Merged No more algebra?

[Hazel]

Just by looking at it, you should understand that 110 miles in 90 minutes is "just a little something over a mile a minute".

I am posting this because I am not sure just how much actual math I needed for that, and how much more for the realisation how much that "little something" would actually be.

True. Doesn't the fact that you think distances in miles almost automatically alert you to the right or wrong of a statement? People who have no habitual concept of what miles are lose that advantage.

I think!

 

[AvalonXQ]

Just by looking at it, you should understand that 110 miles in 90 minutes is "just a little something over a mile a minute".

I am posting this because I am not sure just how much actual math I needed for that, and how much more for the realisation how much that "little something" would actually be.

Agreed. Furthermore, you don't have to do the calculations to figure out that if you were travelling 110 mph, you'd cover 110 miles in the first hour -- so you're covering well over 100 miles in 90 minutes.

 

[AvalonXQ]

True. Doesn't the fact that you think distances in miles almost automatically alert you to the right or wrong of a statement? People who have no habitual concept of what miles are lose that advantage.

Not really. 100 furlongs in 90 minutes should still eyeball at "a little over a furlong a minute."

Where the intuition comes in is whether or not a furlong (or mile) per minute is a reasonable or an excessive speed.

 

[Dinwar]

People who have no habitual concept of what miles are lose that advantage.

They also lose the ability to easily plan around city driving. If all you knew was the distance through Chicago and you weren't familiar with the city you'd grossly underestimate the time it would take to get through the city (I've actually done it myself). If they tell you the time it takes to get through the city, however, you'll have a much more accurate view of the situation.

 

[Almo]

I thought cab meters ran according to the amount of time it took, not the mileage driven. So if you're stuck in a cab in traffic or ask the cabbie to wait on you, she's not getting paid? That seems unfortunate.

If, in fact, the cabs are paid according to to the amount of time it takes, then estimating based on miles, especially in a heavy-traffic city, seems like a bad idea.

ETA: I see Zig got this part already, but I'll leave it anyway.

Cab meters read BOTH mileage and time. So if you're sitting still, it goes up a certain amount per minute. But if you're going fast, it goes up a certain amount per mile. One of these rates will be higher than the other depending on your speed, and the meter takes the higher of the two rates.

On topic, algebra and geometry are most certainly things everyone should learn, even if they can't pass a test on it 20 years later. These things help you learn how to think about abstract concepts in a structured manner, and that is a useful skill.

I don't understand this desire to teach as little as possible in such a competitive world.

 

[Hazel]

ETA: I see Zig got this part already, but I'll leave it anyway.

Cab meters read BOTH mileage and time. So if you're sitting still, it goes up a certain amount per minute. But if you're going fast, it goes up a certain amount per mile. One of these rates will be higher than the other depending on your speed, and the meter takes the higher of the two rates.

On topic, algebra and geometry are most certainly things everyone should learn, even if they can't pass a test on it 20 years later. These things help you learn how to think about abstract concepts in a structured manner, and that is a useful skill.

I don't understand this desire to teach as little as possible in such a competitive world.

Thank you for meter explanation. I also don't understand this notion of teaching less. Well, I fear I do understand why they are doing it but I don't think it a very smart idea and I suspect I'm in good company there.

 

[Blue Mountain]

More than rounded. If it takes you an hour and a half to travel 100 miles, you were not traveling 110 MPH!

I think your problem may have been forgetting that there's only 60 minutes in an hour.

FACEPALM! Boy, am I embarrassed. Although, I kinda miss those old 90-minute hours ...

Sorry, there's no excuse such a silly slip-up rather than a bran fart of some sort. I wasn't drunk, stoned, or tired.

 

[Rasmus]

True. Doesn't the fact that you think distances in miles almost automatically alert you to the right or wrong of a statement?

Avalon already explained why the answer here is "probably not". Let me add that I don't think in miles, and 110 miles an hour seems like a perfectly reasonable driving speed.

Of course, *then* you'd have to remember that you're never going to average that over a journey and 65 miles is actually a very decent average, which makes me wonder just how someone would manage that between any two points in the USA...

People who have no habitual concept of what miles are lose that advantage.

I think!

I know that common speed limits are around 60 or 70 miles or thereabouts.

 

[I Ratant]

On hundred mile or so freeway trips, I can average 80 mph... along with the rest of the traffic.
Phenomenal gas mileage at that rate, also!

 

[xtifr]

FACEPALM! Boy, am I embarrassed. Although, I kinda miss those old 90-minute hours ...

Sorry, there's no excuse such a silly slip-up rather than a bran fart of some sort. I wasn't drunk, stoned, or tired.

Ok, now that the guy who made an elementary mathematical error has acknowledged it, maybe we can stop the derail about that error and get back to the topic of algebra. (And yes, I admit I participated in the derail--I'm not assigning blame here; merely observing that we are derailed.)

As I argued earlier, basic algebra is very simple. In my opinion, simpler than arithmetic. Much of it it is so simple that people use it all the time without even realizing it. At the same time, I am forced to admit that some people find the level of abstraction represented by algebra to be confusing or off-putting. My mother and one of her sisters felt as I did: math class got a whole lot easier when we reached algebra. On the other hand, her other sister had no problems with arithmetic, but felt like she hit a brick wall when she reached algebra. I don't fully understand it, but the three sisters never managed to resolve the issue, so clearly there really is something about trying to abstract mathematics to that level that some people have a hard time with.

Now I know my other aunt uses algebra a lot. She just doesn't seem to realize it. It's ok when you have specific instances in front of you that resolve to, and look like, pure arithmetic, but when you lay out the pure abstractions, she balks. If anyone has any suggestions for getting past that hump, I'd love to hear it. It's probably a little late for my aunt, but it might help others.

 

[Hazel]

On hundred mile or so freeway trips, I can average 80 mph... along with the rest of the traffic.
Phenomenal gas mileage at that rate, also!

"Average"? Which means you are sometimes going far faster than 80? Heaven help us!

 

[I Ratant]

The 80 average is just life-preserving!
I hate being run over from behind!
There's people in a hurry out there on the freeways!
Middle lane, watch the mirrors...

 

[superfreddy]

FACEPALM! Boy, am I embarrassed. Although, I kinda miss those old 90-minute hours ...

Sorry, there's no excuse such a silly slip-up rather than a bran fart of some sort. I wasn't drunk, stoned, or tired.

Yeah, I heard bran can give you gas...

 

[Careyp74]

I just had a flashback to uses of algebra in every day life. Someone mentioned sets earlier. I believe that if it weren't for the teaching of the concept, I wouldn't have the skeptical mind I have today. I think this applies to my wife too. She took the same courses I did in getting her Masters Degree, which included Logic, Statistics, and Algebra.

Now, this isn't really algebra, but the concept transfers. There was a discussion about the use of phrases like "up to 40% off or more." One of those commercials came on the other day and my wife criticized it. This got me thinking.

Many people believe that this means you will either save 40%, or you will save a percentage that is more. However, looking at the set of all percentages included in that statement, we find that 39%, all the way down to 0% also fit into the statement.

With our complete 'set' understood, we can evaluate the statement more exactly. This process isn't obvious, talk to other people that aren't as critical of a thinker as yourself and you will see.

Sure you can teach this without going into in depth algebra, but they don't do that. There are probably other tools picked up this way also. Lastly, going further into a subject helps solidify the simpler concepts in your mind, which is why I never had a problem with having to learn everything that was taught.

 

[cwalner]

I just had a flashback to uses of algebra in every day life. Someone mentioned sets earlier. I believe that if it weren't for the teaching of the concept, I wouldn't have the skeptical mind I have today. I think this applies to my wife too. She took the same courses I did in getting her Masters Degree, which included Logic, Statistics, and Algebra.

Now, this isn't really algebra, but the concept transfers. There was a discussion about the use of phrases like "up to 40% off or more." One of those commercials came on the other day and my wife criticized it. This got me thinking.

Many people believe that this means you will either save 40%, or you will save a percentage that is more. However, looking at the set of all percentages included in that statement, we find that 39%, all the way down to 0% also fit into the statement.

With our complete 'set' understood, we can evaluate the statement more exactly. This process isn't obvious, talk to other people that aren't as critical of a thinker as yourself and you will see.

Sure you can teach this without going into in depth algebra, but they don't do that. There are probably other tools picked up this way also. Lastly, going further into a subject helps solidify the simpler concepts in your mind, which is why I never had a problem with having to learn everything that was taught.

That's more statistics than algebra, but statistics are often used in very misleading ways by people with agendas (political, commercial or ideological).

Some of my favorites common abuses:

'Our drug is clinically shown to be twice as effective as their drug'
(it works 2% of the time instead of 1%)

Misuse of 'average'. Is it Mean, Median or Mode that you are referring to? And remember, the 'average' human has 1 ovary and 1 testicle.

 

[Careyp74]

That's more statistics than algebra, but statistics are often used in very misleading ways by people with agendas (political, commercial or ideological).

well, there isn't really any statistics involved in my example, it is more about what the expectation of the consumer is, and the disappointment when he finds that he doesn't save anything at all, because he doesn't realize that the set of values in the statement "up to 40% or more" also includes 0.

 

[Modified]

well, there isn't really any statistics involved in my example, it is more about what the expectation of the consumer is, and the disappointment when he finds that he doesn't save anything at all, because he doesn't realize that the set of values in the statement "up to 40% or more" also includes 0.

It also doesn't make much sense. If it's up to 50%, you should say "up to 50%". The "or more" is just an attempt to mislead.

 

[cwalner]

well, there isn't really any statistics involved in my example, it is more about what the expectation of the consumer is, and the disappointment when he finds that he doesn't save anything at all, because he doesn't realize that the set of values in the statement "up to 40% or more" also includes 0.

It just reminded me of another misleading use of percents that I consider within statistics.

this would be an example. Bob has 25% more M&M's than Amy, and Carol has 20% fewer M&M's than Bob. Who has more M&M's: Amy or Carol?

ETA: This can actually be solved easily using Algebra to bring it back to the OT.

 

[Careyp74]

It also doesn't make much sense. If it's up to 50%, you should say "up to 50%". The "or more" is just an attempt to mislead.

That is marketing for you. One good reason for critical thinking.

It just reminded me of another misleading use of percents that I consider within statistics.

this would be an example. Bob has 25% more M&M's than Amy, and Carol has 20% fewer M&M's than Bob. Who has more M&M's: Amy or Carol?

ETA: This can actually be solved easily using Algebra to bring it back to the OT.

I am glad you realized that.

 

[Minoosh]

Is (HS) algebra necessary?



Is algebra necessary?
http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all&_r=0

I came across this article recently and found it vaguely disturbing, even though as a short-lived high school algebra teacher I sometimes wondered myself if the near-universal requirement for freshman algebra did more harm than good. Where I taught, the normal freshman algebra flunk rate was 50 percent. My state had recently upped the high school math requirement to four years, and in practice students got algebra twice, as freshmen and juniors; they did geometry in 10th grade and the required fourth year was "financial math" or "consumer math," although calculus and or precalculus were also available.

My first, 29-year-long career was in journalism, and I actually used math a lot. Most of that time was as an editor and I saw very intelligent "word people" mangle statistics and struggle with the concept of area (!) Example, a reporter writing about a billboard ordinance said the size of boards would be cut in half. She didn't realize that halving each dimensions would cut the permitted area by three-quarters. A fellow editor, extremely sharp, told me he had wanted to become a geologist, but that he "couldn't do fractions." Really?

This may be more appropriate for the education subforum, but my question is broader than what public education policy should be. It has to do with the (IMO) potentially crippling effects of innumeracy. My hunch is that math phobia has become so ingrained in the U.S. - over two or three generations - that adults unwittingly carry the message that math is a bogeyman, a semi-sadistic struggle we inflict on children "for their own good," and that the expectation students will fail becomes a self-fulfilling prophecy.

A clue: When I earned teacher certification in my late 40s, the bright young "kids" in my college cohort panicked somewhat at having to prove they could do middle-school math. This wasn't even algebra, for the most part. More like decimals, fractions and percentages. Area or volume, maybe. The Pythagorean theorem.

The author seems to think that if we focused on statistics kids would see the relevance and therefore become more engaged, and this may be true, but I don't see how you get past the fact that math learning is largely sequential, sometimes abstract and mechanical, and that skimping on the foundations can put students at a disadvantage in ways they may not appreciate at age 14.

I now work as a paraprofessional at a small charter school which introduces algebraic concepts in third grade. "Find the missing addend." Most kids seem to have no problem with that. The text doesn't call this "algebra," and it doesn't tell students they're "solving for n," but that's what they're doing.

At this school, 7th graders are using the text my old school used in 9th grade. And for the most part they succeed. Both schools are in low-income neighborhoods. I don't think my school "cherry picks" kids; it just warns parents or guardians that the accelerated curriculum might not be the best fit for some students. Tutors are liberally applied where needed, and there is a schoolwide culture of discipline that IMO reduces distractions quite a bit.

And, things get followed up on.

I hadn't meant to write all that, I just suspect the author of this article has things backwards and I can't quite put my finger on why. Maybe it's his assumption that algebra is confusing - but why should it be? Yes, kids have to learn that x does not mean "multiply," but freshman algebra is usually pretty straightforward - you make $6 an hour, the motorcycle costs $300, how many hours do you have to work to buy the motorcycle? How do you say that in words, how do you say it in numbers and symbols? Why should that be considered confusing, arcane, irrelevant? Is that too much for kids to handle? If so, does it say anything about future U.S. competitiveness?