[Lex Computer & Tech Group/LCTG] common Core Math

[Jon Dreyer]

A lot of people who don't understand math education love to 
make fun of Common Core math, which actually isn't too bad, 
from what I've seen of it.

Of course we all want our kids to learn efficient 
techniques, but, more importantly, we want them to learn to 
think critically and to think critically about how the 
techniques work, so they can adapt them and figure out 
shortcuts.

I have seen far too many high school kids do simple 
arithmetic using the "standard algorithm" when obvious 
shortcuts are available. For example, I've seen kids 
dutifully going through all the motions to do calculations 
like 791-787, when just counting up from 787 is so much 
quicker. Those teachers teaching that stuff (at least the 
good ones) know it's important to teach both the standard 
methods and the critical thinking necessary to figure out 
other methods, and one way to do that is to model the 
critical thinking. So they require kids to work through 
those other methods.

I spend a lot more time with middle school and high school 
kids than elementary kids, and I am often guilty of 
encouraging them to look at some common stuff that they do 
under a microscope, which can take way longer. For example, 
most of us could simplify 2x + (7 + 3x) in our heads, but I 
might ask them to try to put it under a microscope and look 
at all the algebra properties they are using:

    2x + (7 + 3x)
    = 2x + (3x + 7) (commutative prop of addition)
    = (2x + 3x) + 7 (associative prop of addition)
    = (2 + 3) x + 7 (distributive prop of multiplication
    over addition)
    = 5x + 7

Obviously this is way more work, and not the way we'd do 
that every day, but the advantage is that it gives kids the 
intellectual tools to work with expressions in unfamiliar 
patterns. Without firm knowledge of those basic algebra 
properties, kids will make mistakes like this:

    2x + (3x * 7) = (2x + 3x) * 7

Or they will "distribute" inappropriately:

    2x (3x * 4) = (2x * 3x) * (2x * 4) = 6x^2 * 8x

I see that kind of mistake every day. It's a tough sell 
getting them to really get to know the basic algebra 
properties, but those who do get way better.

I'm also a musician, so I make the analogy with practicing 
fast music slowly. Of course we want to perform at the 
desired tempo, but if we never practice it slowly, we'll end 
up playing it sloppily.

Then again, who doesn't love Tom Lehrer?


On 2020-10-16 08:33, john rudy wrote:
>
> Here is a more complete explanation of what Bob is showing 
> from one of my favorites
>
> https://www.youtube.com/watch?v=W6OaYPVueW4
>
> *From:* Robert Primak <bobprimak at yahoo.com>
> *Sent:* Friday, October 16, 2020 12:24 AM
>
> Don't ask that girl how to read an analog wall clock with 
> hands and Roman Numerals!
>
> Then again, don't try to explain Eureka Math (successor to 
> Common Core) to a parent!
>
> Why parents struggle with Common Core math: “The diagrams 
> are absolutely insane.”
>
> https://www.mercurynews.com/2018/06/17/common-core-did-parents-get-left-behind/
>

-- 
Jon Dreyer
Math tutor/Computer science tutor 
<http://www.passionatelycurious.com>
www.passionatelycurious.com 
<http://www.passionatelycurious.com>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.toku.us/private.cgi/lctg-toku.us/attachments/20201016/3171bc9c/attachment.html>