Counting is a form of math. You’ve been tricked!!! You were doing math all this time and didn’t know it.
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Well, if you spend enough 20 [currency-unit] bills, that kinda happens…
I want five pound coins pretty badly. I’m sick of raggedy, ketamine and mephedrone soaked, mucous-smeared fivers. The amount of five pound notes I’ve gotten in change that actually have blood soaked into both long edges is unreal.
Good luck finding a useful definition of “real” math that does not cover counting change but does cover subtractions.
Admit it: you did that on purpose!
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Well yea, but you know what I mean - lol.
Some methods don’t need to be constantly reinvented.
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I had to count change back for a retail job in my teens. I practiced daily for a week with my parents and could do it fantastically. I don’t think any of the other workers bothered to learn it and just relied on the change readout from the computer.
No. writing is slow and painful. demanding that we produce extra writing means demanding that we slow down to the pain of writing. and if we write down the first few problems, then the teacher starts docking points for bad handwriting for the next few problems, and we’re in pain by the last few.
You’re not necessarily wrong, but the problem is it teaches dependency on writing it all out. As much time is dedicated to basic arithmetic in schools, there’s really room for more than one approach here. It’s important to teach different methods of getting at an answer so the child can learn that there are different ways to solve a problem, and can choose the best one for the situation.
I was, somehow, astonishingly bad at following arithmetic algorithms when writing it all out on paper. My number sense is just fine though.
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Yes, it looked familiar to me as well. My daughter’s elementary school approached not just math but all the subjects on a foundation of patterns. ABAB was first introduced, then more complex patterns. We lived patterns. Guess what, patterns are everywhere!!! But then they used this to get into math concepts, as well as of course poetry. At some point they took a detour into 5’s and 10’s.
i thought it’d pay off but she really got hung up in math the same place I did - she wouldn’t memorize the times tables and to this day struggles with doing calculations in her head, quick checking her work to make sure the results meet common sense. She’s ok at math but it’s a big challenge.
[quote=“clayton_coffman, post:21, topic:25228, full:true”]
The new system is a neat idea. However it is too easy to fail at. The normal algorithm is more intrinsically safe than this method. The traditional way will always give you the right answer. “New math” doesn’t have an algorithm, you’re just always starting from scratch.
Doing math “in your head” is a nice idea that some people can do well and some can’t. I am all for teaching this method, after the kids master an algorithm.
I’ve taught 4th graders math, and I will tell you that some of them do poorly because they just try to do it in their head (especially the “smart” kids) and get it wrong. This becomes rather acute when they start with algebra. The formalism of the classic methods feeds directly into the formalism you need when doing anything more advanced than arithmetic. A kid I taught who could do perfect arithmetic in his head (and thus never learned how to keep numbers organized on paper) was utterly lost when doing basic algebra because he wouldn’t work out his problems step by step. Less intelligent students did better because they already had the skills to organize their problems and implement reliable methods.[/quote]
Well, by the time we’re dealing with algebra, math teaching has reduced to ‘do all the odd problems for tomorrow, now let’s go over the problems for today… oh we’re out of time to discuss anything for tomorrow.’ And algorithms are just pain for the sake of pain, they get in the way of actually getting answers.
So for those of us who find algorithms hurt too much, take too much time, and take too much paper, find formulae pointless and impossible to memorize, and find math books indecypherable, math goes from easy to painful to what?. I could get through Algebra 1 by doing things in my head. I could get through parts of through Geometry, Algebra 2, and Pre-Calc that way, and through the rest by ignoring the pain. I couldn’t get through Calculus because of formulae and because the bus ran late and I’d miss the first half of every single class and the other students had cars.
P.S. And, theory makes practice so much easier. As long as teachers implied that 'equals; means ‘makes, produces, these numbers come in and that number comes out,’ math didn’t make sense. Once one explained almost in passing that ‘equals’ mean ‘balances, this group of numbers is the same as that group of numbers,’ math started making sense. That was in third grade, after I’d devoted a lot of time and effort to figuring out the ‘makes’ math.
Back in the dark ages before computers, when I was like 16 or 17, when I started working at the deli counter they showed me once how to count back the change. Took about 30 seconds and then I was an “expert” counter.
A lot of the CC theory is to impress a general idea of where numbers fall, to reduce reliance on calculators when they give a wrong number because of an error. If you can understand that 1704 should be somewhere in the range of 700 you’ll notice your 17040 error that you typed in a lot easier.
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Actually Feynman’s original article is much more better than what wikipedia has at current posting.
Here is the link, PDF:
http://calteches.library.caltech.edu/2362/1/feynman.pdf
Any way that consistently gets you the correct answer is the right way. Whatever approach you take might not be the most efficient, but as long as you get the correct answer you did it right. That’s why it’s helpful to teach multiple approaches to problems, as the most efficient solution can vary from problem to problem.
‘Old math’ and ‘new math’ look pretty much the same to me, two versions of what was taught in school. Both are, as it were, ‘little-endian’ and the ‘new math’ just explains what ‘carry the one’ actually means. If I need to work things out, I tend to use another way which is, as it were, ‘big endian.’
342-173 would break down into
300-100 = 200,
40-70 = -30 = -100+70
2-3 = -1 = -10+9
=169
Which is procedurally more complicated, but gets the most important part first, even if it requires adjustment half the time. I can’t really describe it because I don’t really think about it, and I can’t figure out how I do cascading adjustments, I just do.
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This reminds me of my high school history class. We always bitched and moaned that kids in other schools got multiple choice tests and T/F tests, but we always had essay tests and how unfair it was. So, one day, we walk into mid-semester tests and our teacher says, “Guess what? I’ve listened to your complaints and I’ve decided to give you a T/F test! There is one question and if you get it right, you get 100%. If you get it wrong, you get 0%. Of course, if you are worried that you might get it wrong, you can always write an essay explaining your reasoning and I will take that into account in your grade. Muaaaaahahahahahaha!!!” We of course all wrote essays and stopped asking for T/F exams.
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So did anyone wrote that the teacher is one sick mutherf—?
I’m a trainee maths teacher over in the UK. This whole debate is really interesting from my perspective, coming from quite a different education system.
Something I’ve learnt about (that I never saw at school: an innovation that passed me by) is the concept of the ‘empty number line’, which is a similar idea of ‘counting on’ with a good visual picture.
e.g.: http://www.bbc.co.uk/skillswise/factsheet/ma09subt-e3-f-empty-number-line-for-counting-on
Not all students like this (some prefer the relative safety of the more traditional algorithms) but I find that those who do have a generally better ‘number sense’, if you want to call it that.
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