The lighter side of ADHD
That's the sort of thing "new math" was trying to teach. Those sorts of breakdowns are exactly what the kids who were good at math were always doing, and teaching methods eventually caught up and realized they should just teach the tricks.
Then a bunch of parents who were bad at math asked "new math? How can math change?" The fact that they even asked that question showed how their math education was lacking, but they seem to have won.
Exactly. Math has historically relied on rote memory for most mental math. Kids would have to fill out their times tables, addition tables, etc until they memorized them. I still remember getting pop quizzes in elementary school that looked like this:
You only had two minutes to fill out the entire thing, which meant you only had 1.2 seconds per answer. You didn’t have time to actually calculate them. The point was that you were expected to have them memorized ahead of time instead of calculating each one.
But rote memory is laughably bad at actually teaching concepts. You may know that 12x5 is 60, but you don’t have any understanding on why, or other ways to do that same calculation without rote memory. And rote memory is only decently reliable up to ~12x12. Anything past that, and it becomes too much info to track; kids simply start forgetting answers.
The kids who were good at math (and I mean actually good at math, not just good at memorizing things) quickly devised methods to do this shit in our heads easily. Keeping track of multiple numbers in your head gets confusing. So “line them all up, add straight down, and carry 1’s” sort of falls apart if you’re doing it in your head. Especially if you’re trying to keep track of more than three or four numbers at a time.
Essentially, 127+248+30 is the same as 105+250+50, but the latter is much easier to parse in your head. But yeah, the parents (who primarily relied on rote memory) didn’t understand why the new method would be more effective, because they didn’t understand the concepts surrounding the math.
I think it's good to have a good set of these tables memorized and then based off those you can bounce your tricks. Eg if you know 5x12 by heart, you get 5x24 by intuition. Or even if you know 24/2 for that matter. I use simple examples but this could scale to less memorable numbers too.
I only sort of agree. I still think that by forcing you to do that, by making you practice, makes the calculations "muscle memory" in that you aren't memorizing the answers but can do the calculations faster and faster each time.
Sure. Some people could memorize them. But others will learn to calculate quickly.
Strongly disagree that memorization isn't important. It's THE foundation to be able to do effectively do more advanced stuff.
Take the equation (5678 • 9876). Use long multiplication and you only rely on doing a bunch of single digit multiplications and additions. It's so much faster to be able to instantly know each step instead of having to recalculate these "atomic" steps again and again in your head.
You generally don't need to be able to solve multiplications involving double digits in your head. It's nice-to-have but otherwise useless, as long as you're able to calculate the ballpark of the result.
For example, (38•63) is roughly 2400 and I can then calculate it on paper instead of in my head.
Head calculations are just so much more error-prone than written calculations. Don't do them if you can avoid them. There's a reason why math students (at a university) are infamous for being unable to make the simplest calculations in their head. It takes effort that could be spent somewhere else.
I was trying to explain how and why they were teaching math to a family friend and they didn't get it(multiplication stuff). I broke it down with pen and paper and they didn't get it. Simpler example, nope. Eventually I had to explain how multiplication is just repetitive addition. They responded with WHAT! and I realized why they always wore open toed shoes. I sent them a link for 5th graders.
Hey! Nothing wrong with open toed shoes damnit.
I'm not very good at math (but not an idiot like your example) and I wear flip-flops every day of the year but they're not related.
Are you trying to say something like "too dumb to tie shoelaces?"
Because there are quite a lot of lace-up open toe shoes and sandals, as well as closed toe shoes without laces, so that doesn't track.
Can you count to 20 with your shoes on?
I can count to 20 with my eyes shut but my toes can't breathe with shoes on.
As a parent who is bad at math, you’re not wrong. But given my kids are excelling in math (very high scores), I’ve learned to shut the fuck up about it and let the teachers do their ~~black magic~~ jobs.
Those sorts of breakdowns are exactly what the kids who were good at math were always doing, and teaching methods eventually caught up and realized they should just teach the tricks.
Well... kinda. "Getting to 10" was what New Math was trying to teach. So you'd take the 1 from 7 and give to 9, because 6 + 10 is easier than trying to finagle your way to 8x2.
Then a bunch of parents who were bad at math asked “new math? How can math change?”
You don't have to be bad at math, strictly speaking. But there was a lot of brute memorization in traditional math. Times Tables, for instance, were something you just memorized straight up without thinking too deeply. Getting 16 out of 7+9 was something you just had to do on your fingers until you had it lodged in your head.
Old Math tended to be slower and more tedious. New Math is more logical, but also somewhat counterintuitive until you get into the swing of it.
The fact that they even asked that question showed how their math education was lacking, but they seem to have won.
I've got friends with kids down in Houston. "New Math" appears to be alive and well, in no small part because it helps kids score higher on standardized tests.
Borrow 1 from the 7 leaving you 10 and 6. This is what they tried to teach in schools for awhile but adults weren't getting it. Common Core? Is that what they called it?
As someone who learned not via Common Core, and then found out Common Core taught math how I taught myself to do mental math I was a little envious that kids would learn my “easier” method.
Same, common core is what I came up with to do mental math.
Yup, helping my kiddo with the math portion of Common Core was like seeing professionals finally understanding how easy it is to sort numbers to make stuff easier instead of doing a bunch of rote memorization of tables. Also teaching kids to estimate to know if your math is way off!
Common Core for math was awesome. That was the only one I had to help with so no idea about the rest.
One of my wifes friends was an elemetry school teacher when common core was popular. We asked her what it was and as she was explaining it, i said, "oh, like how you do mental math?"
Im an engineer and i just assumed thats how everyone did math... apparently people just memorized everything
Why wouldn't you just take 1 from 7, add it to 9, and make it 10 + 6? That makes a lot more sense to my brain at least.
Because making shit equal, be in perfect balance or even symmetric makes my dopamine go 🥳.
Finding the correct answer that way is a neat side effect too.
9+anything
10+x-1
Similarly for 8+x is 10+x-2
Multiplying by 5: mult by 10 divide by 2 Mult by 15: mult by 10, add half of that.
Multiplying by 5: mult by 10 divide by 2
A very similar concept for tipping about 20% is taking 1/10th of the bill by moving the decimal one to the left and doubling that. To make it even easier for me I just round to the nearest $10 amount first.
Bill: $66.20 -> move left and round up = $7.00 and double to $14.00. The exact 20% amount is a little over $13 but I tend to round up because it is also faster to add whole dollars to the bill.
I only read this thread to make sure someone was right. Thank you
Heretic here. I just do 10 + 7 - 1.
That's how I do it in my head too. Is this even uncommon?
No many people have their own methods. I don't think this is exclusive to ADHD whatsoever
Why wouldn't you take the 1 from the 7 so it is 10+6?
This is what I go for...Just play in 10s. Alot easier IMO
You’re so adhd you forgot that this was a whole part of your math curriculum that you just tuned out because you already knew it.
This way of thinking is just a different way of doing math and has absolutely nothing to do with ADHD. This type of post is likely responsible for a large portion of the people self diagnosing themselves with something that I struggle with.
Stop posting this shit.
not even ADHD related you're just taking a route to something more readily available in your memory. that's how brains are supposed to work.
to me the detour is -1+10. whenever i see a 9 i take 1 away from the other guy and then add 10.
9 x single digit mumber works similarly; except i take away 1 and complete that to 9 by adding a number next to it.
9x7 = ?
7-1 = 6
6+? = 9
9x7 = 63
Said by someone who never actually told that to a teacher, lol.
OPs description is literally the simplest example of the dreaded "new math" they are teaching in schools.
9+7 is the same as 9+1+6 is the same as 10+6 is 16. New math. Same as the old math.
ETA: one of the points of "new math", iirc, is essentially to teach all kids to use the methods that the kids who are "naturally gifted" at arithmetic sort of figured out on their own. So, congrats?
It's less about "changing the way we do math" and more about "teaching kids to break down problems to their simplest elements"...which is an all-around important life skill, aside from just math.
A very good song by Tom Lehrer as well.
For the last fifteen years, the emphasis in math teaching is that all methods to the right answer are correct. Emphasis is on sharing all the different methods. (Canada)
This is actually how my professor, who has a PhD in mathematics, does math.
This is literally how common core math works.
9+9-2
Just as acceptable
I mean, sure, the choice of the "nice" numbers here is eccentric, but this is essentially the way math is taught nowadays. Only, instead of making 8 in this special case, the goal is usually to make 10 + leftovers because adding to 10 is always easy.
Here's my (upper midwest) spicy mental math take: it should be big-endian and solved with backtracking for ripple carry/borrow. None of this starting-from-the-1's-place-and-successively-incorporating-higher-order-digits nonsense. Extended carry/borrow is rare, and if you start with the most significant digits and give up/get bored part way through, the intermediate answer is in the ballpark of the real answer.
A dozen years ago or so there was a huge uproar about "common core" mathematics, which was a new standard being used in the USA for teaching.
It was a politicized trendy topic and even so-called-intellectuals were jumping on the train and calling it a deranged way of learning math.
I looked into it a bit, and I swear this pic pretty much sums up one of the key methods they were teaching.
Basically just tricks that a lot of people figure out to simplify problems.
My retarded ass: 9 is 0b1001 and 7 is 0b111, 0b1001+0b111 is 0b10000 which is 16.
Am kidding, I take 9's ten friend, sub-stract that from 7 et voilà I have 6 ones and 1 ten which is 16.
And here I always thought it was 1001 + 0111 = 10000.
I've always done it this way and don't have adhd
