Yep, this is absolutely mental. This would have confused the fuck out of me in school.
If you want to get ability at mental arithmetic, work in the trade section of a hardware store or be a checkout chick/dick for a year. Tradies are not always the sharpest tools in the shed, (yes, I know you see what I did there) but they can pretty much all do mental arithmetic like motherfuckers*.
*I’ve been told motherfuckers are exceptional at mental arithmetic.
HUH? Do you think that people have an implicit understanding of imperial that can’t be attained in metric? We used to have the imperial system in Australia, until we wised up and changed to the metric system. The change happened from 1970-88 so in 18 years everything changed to metric and it caused no confusion.
I think Eksrae is saying that if your common units of measurement were based on divisions of 10 then the general population would automatically be better at multiplying/dividing by 10 because of experience.
That’s absolutely not what I meant. I suppose it might have been better to say that most Americans don’t have an intuitive feel for metric units because that’s not what they grew up with. I didn’t mean one was more intuitive than the other in any objective sense. I was making a ham-fisted attempt to get the point accross that Americans have trouble with metric for a similar reason that both Europeans and Americans would have trouble with units used in the middle ages, that being, we don’t use them and don’t grow up with them.
Also, the US has tried to switch over to metric on at least one occasion I know of. It was during Jimmy Carter’s presidency. We simply didn’t have the political willpower and intestinal fortitude back then to get it done. I highly doubt our chances of switching to metric at a federal level are better today than they were back then.
Ah… I was trying to figure out what the middle earth bit was… now I get it 
I understand entirely your point and do agree that we can more easily mentally visualise what we are used to. I was just saying that humans’ ability to get used to new norms is surprisingly high.
One interesting part of the imperial system that has lasted through the switch are certain measurements. Inches are sometimes used to describe small measurements, because a centimetre is too small to easily visualise. Feet are sometimes used the same way, but because a meter is too big. Drug dealers also use imperial measurements because the step from a gram to a kilogram is a bit ridiculous when it comes to drugs, and it sounds silly asking for 28 grams.
“G, Q, half, Oz, QP, Pound & Key” are the dealers’ measurements of choice.
No real complaint about what you are actually saying, but “just cancel” reminds me of all the times I’ve had to grade " sin(x)/x = sin ".
In my experience, a fair number of people who are educated enough to be in college calculus class are fairly bad at recognizing the context in which an algorithm holds — let alone which might be the most efficient.
Heh. Where I am, the only drugs that would be in any way measured in metric are prescription drugs, cocaine and meth. Unless it’s at a dispensary, in which case pot is usually sold $/gram.
I don’t buy weed often enough to know what the prices should be, so usually I just say I want a dime or a dub, so at least I know what I’m paying, if not how much I’m getting.
When I did math routinely, I could do that. It’s a novelty skill though since we invented machines that are better at the job.
rest of us.
No, just some of you.
I’m not mocking anything, I’ve just never heard anyone make such a preposterous argument in favour of crippling how a subject is taught. You’re saying teachers should change the entire system to accommodate you. I’m seriously sorry if you have a disability that makes typing and writing painful but there are a ton of speech to text programs out there, so I’m not sure why you’d be enduring pain when you don’t have to.
I went looking when my arm injuries reached the point of constant pain. I wasn’t able to find any that would work with my computer at the time, and wasn’t able to see if they would work with my other accessibility requirements either. I can’t install anything at this time so it’s moot. except for the constant pain.
I seriously doubt I was ever the only student facing these issues either.
I remember this, except I don’t recall having a friend named Rojo. 
Your story sums up my educational experience. I typically got very very high marks on tests and homework and would calculate how much homework i could just skip and still get the final grade i desired. The teachers hated and loved me and more often than not didn’t know what to do with me.
Now I’ve gone from a troll to a helper, but who exactly is disallowing you from installing a program to accommodate a disability? There are laws against that sort of thing.
What, not who: software and repository issues.
Well, since the “new math” example is rightly pointed out as having nothing to do with common core. How about actually looking at a problem for 6th graders, as found on the Smart Balanced portal example CC test? I believe Smarter Balanced is the California flavor of Common Core testing. You can log in as guest and take any of their tests.
The problem is not doing the studies per se, it’s getting the decision makers to care.
Also, what outcome are you measuring? On what time scale? That day, the next month, twenty years from now?
For example, for long term retention it may be that inventing it yourselves as a class a la http://www.themathcircle.org/ may be better even for not-exceptionally-intelligent kids, and in the long run may be faster, but good luck fitting the slow start-up period and unsteady pace for that into a school curriculum.
Me too, I might have subtracted the twos from each side, then do the easy 30 minus 10 or simply do it in one step - 32 -12 = 20. But then again, why do it in one step, when 12 will do the same job, eh?
As for working a cash register, the 'add till you get a multiple of five method is a little strange to me, especially for working out change.
When someone hands you paper money plus some change, subtract the change from the balance due, then figure out the change for the new balance due.
Say the total is $12.31 and you’re handed $20.06. Just like when you’re doing algebra, $20,06 - $.06 = $20.00 = $12.31 - $.06 + change = $12.25 + really easy to figure out change.
In a similiar vein, when you’re handed foreign currency, convert that currency into your currency and figure out the change from that. Think of that, for example, CDN20$ = US19$.
I used to work at a cash register, and in my day, I’d have to calculate the sales tax in my head. I never made a mistake, as far as I know.
Why is everyone these days so scared of ‘technique, technique, technique’?
Yay, I can still do 6th grade math! I don’t have to take my BMath degree down off the wall just yet.
You aren’t put off by the somewhat peculiar notation? If I were to be creating a problem such as this, I’d not mix notation for my unknown (x) with rays or lines using X, Y, Z, lest someone think x is a variable and (3x+4) and (2x + 6) represent a function. What is shown is technically correct, but for the sake of clarity, I’d choose different labels. If I want to stick with A, X, Y, Z for labeling geometry, then any lower case anything but, a, w, x, y, z makes a better choice. If I’m going to construct a 2D diagram with rays having a 90° separation and an intersecting line with a Y label, I’d probably choose labels that don’t overlap with conventional axes labels X, Y, and Z. Just for clarity. So I ask myself why the test creator didn’t make different choices, given that they had any letters to choose from. What knowledge drove their choice? I can’t tell if the test creator was being purposefully mean, lazy, or just didn’t know better.
My job has involved a lot of geometry and working in 2 and 3 dimensions as well as teaching professionals to use software involving the same. Though I have drawn very similar looking diagrams over the years, I could never had made these sorts of choices without raising questions about my credibility or at least causing frustration to my students.
Funnily enough, I didn’t even notice that X was used to refer to two different things. But maybe that’s just the math-oriented part of my brain that automatically ignored all the point labels until I solved for x to determine what the two angles were, and only then did I bother looking at how the line fragments were labeled - and by that point I had completely forgotten about the other x.
Exactly. When calculating change, you don’t even care what the exact answer is, you just want the correct number of coins. This method is great for that.
It’s not so great for calculating in your head, though; while doing 4 additions, you also need to remember all the numbers you added and then add those together again.
What works best in my opinion is a hybrid of several techniques; every technique has its own advantages or disadvantages. Starting with rounding and then later correcting for it can be very effective in some situations, but not in others. Simple substraction works better in others. Usually when doing it a lot, you learn through experience what works for you.
I was reading the lyrics for Tom Lehrer’s “New Math” and still can’t get my head around it:
342 -
Now remember how we used to do that. three from two is nine; carry the one, and if you’re under 35 or went to a private school you say seven from three is six, but if you’re over 35 and went to a public school you say eight from four is six; carry the one so we have 169, but in the new approach, as you know, the
important thing is to understand what you’re doing rather than to get the right answer. Here’s how they do it now.
This all sounds like voodoo to me 
