Comment by mratzloff | Hacker News Reader

Comment by mratzloff | Hacker News Reader

When calculating in my head or on paper, I value quick estimations moving to greater refinement. Common Core math seems somewhat similar to this.

I never subtract, only add up from low to high. If the two numbers have the same number of differing digits, I move from most significant digit to least: 73-57=10+6. If they cross a round number threshold greater than 10s, I get to a convenient base first: 2018-1995=5+18; 173-57=43+73=110+6.

For multiplication, I do something similar: 6x57=300+42; 42x23=(42x20=800+40)+(42x3=120+6).

For division in my head, I use a kind of binary search to get a quick estimate and then refine it. 846/42=42x10? 42x20+6. 20r6. 6/42=1/7. 0.15x7>1, 0.14x7<1. 20.14.

From my understanding, the Common Core approach to math is much closer to this approach I developed intuitively than the traditional methods. I'm sure many others developed similar approaches. If I want an answer accurate to more than two decimal places, or if the math gets too complicated to keep in my head, I just use a calculator.

>From my understanding, the Common Core approach to math is much closer to this approach I developed intuitively than the traditional methods.

It is. I recently had to help my daughter with common core math and I saw the similarities.

I think the biggest problem people have with it is at first it's impossible to help your kids with homework which is frustrating for both the parent and the kid. I had to learn it before I could help her with it.

Now all we need to do is finally covert to the metric system.

I grew up being taught ‘borrow and carry’ methods. They are really methods of ‘apply the algorithm and success’. Common Core can be a better way of getting an intuitive sense of the numbers and quantities.

Some examples are over the top, like the 32-20 in the article. But one of the common criticisms my parents and grandparents used to level at people my age (when I was a teenager) was that we couldn’t run a cash register—-we didn’t know how to make change.

Kids won’t start out adding and subtracting as quickly. The ramp-up to learning may be a little slower but they’ll come out with a more intuitive sense of numbers.

All of this is just my opinion. I studied Math and have a couple of young kids going through these methods in school now.

This is why I'm not opposed to the Common Core approach. It seems that they really emphasize math conceptualization and chunking instead of a formulaic process list that was used when I was a kid. Given the poor math scores in the US compared to other advanced countries, I really hope that this helps more younger people understand math.

These things all go in cycles though. People were complaining about the "new math" back in the 1960s. As Tom Lehrer put it "Understanding what you're doing is the important thing, rather than to get the right answer."

https://www.youtube.com/watch?v=wIWaJ0sy03g

https://en.wikipedia.org/wiki/New_Math

Well, it is super useful do be able to do exact arithmetic. For example, to not get scammed when you buy anything, or share a bill. I've seen American university students who don't know how to compute a percentage of a given amount - so I'm not very impressed by common core math to be honest.

That being said, it's probably a cultural thing too. I noticed that in the USA (at least in California?) it is customary to exclude the taxes from the price that is displayed on the price tag. Since the tax rate is different for different products, it's pretty hard to compute the actual price that you pay, and in practice you just take whatever you need and don't have an idea what you pay. In addition, it is not very usual to split the bill (I'm not talking about simply dividing the price by the number of people, but about actually computing the price of the stuff you ate, and not paying more than that).

When I go to the grocery store, I usually keep a sum of the price in my head while I pick products. That way I'll know if something is off at the counter.

> When I go to the grocery store, I usually keep a sum of the price in my head while I pick products. That way I'll know if something is off at the counter.

I wouldn't be able to CBA w/that during grocery shopping, I got way more to do whilst grocery shopping. Adhering my shopping list whilst checking for deals, and getting the correct items and correct amount. Figuring out in my head what combines with what recipe-wise.

For grocery shopping I ask for the receipt and then verify afterwards while discussing with my partner. Sometimes something's off in our advantage, sometimes in our disadvantage. Since its grocery shopping, we're talking about a few EUR here and there. If its non-grocery shopping, then I take quicker note.

As a rule of thumb the following rule appears to apply for me: the more expensive the item(s) the more cautious I am (denotes quality), but the more items the less cautious I am as well (denotes quantity). Why? Because its easier to do the former, and the latter becomes more difficult till we get to the CBA point.

Instead, I go for some deals, and then allow myself some treats as well, but never too much of either. The result is I mostly follow the grocery shopping list but I never know beforehand how much I exactly gotta pay, but I pay electronic either way; not with cash. I noticed when I've been in Germany and paid with cash, I took far better note of prices. Incidentally, groceries are generally cheaper in Germany as well...

> When I go to the grocery store, I usually keep a sum of the price in my head while I pick products. That way I'll know if something is off at the counter.

I do the same thing, but it does depend on how much I'm shopping. If its big for the whole family I keep a rounded tally in my head, and use that sum to determine whether or not I look at the actual receipt to see if something was wrong. If on the other hand I'm buying say less than 15 items then I'll keep up with the actual to the cent sums when I'm paying in cash.

You get a weird look sometimes when you get to the counter, they say 23.45 and you hand them the money immediately.

I've done this ever since I can remember, but growing up in the USA you just had the added step that you needed to know what the sales tax rate was for the area you were currently in, and if you didn't know it then I'd just use a default rate of 8%.

The mathematics standards for Common Core were released in June 2010. So college freshmen this year would have been in 5th grade (seniors in 8th grade) at the earliest when introduced to Common Core style mathematics. Probably later, since schools needed time to adapt to the new curriculum and train teachers in the new methods. Seeing as how Common Core places a heavy emphasis on developing skills in grades 1-8, I don’t think that current college students are a good benchmark for the Common Core standards. Talk to some college students in 5-10 years to get a better idea of how things are progressing.

Also I would say that early CA Common Core for math basically just pushes up the current curriculum up about half a year, a mild improvement; more importantly it's a cleaner spec for outcomes.

It doesn't really re-order the curriculum, it uses a few new terms, there's mildly more emphasis on word problems, and there's earlier introduction to linear sequences. It's just a few touch-ups here and there, presumably to prepare kids better for Algebra 1. The whole reform is a modest start.

> 2018 - 1995 = 8 + 15.

Now I too start with the addition, but my brain very much thinks in the vertical stacking of the numbers, moving right to left. How do we get from 5 to 8? Add 3, how do we get from 9 to 1 when adding: plus 2. How do we get from 9 to 0: plus 1, which we already have from the 9 to 1 case, so we pass the 1 here to the left. 1 to 2, plus 1, again using the value passed to us.

Little surprise I prefer functional languages.

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