Who needs algebra?

[TheBigH]

You can't do statistics without at least some algebra, so this seems like complete nonsense.

[Bill Spight]

You can't do statistics without at least some algebra, so this seems like complete nonsense.

I wondered about that, too. We would have to see more to know exactly what they meant by that. I certainly think that a course in statistics would require algebra as a prerequisite, myself. OTOH, learning how often to bluff in poker doesn't take much algebra.

To solve the Wason task, most people might need to have studied some logic. OTOH, if the task is framed in a social context, nearly everybody gets it right. Algebra per se is context free. People might be able to utilize algebraic reasoning in certain contexts without having mastered the formalities.

One possibility might be that they mean statistics in the original sense, such as the rate of unemployment or the size of the population. Citizens need to be able to think about those statistics in everyday life.

[DrStraw]

You can't do statistics without at least some algebra, so this seems like complete nonsense.

I cannot agree with that. At least not these days. And I have taught Intro to Stat many, many times. Of course, if you are talking about calculating your own statistics instead of punching them into a calculator that is a different matter. But these day it is perfectly possible to do statistics by learning which buttons to push on a TI-84 or equivalent.

[Mike Novack]

I've been staying out of this so far even though I have taught it (and tutored folks going for their HS equivalency math exam which in theory doesn't require algebra).

You are forgetting what algebra is. Or what it is not. Arguments about the way being taught shouldn't be part of this more general question.

I am old enough to remember being taught math in elementary school where being able to solve word problems without the aid of algebra (in theory we hadn't been taught any) was in effect a gateway to algebra. In other words, if you couldn't somehow learn to solve these problems without the aid of the tool invented to make this easy you didn't get to learn "how to cheat".

I'm sorry Dr. Straw, but does your calculator allow you to enter the words of a typical "word problem" in two unknowns and give you the solution (and yes, I know that computer programs capable of this have been around for decades). Let's see your calculator handle "Tom is three times as old as Mary. In five years Tom will be just twice as old as Mary. How old are Tom and Mary?"

BTW --- because the kids I was tutoring for their GED were going to be faced with basic word problems I thought them "basic algebra". Enough to be able to solve simple sets of linear equations and the rules that would enable them to be able to correctly translate ~95% of word problems into the equations. This was a small "class" so close to 1:1 tutoring, three nights a week. But in only 5-6 weeks when the program wanted them to try the exam (see what they still needed to pass it)they all passed the math part << so I lost my "class" to more concentration on the language skills part >>

[DrStraw]

I'm sorry Dr. Straw, but does your calculator allow you to enter the words of a typical "word problem" in two unknowns and give you the solution (and yes, I know that computer programs capable of this have been around for decades). Let's see your calculator handle "Tom is three times as old as Mary. In five years Tom will be just twice as old as Mary. How old are Tom and Mary?"

Not sure what this is in reference to. It has been a long thread and I don't remember it all, but I can say that I strongly disapprove of calculator usage until someone understands how to put a problem together. I am totally with you on this.

[Marcus]

"Tom is three times as old as Mary. In five years Tom will be just twice as old as Mary. How old are Tom and Mary?"

I was curious to see if, with all the recent additions to Google, there would be an answer provided if I put this exact string into the search box. Alas, even Google doesn't provide an answer directly to word problems (yet).

[Mike Novack]

Whether or not Google can not relevant. Computer programs capable of translating word problems into algebra and then solving the equations have existed for decades. For all I know, even better these days, but back then I saw one written in LISP that was about as successful as a typical h.s algebra student who was getting say a grade of A- in math. Not perfect but pretty good.

[quantumf]

I'm sorry Dr. Straw, but does your calculator allow you to enter the words of a typical "word problem" in two unknowns and give you the solution (and yes, I know that computer programs capable of this have been around for decades). Let's see your calculator handle "Tom is three times as old as Mary. In five years Tom will be just twice as old as Mary. How old are Tom and Mary?"

Not sure what this is in reference to. It has been a long thread and I don't remember it all, but I can say that I strongly disapprove of calculator usage until someone understands how to put a problem together. I am totally with you on this.

Umm, you don't need a stellar memory for this - it was the very last post before Mike's comment, a mere two days ago, where you suggested or implied that learning statistics by learning the right buttons on a calculator without understanding algebra was a perfectly reasonable thing to do. I suspect Mike and I may have misunderstood your point.

[EdLee]

you suggested or implied that learning the right buttons on a calculator without understanding algebra was a perfectly reasonable thing to do.
I suspect Mike and I may have misunderstood your point.

Small mis-read, yes.

perfectly possible to do statistics by learning which buttons to push

[DrStraw]

I'm sorry Dr. Straw, but does your calculator allow you to enter the words of a typical "word problem" in two unknowns and give you the solution (and yes, I know that computer programs capable of this have been around for decades). Let's see your calculator handle "Tom is three times as old as Mary. In five years Tom will be just twice as old as Mary. How old are Tom and Mary?"

Not sure what this is in reference to. It has been a long thread and I don't remember it all, but I can say that I strongly disapprove of calculator usage until someone understands how to put a problem together. I am totally with you on this.

Umm, you don't need a stellar memory for this - it was the very last post before Mike's comment, a mere two days ago, where you suggested or implied that learning statistics by learning the right buttons on a calculator without understanding algebra was a perfectly reasonable thing to do. I suspect Mike and I may have misunderstood your point.

I think I said possible, not reasonable. It is totally unreasonable if you want to learn anything. It is completley possible, with the right "teacher", if all you waant is a grade. When I was teaching a lot of statistics there is no way they would have passed just by using the calculator, but that was not true had they taken it with a certain other person in the department.

[daal]

http://sploid.gizmodo.com/genius-app-so ... 1649161239?

[drmwc]

Typical mathematics education is a fantastic way of obscuring the fact that discovering maths should be playful.

It's a topic I could write about for a long time. However, someone else has put their thoughts to paper far more eloquently than I can ahieve:

https://www.maa.org/external_archive/devlin/LockhartsLament.pdf


Here is a very small sample:

Mathematics is the music of reason. To do mathematics is to engage in an act of discovery and conjecture, intuition and inspiration; to be in a state of confusion, not because it makes no sense to you, but because you gave it sense, and you still don't understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it.