[kenberg]

Math education has to address the advanced issues needed for international competition in technology and the everyday issues of folks. Degrees in a triangle would be nice, but a trip to the grocery today inspired a different take on everyday math.

The store gives you points as a reward. Every $100 gives you ten points, and every 10 points reduces the price at the pump by ten cents. Also, there are specials. I just picked up a vegetable tray (we are having people over tomorrow) and a 40 point bonus came with it. So often I get around sixtyu cents or more off when I fill the tank.

Here is the everyday question: What is the right strategy? Build up points and use them all at one time, or use them as soon as you get them? The answer of course is neither. The right strategy is to make sure that whenever you do cash in the points you have your tank down as much as you are comfortable with. If you use 30 points on 10 gallons and then later use, again, 30 points on 10 gallons you save a total of $6. If you hoard your points and use all 60 points at once on 10 gallons you also save $6. If you run the tank low and fill it up with 20 gallons, you save $12 whether you do it all at once with the 60 points or twice, redeeming 30 points each time.


I would like to see someone be able to handle such reasoning by the time they finish 8th grade (earlier is better of course but ...). Note that calculators are basically irrelevant here. If they really need a calculator to figure out the savings on 10 gallons at 30 cents a gallon then, sigh, I suppose they must. But the real issue is knowing what to calculate and the significance of the result.

If they can do the above, I am willing to cut them some slack in their knowledge of triangles.


And yes, they get bonus points if they note that this must be a plot to get everyone to drive an SUV or some other vehicle with a large tank. I am joking here. Sort of.

[matmat]

kenberg, on 2011-January-01, 10:05, said:

And yes, they get bonus points if they note that this must be a plot to get everyone to drive an SUV or some other vehicle with a large tank. I am joking here. Sort of.

I hate how vendors manipulate math to trick consumers. On the flip-side of our discussion I would really like to see companies try to exploit people's lack of math knowledge less. I know this is a pipe dream, but hey... new year new hope?
*grumble*

[TimG]

matmat, on 2011-January-01, 12:41, said:

I hate how vendors manipulate math to trick consumers. On the flip-side of our discussion I would really like to see companies try to exploit people's lack of math knowledge less. I know this is a pipe dream, but hey... new year new hope?
*grumble*

In Maine, and probably most states, grocery stores are required to post per unit prices for all items. The idea is that consumers shouldn't have to figure out whether a 12.7 ounce can that costs $1.29 is a better or worse deal than a 23 ounce can that costs $2.49. But, there doesn't seem to be any requirement that similar products be priced by the same unit. A large can might be priced per pound while a smaller can is priced per ounce. Some items are priced per fluid ounce in one container and per ounce of weight in another. It seems to me that these switches happen most frequently when the larger size item costs more per unit -- that is when a consumer would be wrong to buy the larger size -- but that may well be selective memory.

[helene_t]

haha yet another reason to switch to metrics

In Europe, while most products are priced per 100g you occasionally see prices per kg or per gram but it doesn't require that much math skills to convert between those.

[kenberg]

When 14 or so I stocked shelves in a grocery (yes I also set pins and I also delivered papers, there are reasons I could buy a car shortly after I turned 15). I went to the owner to point out that there must be a mistake on cans of corn that were marked 8 cents apiece and three for a quarter. "Shhh" was the response.

[helene_t]

Once I worked in a supermarket. They had rye bread for 4.32 a piece and three for 12.95. Save one oere (0.01)! One smart customer came with three loafs and asked me to put them on three different bills. Then each bill of 4.32 would be rounded to 4.30 when he asked to pay cash because the smallest coin was 5 oere. (If he had payed with checque or debit card he would have had to pay the full price of 4.32 a piece).

[kenberg]

A math issue came up yesterday. My younger daughter is taking out a mortgage and I am assisting. She is getting a 15 year mortgage with a 3.75% interest rate. This interest rate comes with points, but the deal appears to be worth it. Part of the paperwork is a "Truth in Lending" document, required by the government to make sure everyone understands what they are getting. Uh huh. The document gives an APR of 4.78%. What does this mean, I inquire. It's the number that the software prints out, is basically the response. I would like to see the calculations, I say. The software doesn't print out calculations, only the result, I am told. OK, there is a document that comes with the Truth in Lending document explaining what it means. My daughter has already signed a statement saying she has been given the Truth in Lending document. My wife is making noises of the let's move on sort. Mathematicians are seldom popular. Here is what it is: You get a mortgage for x dollars at 3.75%. There are closing costs for the appraisal and such, and in this case for some points. You really get y dollars, not x, to work with. A mortgage for y dollars at 4.78% has the same monthly payments as a mortgage for x dollars at 3.75%.

What most people fail to get from their education is that the numbers in such documents actually have meaning AND this meaning can, with persistence, be understood. It does not at all require a Ph.D., or calculus, or algebra. And again: A calculator is useful here for determining what the payments would be. I don't do this by hand, why would I? But as is so often the case, a calculator is useless unless you know what to compute and what to make out of it. And it seems to me the Truth in Lending document is also totally useless unless you can track down what the numbers mean.

Of course it's true that we then moved on. So the non-mathematicians have the last laugh. But if someone puts a figure in front of me that is supposed to reveal a truth, I would like to know what truth it reveals.

Mostly, I would like students to learn that numbers have meaning, and that they can understand that meaning.

[onoway]

Not specifically dealing with math education but she is discussing education and presents some ideas that I haven't seen mentioned so far in this discussion which might be of interest http://www.ted.com/t...tm_medium=email

[kenberg]

Yes, it is of interest.
She mentions three issues
1. Zero tolerance
2. Few male teachers
3. Compressed curriculum
She is speaking about boys 3-13. I will comment on my own experiences and what I have seen.

Zero tolerance, especially her reference to toy guns: It's nuts, simply nuts. We all played with toy guns when we were kids. We all understood the difference between a toy gun and a real gun, more generally we understood the difference between fantasy and reality. Forbidding toy guns simply gives kids the idea that the adults around them lack the ability to distinguish between fantasy and reality.

Few male teachers: In my K-8, the only male teacher I had was in wood shop. This bothered me not at all. But then this was how society was. During the day, Monday through Friday, children were cared for by women. Moving on to high school I did, often but not always, prefer male teachers. Definitely not always though. My physics teacher was a capable woman, my biology teacher was a male idiot.

The compressed curriculum (i.e. learning too much too soon): Far and away, this is my biggest concern with the life of the modern child. Among other things, it's in many ways phony. The first grade twins I spoke of get a lot of homework. It keeps their mother busy. Or, another example, I called my older daughter the other day. My son-in-law answered and explained she was helping the sixth grader with his homework which, it turned out, was to compare and contrast the attitudes displayed by different main characters toward adventure as exhibited in different stories that they had read. I can recall a theme I wrote when I was at a similar age. It was about frogs. We had gone fishing for a few days in northern Minnesota and I brought home some frogs that I had caught. They got loose and were hopping through the neighbor's yards and gardens, and I had to round them up. I wrote about this with no help whatsoever from any parent and turned it in. It got a good grade. Returning to the present, my daughter was too tired to call back when they finished with the compare and contrast stuff, but she dropped me a somewhat joking email the next day explaining the assignment and saying that she really hoped she passed.

Surely one of the things we want to teach is independence. Giving a kid an assignment that he can understand and do, and then letting him do it on his own, seems like a sensible approach.

[kenberg]

http://www.washingto...1013003556.html

Short version A woman was convicted of a felony for lying about her address so that her kids would be assigned to a better school.

In the Washington suburbs some of the high schools are among the best in the nation and others are truly atrocious. This difference far exceeds anything that I knew of growing up, and parents cope with this as best they can. The oldest grandchild went to Whitman. I seriously believe that the house she grew up in has a market value of (at least) 100K more than what it would have if were in a location feeding into a different school, even into a simply average school. Parents pull various strings to get their kids into the preferred school and certainly lying is one of the techniques.

This is of course not entirely new. My wife Becky went to Lowell hs in San Francisco. A good school that required a substantial early morning ride on public transportation. She never knew how her parents pulled that off. Her younger sister Janine did not get into Lowell but she did not go to her assigned school either. There was a better school that had Russian language instruction and so Janine, like a lot of other kids, developed a sudden overwhelming enthusiasm for studying Russian. Or so the parents explained to the city. Naturally she got her transfer since the assigned school could not accommodate her passionate need to learn Russian. Da.

My recollection of adolescence is that we did not much pay attention to what adults told us but we paid a lot of attention to our environment, our friends, our perceived choices. We have to do better in our offerings to kids who come from backgrounds where the parents are less savvy about such manipulations. That would describe my parents, for example. But in the 1950s the differences were much less stark. No comparison.

[onoway]

an interesting article here http://www.sharpbrai...ety-management/ which talks about programs which are apparently now reaching quite a few schools in one form or another. I watched an interview with Goldie Hawn who is intensely involved with one program. She said that aside from less aggression in the kid's interactions, and better performance on tests, the teachers noticed that kids who had been skipping school were no longer doing so. All measurable results, unlike such things as the kids seemed happier and more relaxed...

[Elianna]

kenberg, on 2011-January-31, 07:30, said:

http://www.washingto...1013003556.html

Short version A woman was convicted of a felony for lying about her address so that her kids would be assigned to a better school.

In the Washington suburbs some of the high schools are among the best in the nation and others are truly atrocious. This difference far exceeds anything that I knew of growing up, and parents cope with this as best they can. The oldest grandchild went to Whitman. I seriously believe that the house she grew up in has a market value of (at least) 100K more than what it would have if were in a location feeding into a different school, even into a simply average school. Parents pull various strings to get their kids into the preferred school and certainly lying is one of the techniques.

This is of course not entirely new. My wife Becky went to Lowell hs in San Francisco. A good school that required a substantial early morning ride on public transportation. She never knew how her parents pulled that off. Her younger sister Janine did not get into Lowell but she did not go to her assigned school either. There was a better school that had Russian language instruction and so Janine, like a lot of other kids, developed a sudden overwhelming enthusiasm for studying Russian. Or so the parents explained to the city. Naturally she got her transfer since the assigned school could not accommodate her passionate need to learn Russian. Da.

My recollection of adolescence is that we did not much pay attention to what adults told us but we paid a lot of attention to our environment, our friends, our perceived choices. We have to do better in our offerings to kids who come from backgrounds where the parents are less savvy about such manipulations. That would describe my parents, for example. But in the 1950s the differences were much less stark. No comparison.

I just finished reading Jonathan Kozol's Savage Inequalities. Even though it was written twenty years ago, not a lot has changed. I bring this up because it contains a lot of side-by-side comparisons of schools in the same place, and the comparisons are horrific. If I were on the jury there is NO WAY I could convict the lady for trying to get her child into the better school, and I think that the state of some our schools is an embarrassment to our country.

[jschafer]

I agree with a lot of what Ken Robinson has to say on education (although that talk is a few years old now).

[blackshoe]

Very interesting talk.

[kenberg]

I think I am interested in hearing more of what he has to say although I am not sure I will agree. Some years ago I was at a conference where I participated in a number of imaginative presentations. Mr. Robinson reminds me a bit of one of them. Afterward we were to review the experience. In response to the question "Would you attend another presentation by this person?" I responded "Only if you chained me to the wall".

I am highly sympathetic to complaints about the conformity required in schools. But I am also more than a little suspicious of suggestions to eliminate it. A middle school teacher I knew told me how pleased she was that her school was now emphasising imaginative thinking in mathematics rather then getting the right answer. She used to have to have her husband help her because really she didn't much understand the math, but under the new approach this no longer mattered. Seems like something got lost between the top level planning and the execution on the ground.

My daughter spent a year at a middle school where they emphasized the importance of students following their own interests. She certainly did so. People who advocate such things had better be prepared for the results.

Anyway, his presentation is provocative. On my computer at least it stopped after ten minutes or so although he wasn't done yet I think. But I may follow up some.

[jschafer]

You are right that it was a short version of his talk, if you are interested in the whole presentation:


or a more entertaining talk from 2006:

[kenberg]

I am indeed interested. It's for later, I need to get going, but I'll watch it.

[y66]

I watched Sir Ken's TED speech. Hard to take issue with his main premise that the creative impulse takes a beating as kids venture out into the world and that the main goal of most schools isn't to provide maximum nurturing of this impulse.

When he talked about insects at the end, I thought he was going to start channeling Heinlein. I think that would have helped clarify his argument actually.