpieces are problems and proofs. High
school math educators are largely the folks who hated doing proofs during
their education, and they're just as uninformed about what the interesting
open problems are as their students.

~~~
arbitrage
Wow, that's a really bold statement. Do you have a proof of that?

~~~
j2kun
This comes from my interactions with colleagues at my own undergraduate
institution. So it's biased evidence, but my institution was also one of
California's largest math teaching credential programs, so I think it's a
reasonable sample.

I can't say how many times my 'teaching concentration' colleagues would look
at a basic linear algebra problem (which requires a proof) and whine saying
things like, "I don't care about this stuff, it's so stupid and pointless, I
just want to get my degree so I can go teach high school math."

All irony aside, these are the students who actually _enjoyed_ the structure
of high school math, and were rudely awakened when they were asked to apply
their minds to reason. As a result, 'teaching concentrations' in undergraduate
and graduate school usually provide mathematically watered down courses and
automatic passing grades, and the teachers-in-training don't learn anything
new. They __certainly __don 't learn, for example, any mathematics that has
been done since 1900, or any open problems that aren't Millenium Prize
Problems. And god forbid they ask and try to answer an original question (as
they expect their students to do when they're confused).

This is what they mean by the "blind leading the blind."

------
WalterBright
Math curriculum may be rote and boring, but if you don't master arithmetic,
fractions, exponents, etc., you're going to have a lifetime of poor decisions
regarding investments, financing, etc., which will be very costly.

~~~
sitkack
You can teach exponential growth, compound interest and ratios before mastery
of the mechanics. To many, mastery of the mechanics inoculates them not from
darkness but from a scientific mind.

I know many people with a mastery of arithmetic and fractions yet still make
poor mathematical decisions. Conversely, I see people make projections and use
algebra w/o even knowing they are doing it.

Learning assembly isn't is a prerequisite for making useful higher level
software. Knowing all the words doesn't make us a better essayist. Yes the low
level stuff can make the result _better_ , the spark still has to exist for
the flame to grow.

~~~
WalterBright
I've talked with people who sell finance, and they make bank off of people
with a poor grasp of mathematical fundamentals. And that's just a small bit of
what it will cost a person to not master it.

~~~
sitkack
These people also don't understand concepts like exponential growth, I think a
lack of fundamentals is a symptom not a cause.

------
dalke
It sounds like a return to the "new math" of the 1960s. Compare this article:

> If we are to give students the right tools to navigate an increasingly math-
> driven world, we must teach them early on that mathematics is not just about
> numbers and how to solve equations but about concepts and ideas.

> It's about things like ... clock arithmetic — in which adding four hours to
> 10 a.m. does not get you to 14 but to 2 p.m. — which forms the basis of
> modern cryptography, protects our privacy in the digital world and, as we've
> learned, can be easily abused by the powers that be.

to the Wikipedia entry at
[http://en.wikipedia.org/wiki/New_Math](http://en.wikipedia.org/wiki/New_Math)
:

> Other topics introduced in the New Math include modular arithmetic,
> algebraic inequalities, matrices, symbolic logic, Boolean algebra, and
> abstract algebra.

~~~
j2kun
Any attempt to force a particular mathematical subject matter on students will
undoubtedly be ruined by a committee.

~~~
dalke
Such cynicism. What do you have against Feynman's presence in the California
committee to select, among other things, math books?

Ahh, I see. If you are the person behind "Math ∩ Programming" then I can see
what you have against that committee. Feynman wrote, arguing against new math:

> It will perhaps surprise most people who have studied these textbooks to
> discover that the symbol ∪ or ∩ representing union and intersection of sets
> and the special use of the brackets { } and so forth, all the elaborate
> notation for sets that is given in these books, almost never appear in any
> writings in theoretical physics, in engineering, in business arithmetic,
> computer design, or other places where mathematics is being used. I see no
> need or reason for this all to be explained or to be taught in school.

~~~
j2kun
The reason new math failed is because it was organized and administered by
committees (comprised of people who don't do math). So your example is
humorously evidence to my claim.

What does a committee do when they are tasked with designing a curriculum or
standards? They identify what should be tested, and then they pick the order
that the topics are taught, likely outlining a time constraint on how long
should be spent on each topic.

This is the problem. If you're looking for things to test your students on
then you will invariably add pointless content.

Physicists are no exception (they invented the elaborate and pointless
notation for vectors, the bra and ket). I don't propose we test students on
mathematical notation, not at all. I propose we actually have them _do_
mathematics (craft proofs, make conjectures), and I assert that any committee
trying to craft a curriculum would ruin that. They have already ruined proofs
in high school geometry.

~~~
dalke
"evidence to my claim"? But it's an example of a committee rejecting new math,
not proposing it. And do you seriously want to argue that Feynman doesn't "do
math"? Actually, it looks like you do. Why should only a certain type of math
practitioner determine the curriculum? Do we only let people like Ramanujan
set the curriculum? 'Cause _that_ won't work.

What you're complaining about is called "democracy." Yes, democracy is messy.
The current movement towards high-stakes testing in the US is anti-democratic
in part because it coalesces more power into fewer people. If you don't want a
committee then what do you want? A so-called "education czar" with absolute
power to make things work the way you think it should?

------
spenrose
Frenkel laid out his perspective in a mathematical memoir, much admired:

    
    
      http://www.amazon.com/Love-Math-Heart-Hidden-Reality/dp/0465050743

------
AutoCorrect
And then there's Common Core, which seems to teach children insanity.

~~~
Shivetya
I thought some if not most of CC in regards to Math was to follow the
Singapore model? Is there something inherently wrong with that approach?

------
SixSigma
it should be taught as two different subjects: arithmetic and mathematics

just like painting and decorating isn't called interior design

