CW responds:
Print it out in multiple sheets, lay it on the wood and run a pounce wheel along the lines to be cut. Dust chalk on the line, and remove the sheets.
Charlie Self
"It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so." Mark Twain
"New Math" is _easy_ for me to date. I'm 50, and my brother is 3 years younger. He had the 'new math' stuff inflicted on him in grade school. I didn't. Same shool system, same school. Mostly even the same teachers. (we both tended to be 'far in advance' of class-level, due to parental involvement. e.g. reading and vocabulary skills at 11th-grade level, in _fourth_ grade -- not a way to make friends with classmates!)
"New math" involved introducing a number of 'abstract mathematical concepts' -- primarily the basics of 'set theory', at an early stage in the educational process; frequently to the detriment of 'drill' on basic arithemetic skills.
For those who survived the process -- _and_ managed to retain an interest in the subject -- "advanced math" (probability theory, trigonometry, calculus, etc.) classwork, later, was *much* easier.
Most of the 'concepts'/'ideas' behind the 'new math' teaching were good; the implementation *was* flawed, in large part by pushing the abstract concepts *too* early.
Seems to me, I learned about sets and subsets about three years in a row in early grade school, when I should have been learning arithmetic. Others say what they want, I think it did hurt my math abilities. How could it not?
It's all a matter of 'viewpoint'.
Rather than 'play games' with the number you're "subtracting from" -- i.e., 'borrowing' from the 'next higher place' -- they play games with the number that they are subtracting (e.g. when you would do a 'borrow', they do the same subtraction from the 'ten larger' value, and then, *instead* of the 'borrow', they 'add one' to the next digit of the number they're subtracting. Thus, they subtract 'one more than the original' from the first number, rather than subtracting from 'one less than the first number'. The result
*is* equivalent, and you only have to worry about a -single- position at a time. Even when, say, subtracting 9, from 2,000,000,008.You try to subtract 9 from 8, but it's too big. classical math would have you do the 'borrow' from the 10's column, _but_ there's nothing there to borrow from, so you have to keep going till _eight_ places, and convert the 2,000,000,008 into 1,999,999,99(18).
New style goes like this: subtract right-most digits 8 -9
doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from): 18 -9 == 9
Now, consider the 'tens' digits, and *ADD*ONE* to the lower digit, to make up for the ten you added above -- _ignore_ the 'ones' digits, we're done with them:
0 8 -(1) 9 ==== == 8doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):
10 8 -(1) 9 ==== == 9 8Now, consider the 'hundreds' digits, and *ADD*ONE* to the lower digit, to make up for the ten you added above -- _ignore_ the 'ones' digits, we're done with them:
0 08 -(1) 09 ==== === 98doesn't fit, treat the upper digit as ten bigger ("don't worry" about where that 'ten' comes from):
10 08 -(1) 09 ==== === 9 98etc., etc., ad nauseum. or at least until you run out of digits. Note that whenever things "don't fit", you 'add ten ones', and then at the next stage, you 'subtract one extra ten', so things *do* come out right.
Note that you -never- are considering more than one digit from each number at a time, and that there is only a _single_ 'borrow digit' at any time. (*UNLIKE* the old-style method, where you had to adjust _eight_ digits at one time.)
The 'new style' method _is_ better suited for manipulating -large- numbers 'in your head', faster, and with lesser probability of error. *WHY* it works _is_ harder to understand, _and_teach_, *unless* you have an under- standing of 'decomposing' the subtraction into a series of operations, and understand that you can do "equivalent transformations" to the individual pieces of that series, *without* affecting the answer.
One of the points 'new math' teaches, although it is -never- expressly so mentioned, *is* that 'decomposition' of big problems into a series of littler ones,
Aside: until _well_into_ college, nobody _ever_ tells you "what it is" that they're trying to teach -- the best you get is a 'bunch of examples', from which *you* must deduce/'internalize'/"generalize" the -process-.
"Problem solving" is a skill that _nobody_ knows how to *teach*. Even those who _do_ it well, don't know how they learned it.
Anybody who _does_ figure out how to (a) teach it, and/or (b) test for the ability to _learn_ how to do it, will get *RICH*.
Actually, "WTF's" are a _fourth_ grade course.
It's all basic 'set theory' stuff. The properties of a 'collection of objects' -- properties which are separate from the individual objects that make up the set. "Mode" is a fancy word for 'the most commonly occurring value'. "Mean" is what you think of a the 'average' -- add 'em all up, and divide by the number of items. And there's also 'median' -- sort 'em in order, and pick the one physically in the middle of the sorted list.
It's like ordering "500 bd ft of FAS" lumber by phone. You _don't_ know what size each individual piece will be, but you _do_ know things about the 'totality' of the order. A "500 bd ft" order is s 'new math' concept -- you don't know the precise details of each board's dimensions; and you *DON'T*
*NEED*TO*, to know that is, or _is_not_, sufficient for your needs.This is actually one of the 'core concepts' that "new math" sets out to instill -- that you *can* "get answers" *without* having to know _all_ the 'details'.
DON'T count on it:
e.g: Mix 1 cup water, and 1 cup alcohol. measure the result *carefully*. It comes up several percentage points short of a pint.
Or: One raindrop running down the left side of the window One raindrop running down the right side. They run _together_.
1+1 = 1And we won't discuss how many rabbits you get, when you put one male and one female in the same cage.
(SWMBO is a teacher & I pick these fights from time to time. )
Arithmetic & math are not the same thing. Arithmetic is the grinding of numbers, in this day and age most properly done with a calculator or computer. Math is applying principles towards the correct solution of a problem. The most brilliant person I ever met was a Ph.D. who was fantastic at math but LOUSY at arithmetic. In the "real world" that's not a handicap because computers do all the boring arithmetic anyway.
Your learning set theory in grade school detracted from your arithmetic skills learning in the same way that an extra period of French, Social Studies, or even Recess would have. It was simply time devoted to a completely different subject. IMO it's more important to learn how to think than to attempt to learn to beat a $5 calculator.
-- Mark
Not fighting. Why are you paying that much for a calculator to do arithmetic?
I recall my college math teacher as being young, confused and not a teacher. He simply didn't like it, so stayed home whenever he or his wife had a hangnail or ingrown hair. He showed up for class almost as often as I did, which was about
1 in 3, so none of us were taught, or learned, a thing.Charlie Self
"It ain't what you don't know that gets you into trouble. It's what you know for sure that just ain't so." Mark Twain
Sorry, GIGO applies here.
Punching at the calculator can give the most amazing results for those who have no concept of the range of possibilities. You HAVE to master arithmetic.
I like to go to the under 30 checkout drudge and give change to make up the even quarter or dollar _after_ they've had the machine calculate the change. Amazing.
As to math majors - >
I'm in the same county as you, and I remember when my daughters were in middle school and high school they had some very odd stuff having to do with drawing parabolas and other graphing techniques where they actually learned to estimate what a curve would look like on a graph without having to plot any points. They did pretty well with it too. Some math professor at Virginia Tech apparently decided students weren't getting good enough instruction before college, so he helped develop the curriculum. In other words, your kids may be getting stuff unlike anywhere else. On the other hand, the new Standards of Learning requirements have had a big effect on things as well, and my kids just missed that, so it may be different now than it was 10 years ago.
I know the feeling. I was OK till they started in on that graphing stuff. Did your kids get the "mini computers?" Those through me for about 10 minutes till I realized it was just binary arithmetic being done in a funny way.
Bill Ranck Blacksburg, Va.
When there is alcohol concerned it is quite common for some to go missing. Or for the measurement to go awry.
Is it single or double paned glass?
Not really
this is some variety of exponential series, not addition.
-Jack
BUT: Without the arithmetic skills, math is a drag, you fall behind, without the math, the higher level stuff is near to impossible, because you don't have the basics of number manipulation.
BTW, my first calculator was bought as a junior in HS, and it cost over a hundred, and did what a 5 buck calculator does now. Before that, calculators did not exist.
yes they did. they came from hp, and cost $400. i still use mine, purchased in 1972.
"Charlie Spitzer" wrote in
You have me beat by about 1 year. Mine was a HP, also.
Perhaps for learning, but maybe not using. How many of today's engineers are 10% as good at arithmetic as the slide rule generations? My late great uncle was a EE in the 1920's - 60's. He showed me once how they roughed out on a slide rule something having to do with (IIRC) hanging long-span transmission lines, like over a gorge. He slid the slide & cursor around a few times on on one side, subtracted the result from 1 in his head, flipped the rule over, made another setting, & read the answer -- including the correct power of 10. Multi-volume log tables were used for the final answer, but the 10" slide rule was accurate enough for most estimations. Those generations were *good* at arithmetic. Are today's engineers less capable because they don't have to do that stuff? I don't think so.
I'm not 100% sure I know my children's birthdays -- they're written down in my wallet ;-) -- but for some reason I know my first calculator, a 1976 HP25C, cost $214.48. Can anyone tell what this does? 01 1 02 STO + 0 03 RCL 0 04 GTO 02
-- Mark
Greetings and Salutations....
On Thu, 16 Oct 2003 20:02:10 GMT, "Mark Jerde" wrote: *snip*
2^n series. My HP 25C cost a bit more than that...$250 or so, but, it was a great tool to have and made some parts of college a lot less painful. Plus. it was really fun to poke around with the "calculator games" that quickly came out for it. Regards Dave MundtNot sure who even started this thread but it appears to have ended up as a thread on new math And i do not know even if this will work for you. It is what i use to draw an oval
Bingo!
Now that you mention it, the $214.48 was probably for the HP 25. A day or two after I got it the college bookstore got in the continuous memory 25C. I got my money back on the 25 & got the 25C. No, I don't recall that exact amount. ;-)
-- Mark
I can't remember the model number of my early '70's HP, but talk about new math! RPN was/is a kick. Used RPN later in writing interpretive languages.
-Doug
Sounds like mine. He had a 20-point D range.
Funny. My wife has been a "checkout drudge" at Wal-Mart for some 10 years now. She was a math major.
She's over 30 though.
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