Math is the main requirement for engineering. If you can’t do basic math, it’s incredibly unlikely you could earn a degree in any kind of engineering. If your wife couldn’t write a sentence I would also doubt any journalist credentials she claimed, if she couldn’t do basic arithmetic I would doubt any degree she claimed. There are basic minimum requirements to graduate that you don’t seem to meet. So much for your stupid rebuttal.

Clearly it’s not…but what is? Not math. Not critical thinking. Not history.

As I’ve said repeatedly, clearly, and directly, no. I don’t think he’s achieving as much as even I hoped for in my unbounded cynicism, and I never had high hopes from him, he’s not my choice….but I understand exactly why he’s not getting much done and don’t hold him 100% accountable for much of it. Without a functional congress, his hands are tied on many fronts.
Foreign policy, that’s on him. I wish we had soldiers in the Ukraine so Russia would be forced to attack America if they want to attack the Ukraine….like we said we would when they gave up their nukes by treaty.

I invite you to explain how I’m wrong at any time, but without facts and reliable sources to cite you’ll likely fail like so often before.

? Grand master? I pointed out a basic fact, GDP under Obama was double GDP under Trump. What delusional fantasy are you railing against now?

Didn’t watch. Guaranteed it was more informative and less self aggrandizing than any Trump “press conference” ever, with fewer exaggerations and outright falsehoods.

Incomprehensible. Take a deep breath and try again. Use your words.

Massive debt, unequalled corruption, isolationism, nationalism, and division certainly don’t make America better, and that’s the Trump legacy. Investment in America makes it better, Biden’s already done that and wants to do more.

The problem is that it's confusing theory with the method. The right hand method(henceforth referred to as right method) shows that 35*2+35*10=35*12. It takes all of a couple minutes to show a class that. Spend a little time reminding them of the theory, put have them practice the right method. This isn't a mathematical theory exercise, this is performing basic arithmetic. It's why you segway into algebra later and show kids a(x +y)=ax+ay

@drradon: I agree with you 100% on teaching both and teaching basic arithmetic first and then leading on to proper math once that foundation is established.

@dannym3141,

I was first blindsided by it when my kids came home with multiplication homework and were adamant they couldn't answer it the way I was showing them because it would be marked wrong, it was the wrong way to do multiplication.

The link to the full Manitoba math curriculum is below. The worst sections are under 'Mental Math' with the idea being that you should be able to add/subtract/multiply/divide all numbers in your head with a dozen pages worth of tricks. The tricks being what newtboy was calling 'proofs'. Our curriculum calls them 'techniques' though and I've included an example from the Grade 3 curriculum verbatim after of how it is supposed to be 'taught'.

Overall Math curriculum:
http://www.edu.gov.mb.ca/k12/cur/math/index.html

Grade 3 example:
http://www.edu.gov.mb.ca/k12/cur/math/support_gr3/number.pdf

From page 56:
Describe a mental mathematics strategy that could be used to determine a given basic fact, such as
-doubles (e.g., for 6 + 8, think 7 + 7)
-doubles plus one (e.g., for 6 + 7, think 6 + 6 + 1)
-doubles take away one (e.g., for 6 + 7, think 7 + 7 – 1)
-doubles plus two (e.g., for 6 + 8, think 6 + 6 + 2)
-doubles take away two (e.g., for 6 + 8, think 8 + 8 – 2)
-making 10 (e.g., for 6 + 8, think 6 + 4 + 4 or 8 + 2 + 4)
-commutative property (e.g., for 3 + 9, think 9 + 3)
-addition to subtraction (e.g., for 13 – 7, think 7 + ? = 13)."

Now before you think me and observe there's nothing wrong with showing kids some extra tricks to help them, that is NOT how this is supposed to be used. If you read further, students are REQUIRED to "explore" multiple methods of calculating answers and must demonstrate they know and can use all these 'tricks'. So instead of providing assistance for difficult calculations as it should be, it's used to make ALL calculations difficult, and create extra work, AND makes kids just learning the concept completely overwhelmed with everything you MUST know to get a right answer to 2+2=4.

And here's the link to the Grade 11 review of the basic arithmetic:
http://www.edu.gov.mb.ca/k12/cur/math/ess_mm_gr11/full_doc.pdf

And for the Grade 11 students and teaching them to add/subtract/multiply and divide, the teacher's guide describes this like a subjective discovery process with quotes like this:
"Consequently, mental calculation activities should include periods for thought and discussion.
During these periods, the teacher should encourage students to
-suggest a variety of possible solutions to the same problem
-explain the different methods used to come to the correct answer and their
effectiveness
-explain the thought process that led to an incorrect answer"

An important note is we are not talking about solving complex word problems here or anything, but specifically for calculating a basic arithmetic operation with the different methods being those described from back in Grade 3 already outlined above.

I don't disagree with that. I don't understand how one could do any advanced mathematics without knowing arithmetic, so clearly it should be taught first.
As far as I was concerned, proofs were just demonstrating an understanding of arithmetic and how numbers and functions can be deconstructed in different ways. I hate showing my work, and almost failed that portion of algebra 2 because I just refused.

Interesting discussion here. This is what comes of awarding PhDs in university Education departments: "must make simple complex", "must make simple complex", "must make simple complex", "must make simple complex"... keep repeating until PhD is awarded. I disagree with both newtboy and bcglorf to a degree - one approach to teaching is arithmetic and the other is math. There is a place for both in the curriculum: teach arithmetic to enable students to gain facility with numbers; in the higher grades, introduce concepts of mathematics theory so that they understand why arithmetic works and extends to higher math...

Your missing the point though.

They start in grade 1/2 teaching you that 2+2=4 is incorrect. Instead you were supposed to write down:
2 is 1+1 and 1+1+1+1=4.

Then by grade 3/4 they are asked to solve 2+2. They now answer:
2 is 1+1 and 1+1+1+1=4

and are told incorrect. They are now supposed to use two different methods to solve the same problem and the correct answer is:
2 is the same as 1+1 so 1+1+1+1=4.
Alternately, 2 is 1 more than 1. I know 1+2 is 3, so If I add 1 that's 4.

Those aren't proofs. The addition operator isn't even a theorem to be proven, it's a definition.

I'm on board with teaching more advanced and abstract concepts in grade school. However, actually DO THAT. The stupidity of our provincial system is that they aren't doing that at all. They are performing all this mental masturbation to make basic arithmetic into some bastardised thing that kinda resembles proofs. You know, except the part where your 'proof' is worthless because solving 2+2 by replacing 2 with 1+1 is just substituting one axiom for another.

Teach kids the arithmetic and then teach them actual MATH proper, ideally easing them into the abstract aspect through algebra and not stupid tricks that fail to give them a good understanding of the actual concepts.

The point I underlined about Grade 11 still covering it is important. The students are being left so confused about what they are expected to give as an answer that so many still don't know basic arithmetic by Grade 11 that they still include it as part of the basic curriculum.

Har har har.

I went through every calculus class my uni offered, so not so much.

Mayhaps I didn't explain the example given in enough length. The simple operations of addition, subtraction, multiplication, division all have a single correct answer. Insisting that students find multiple methods of performing those operations and demonstrate multiple different learning methods for them is mental masturbation. You could spend that same time actually moving on to the more advanced stuff that is supposed to 'in theory' prepare them for.

Another example was solving a double digit multiplication problem like 37*86. The marking example showed a student using the old school vertical method and showing their work to arrive at the correct answer. The provincial grading system declared that as WRONG. The student was 'falling back' on the algorithm and should have demonstrated the use of multiple methods of solving the problem. That is idiocy.

Basic add/subtract/multiply/division isn't MATH it's arithmetic and it's a basic operation with a single answer and so long as you use a correct method to arrive at the correct answer you are good to go. Teach students that foundation and then move on to teaching them actual MATH. Read through our provincial curriculum, they are STILL teaching add/subtract/multiply/division at the Grade 11 level in the curriculum on the premise that students are still 'mastering' something that should've been a given by junior high.

As much as I'd love to pile more hate on some faceless / heartless corporate entity that doesn't care about anything other than profits, I find it somewhat unreasonable to be TOO hard on Takata here.

Just by sheer Philosophy 101 arithmetic of lives saved vs lives taken, airbags in general are massively beneficial. Take a worst case hypothetical scenario -- I know that my car has Takata airbags, AND I live in a very humid environment, AND my car is pretty old, AND the waiting list on the recall means that I can't replace the airbags for another 2+ years. Even in that scenario, I think I'd *still* opt to keep the thing in and active until it could be replaced. It would be nice to have further information on the 10 fatalities (roughly where, make/model, age) and corresponding information from other recent crashes under similar circumstances where the airbags *did* work properly, but I'd wager that even in that kind of worst-case scenario the good outcomes still handily outweigh the bad outcomes.

It is hard to foresee everything that can go wrong years and years into the future. We put lots of hardware through robotics that open doors / actuate things / etc. every few seconds continuously for months in an effort to predict how they will stand up to normal wear and tear for years, but that's harder to emulate with chemical processes.

So, until/unless there is evidence that they used the Ammonium Nitrate while knowingly and intentionally ignoring the potential long-term risks as the stuff ages in some environmental situations, I would be very hesitant to call for their heads over this. I guess that is the purpose of a "criminal investigation", but I really hope that isn't code for "witch hunt".

I'm sure there are some dumbing down going on, see the related video in the comment above, but what this woman is talking about/objecting to is insane.

"He said education was about challenging and changing students mind.."

YES IT IS!. Thats excactly the point of education: LEARNING something that gives you something to think about, she says it like its a bad thing!, its a good thing, having your views challenged. And then she continues: "I thought education was about reading, writing and arithmetic" Well, you need those things, but sureley, if anything is dumbing down, it would be to create mindless reading math robots with no understanding of the context and purpose of learning stuff.

"He could turn a god-fearing patriot into an atheist in an hour" Well duh, thats because religion and nationalism doesnt make any sense, of course kids with actual open minds would realise the truth very quickly.

I'm not sure about the American education system, but here in Canada the dumbing down of it is appalling to me. It's been getting dumbed down in the name of being 'open minded' and other nonesense by people that don't understand basic reading, writing and arithmetic are not subjective studies and can't be taught in a everyone can do it how they feel manner. Our curriculum is being designed around 2+2=5 isn't 'wrong' it's just that a student applied a different method and should still get partial marks. Our schools are also implementing 'no-fail' policies that basically do away with the 'social stigma' attached to failing and insisting that all students pass each grade unless parents agree, teachers and all staff agree. It's no wonder our western standards are falling, as we are exploiting every last inch of the luxury we have to do so.

That said, I do believe comparisons of students here to those in places like say China are misleading. Shanghai may top the global charts on student results, but I question how complete those statistical methods are. China is very focused, and understands you don't need or even want EVERYONE to be an expert in politics, economics and astrophysics. As a result most people aren't going to go beyond our equivalent of middle years or maybe junior high before entering the workforce. The students that remain in school will be the best and brightest. If you then take ONLY students enrolled in high school from a place like that and compare it to the west, your numbers will of course badly favor the countries limiting student enrollment.

As I noted above, it's no reason for complacency. I'm spending hours and hours each week compensating and supplementing the education my kids aren't getting because of systematically flawed education system .

Actually, you're the one making an unwarranted logical leap by assuming you can apply standard arithmetic logic to an infinite series. In the vid, it's done to explore the issue but it does not qualify as mathematical proof.

Yep, very similar. That extra one I gave appeals to people who relate well to patterns. No arithmetic is required at all, as long as you accept the fraction to decimal conversions.

And thanks for pointing out the quote. I didn't know what she was talking about there. Might have known it was a meme.>> ^Zawash:

>> ^messenger:
I'm not going to argue with anyone here about this, but I will add an 10.999.th reason:

That's just about the same as #8 in the video - that 0.9999.. = 0.1111.. 9, like 0.333.. 3 is.
It's also the same one I discovered one day in school, and concluded that 0.9999.. had to be one.

As well - upvote for the reference "If you're having math problems, I feel bad for you son (..)"

You're right on two counts: first, I did think you were arguing against the point made; and second I shouldn't have insulted you. Sorry 'bout that.

FWIW, I dropped out of high school after grade 11, I have no college math except what I've been teaching myself recently, and I used none of it when I figured this out for myself. Everything Vi uses in her vids is high school or even grade school math, and if you trust yourself to do arithmetic, then this proof is accessible. She doesn't even hint that the idea of "limits" from calculus gives a quick solution to her 9th reason, the sum of an infinite series.

Anyway, I'm happy to see then that my original prediction has held so far, and nobody here is starting a stupid argument about their feelings about whether this is true.>> ^entr0py:

No reason to be quite that much of a jerk about it. Not everyone has had as much college level math as you. And presumably her videos are about teaching people who don't already know everything she does.
But if you thought I was making an argument against the idea, you're wrong. Vihart presents it very convincingly. I was just trying to think of the implications.
Honestly after watching that video late at night I could no longer wrap my head around inequalities like X < 1. I used to think that meant X could be a number infinitely close to one, but that doesn't work because infinitely close to one is one (most of the video is about explaining why this is true). So, what is the highest possible number that satisfies X < 1? It seems there might be no sensible way of expressing that boundary, and thinking about it just puts you into a spiral of non-working logic exactly like Zeno's paradoxes. Looking back, at 1:23 she mentions what I'm talking about, but doesn't go into it.
Ultimately, she finds this interesting enough to talk about for 10 minutes, and we find it interesting enough to watch. So why should it evoke rage and insults when there's a chance we might talk about it amongst ourselves?

>> ^pyloricvalve:

Thanks for the reply. There were things I really didn't understand about Krugman's Hangover Theory article, especially that very point that you quote. In fact I tried to ask in a post above about this but maybe you missed it. To me it seems only natural that there is no unemployment in the boom and there is some in the bust. Both are big reorganisations of labour, it is true. However, to start with the boom is much slower and longer so adaptation is easier. Also the booming industry can afford to pay slightly above average wages so will easily attract unemployed or 'loose' labour. As it is paying above average, there will be little resistance to people changing work to it. The boom is persistent enough that people will train and invest to enter the work created by it. The information for entering the boom industry is clear and the pay rise makes the work change smooth. I see no reason for unemployment.
The bust however is short and sudden. There is no other obvious work to return to. That information of what the worker should do is much less clear. The answer may involve taking a small pay cut or on giving up things in which people have invested time and money. Many people wait and resist doing this. They may well not know what to do or try to wait for opportunities to return. Thus there is plenty of reason for unemployment to be generated by the bust.
If I hire 100 people it can probably be done in a month or two. If I fire 100 people it may be a long time before they are all employed again. For me this difference seems so obvious I have a real trouble to understand Krugman's point. I know he's a very smart guy but I can't make head nor tail of his argument here. Can you explain it to me?


I'm trying to think how to connect what you're saying to the point Krugman's making (at least as I understand it).

At a minimum, he're Caplan making the same point in less space:

The Austrian theory also suffers from serious internal inconsistencies. If, as in the Austrian theory, initial consumption/investment preferences "re-assert themselves," why don't the consumption goods industries enjoy a huge boom during depressions? After all, if the prices of the capital goods factors are too high, are not the prices of the consumption goods factors too low? Wage workers in capital goods industries are unhappy when old time preferences re-assert themselves. But wage workers in consumer goods industries should be overjoyed. The Austrian theory predicts a decline in employment in some sectors, but an increase in others; thus, it does nothing to explain why unemployment is high during the "bust" and low during the "boom."

Krugman saying the same thing in more accessible language:

Here's the problem: As a matter of simple arithmetic, total spending in the economy is necessarily equal to total income (every sale is also a purchase, and vice versa). So if people decide to spend less on investment goods, doesn't that mean that they must be deciding to spend more on consumption goods—implying that an investment slump should always be accompanied by a corresponding consumption boom? And if so why should there be a rise in unemployment?

And as a bonus, here's Brad DeLong making a similar case.

My real handicap here is that I'm not familiar enough with the fine details of the Austrian theory to say with authority what they believe. So if I misrepresent their position, it's out of ignorance.

What I gather is that ultimately the Austrian theory of boom and bust is that central banks are messing with the "natural" balance of investment and consumption goods, with a boom happening when investment is being artificially stimulated (by low interest rates), and a bust happens when interest rates eventually go back up (due to inflation, or expectations thereof).

The response from people like Caplan and Krugman is to point out that since aggregate income has to equal aggregate expenditure (because everyone's income is someone else's expenditure, and vice versa), a fall in investment should mean a rise in consumption, and a rise in investment should mean a fall in consumption. Which means we should never see an overall boom or an overall bust, just periods of transition from a rise in consumer goods and a fall in investment, to a fall in consumer goods and a rise in investment. We should never see a situation where they both fall at the same time.

But we do see a fall in both during the bust. Why?

Keynes's answer was that it happens because people are hoarding cash. Either people are themselves stuffing mattresses with it, or more likely, banks start sitting on reserves and refusing to lend out, either out of a fear of their own solvency (Great Depression), or because a deflationary cycle with high unemployment makes sitting on cash look like a good, safe investment for them (Great Depression, and now). Put simply, depressions are the result of an excess demand for money. And since money is an arbitrary thing, it doesn't have to be a scarce resource, we can always just make more...

Talking about the morality of various tax codes with someone who disagrees is nonsense. If you've been posting on the internet for years and haven't figured out that other people are quite attached to moral values that are incompatible with your own, then taxes are the least of your problems.

I'd be curious to find out where WP gets his talking points, especially since so many of them are refutable with official government data and a pocket calculator. Actually I skipped the calculator, so forgive my rounding errors:

People in the top bracket pay 38% of the income tax. Income taxes are 33% of revenues. Revenues are around $4.4 tr. So they pay about 500 billion a year.

The top tax bracket is 35%. If as WP claims we raised that to 100% We would be roughly tripling the income from them. Even only doubling it is still an extra 500 billion a year or 5 trillion over a decade, assuming the income of the rich stays steady (which it never does, rich people are much better at increasing their income than the middle class).

Both sides have hired legions of economists to support their viewpoints. I'm sure there's a right wing economist who could explain what's wrong with my arithmetic and make me look dumb (which I am, relatively), though I wonder how the author of that $2trillion figure would do if a liberal economist like Paul Krugman or Robert Reich were in the room while he made his arguments.

For our purposes, we should accept that parroting the talking points bought and paid for by your favorite political movement will not convince anyone.