By Professor Doom

In
previous posts, I’ve discussed how to add fractions. One way is very
simple, simple enough a child can learn. The other
way is how it’s done in public schools, using far more theory than an 8
year old can reasonably be expected to grasp. The result is a generation of
students that have learned to be terrified of fractions.

Common
Core, as near as I can tell, is going to address basic addition and subtraction
in a very theoretical way as well…I expect the results to be as disastrous as
we’ve already seen in fractions.

*Parent: “Close the bag of potato chips tightly.”*

*--how many times has the child left the bag open, causing the chips to become stale? Should this discussion be addressed in terms of relative humidity, bacteria growth, and chemical reactions, or should the child just be directed to close the bag properly?*

The
point: a child really doesn’t need a complicated explanation for how and why to
do something. Starting simple, and mastering foundation skills to build upon
later, is really the way to go. Let’s take a look at a Common
Core problem:

“Use number bonds to help you skip count by ten
by making ten or adding to the ones.”

7 + 7 = 7
+ 7
= 10 + 4 = 14

/ \

3 4

The basic theory here is to exploit the base 10
numbering system. Presumably, our 8 year olds have already mastered the
underlying theory of how a base 10 system works. So, they take off the second
7, and pick off 3 of it (so breaking into a 3 and a 4, connected via “number
bonds” I presume), then exploit that 7 + 3 is 10, making it easy to add the
leftover 4.

I’ve taught mathematics for over 20 years, and
I’ve never seen the phrases “number bonds” (a bad idea, since “bonds” has other
meanings) and “skip count” (a real problem for a child, who thinks of “skip” as
something completely different). The new language will separate the parent from
the child.

I get the underlying theory, but this is no
easier than the old “carry the one” method, AND it requires the student to have
already mastered subtraction (so that he can quickly realize that 7 – 3 is 4),
AND to have already mastered how a base ten numbering system works AND to have
realized that it’s easier to add powers of ten to units.

Now the Common Core method here is certainly
graceful, but look at how much more the student needs to know to do it. It’s
the same with the public school fraction method—it requires so much knowledge
at once that most students get overwhelmed, and can only know fear at the sight
of a fraction.

Another issue, of course, is the separation in
language from the parent and child. It harms the ability of the parent to help
the child with schoolwork. While I imagine most parents can follow the
silliness of the Common Core method, it’s still rather strange-looking, and
completely different than the “carry the one” method the parent was taught in
school.

Basic subtraction is likewise handled in a more
complicated way. Instead of a “borrow a ten” method (the graceful counterpart
to “carry the one”), small children are instead directed to break the ten up
into ones, and subtract off from there. The end result is a problem like “134 –
52”, which used to take 3 lines of text and a few seconds, now will take
up a quarter of a page and a couple of minutes. Go and click on that link
to see what a mess the new method is; it’s the same thing as borrowing a ten,
but requires much more writing to achieve the same effect.

That’s a bit much for an 8 year old.

Again, parents will simply be annoyed and
confused at handling problems in such a verbose, excessively symbolic, and
arcane way.

The alleged benefit of the more complicated
method is the child supposedly will have a better grasp of the underlying
theory…I strongly suspect the reality will be that the child will simply be
overwhelmed by basic arithmetic, much as many students today are overwhelmed by
fractions.

The Common Core method may be mathematically
sound, and possibly more revealing of the underlying theory…but I remind the
gentle reader that this stuff is intended for a 6 to 8 year old human child.
Honest, a simple method, combined with repetition, is the way to go with an
eight year old. An eight year old can certainly be shown the more complicated
technique, but the reality is still going to be the child will use the simple
method when the time comes to calculate.

It isn’t simply the higher degree of complication
in the Common Core methods, there is also the change for change sake we have
here. Parents are going to have a hard time following the new vocabulary,
although luckily a Cheat
Sheet, translating old phrases to new, is provided.

I want to talk about these translations case by
case, and why changing the language and techniques is a recipe for destruction,
next time.

You do realise that the math common core has been put together by a brain-dead committee of people with doctorates in math education? These scum have to justify their sinecures and salaries. Empty and confusing verbosity is the way they do it. And their legacy is generations of adults with math anxiety, whose blood pressure rises each time they see a fraction. The way to teach is to give rules, then present an example or two, then make the students practice and practice, gradually moving onto more difficult and involved calculations, until the skill is reflexive and resides in the hand. What they don't need to know is that fractions constitute a commutative division ring or that the reals constitute a complete ordered field.

ReplyDeleteNow that you mention it, I recall that the only actual graduate math course math educationists had to take (in the 80s), was abstract algebra. I would suspect you're on to something, but then they changed it so educationists, even for a Ph.D. in math education, only had to take a graduate level joke "history of mathematics" course instead.

ReplyDeleteThere are courses in the math department that are meant for the math educator cohorts. At the U of Minnesota, for example, there's a 5000-level combinatorics course for regular math majors -- and then a watered-down 4000-level version meant for the educators. Likewise there's a 2-semester course in geometry that's meant for the educator brigade (hence no serious geometry). Abstract algebra also comes in two flavors -- there's a serious 2-semester 5000 level course based on Herstein, but then a watered down 4000 level course for educators, where they introduce terms like group, ring, field, integral domain, etc. -- but don't cover important results like the Sylow theorems or the Galois correspondence. The history of math course is an utter joke.The net result, of course, is an ill-educated semi-educated brigade of math educators proud of their modest and superficial morsels of math, and intent on introducing them into the school curriculum. Big mistake.

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