I feel like today is a good day to share the spectacular fail of the one and only time I was asked tk tutor, and why I support “new” /common core math but not always how it’s implemented.
When I was about 12 or 13 my parents, and some friends of theirs, had the brilliant idea to have me help the friends’ daughter with her math homework.

She was a couple years younger than me, and struggling.

One of my treasured memories from 6th grade is getting to do algebra.
Her homework was seriously the simplest thing ever (to ME) and I vould have done it in like second grade? Maybe first, if someone had taught me how.
It was mostly just converting various measurements...

...in METRIC
and this was my reaction at the time - oh I can totally show her how to do this! it’s just moving the decimal/multiplying or dividing by ten/adding or subtracting zeros.
No. Absolutely not.

What was obvious to me was not obvious to her, and we both left the session frustrated and feeling stupid.
the thing is, I hadn't really thought about _what_ I was doing when I converted centimeters to meters, I just did it.

and as frustrating (and ill conceived) as that session was, it was really valuable for me to realize that. and to think about how I would explain it
I think a lot of the debate about "new" and common core math, versus the way a lot of us Xers (and Boomers, and Millennials) learned it comes down to:

WHY do we teach math?
and, honestly, a lot of the Why? has changed in the time that we've gone from slide rules to smart phones.
It's not that the why was never important, it's that the "how" has become less so.
We teach math not merely as a practical matter (it is). But we also teach it to exercise kids brains.

and as the "how" becomes less relevant, the exercising has shifted to "why"

the technical has shifted to the conceptual
It's not nearly as important that kids be able to subtract 59 from 100 correctly _every time_

they will almost always have a calculator to check their work
so what becomes more important, what there is now more time for - which is a very good thing!

is to understand math in terms of patterns and relationships
when you subtract 59 from 100, how do you do it?

on paper?

can you do it in your head?
when you do it in your head...

is it: 59 is 1 away from 60, and 60 is 40 away from 100?

or some other way?
unfortunately though, a lot of elementary school teachers are not, themselves, comfortable with math as a conceptual exercise

and of course every new thing is done to death, even when it's a good idea
so you end up with a lot of kids being asked to explain things when it's really not necessary or helpful

on the grounds that, that's what they are supposed to do!

(but why? and in what way?)
the really hilarious thing though is: almost nobody actually likes HOW they were taught math, and while there are valid frustrations with certain implementations (especially from the kids)
I get the impression that a lot of the parents are frustrated because they never learned the why, and so trying to help their kids with their math homework doesn't only bring up their own anxiety, it increases it because now what they learned themselves isn't enough
and I have a lot of sympathy with that.
what I have less sympathy for is the parents who _are_ good at math, but never had to explain themselves _also_ feeling frustrated because they are now, at age 30, having that moment I had at 13.
and blaming educators who DO know what they are doing, instead of reexamining their assumptions.

and blaming the whole concept of math as a concept, and not arguing for improvements in implementation
data point towards the argument "we are shit at teaching math": I just spent 20 minutes unsuccessfully trying to find a link to this AMAZING series of books that actually helps teach numbers sense...

...and all I found were ...counting books. NO.
counting books should NOT be the top result when I look for children's books and number sense
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