More on math...
 

I'm sure this is Clinton's fault.

http://www.eurekalert.org/pub_releases/2005-09/uons-nti091305.php

New trigonometry is a sign of the times
Mathematics students have cause to celebrate.

A University of New South Wales academic, Dr Norman Wildberger, has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit.

What's more, his simple new framework means calculations can be done without trigonometric tables or calculators, yet often with greater accuracy.

Established by the ancient Greeks and Romans, trigonometry is used in surveying, navigation, engineering, construction and the sciences to calculate the relationships between the sides and vertices of triangles.

"Generations of students have struggled with classical trigonometry because the framework is wrong," says Wildberger, whose book is titled Divine Proportions: Rational Trigonometry to Universal Geometry (Wild Egg books).

Dr Wildberger has replaced traditional ideas of angles and distance with new concepts called "spread" and "quadrance".

These new concepts mean that trigonometric problems can be done with algebra," says Wildberger, an associate professor of mathematics at UNSW.

"Rational trigonometry replaces sines, cosines, tangents and a host of other trigonometric functions with elementary arithmetic."

"For the past two thousand years we have relied on the false assumptions that distance is the best way to measure the separation of two points, and that angle is the best way to measure the separation of two lines.

"So teachers have resigned themselves to teaching students about circles and pi and complicated trigonometric functions that relate circular arc lengths to x and y projections � all in order to analyse triangles. No wonder students are left scratching their heads," he says.

"But with no alternative to the classical framework, each year millions of students memorise the formulas, pass or fail the tests, and then promptly forget the unpleasant experience.

"And we mathematicians wonder why so many people view our beautiful subject with distaste bordering on hostility.

"Now there is a better way. Once you learn the five main rules of rational trigonometry and how to simply apply them, you realise that classical trigonometry represents a misunderstanding of geometry."

Thom - this is interesting. I want to learn more about this. I've been working with my son on his math skills, he does very well in math but struggles big time with spelling and reading and writing. He also has had speech classes sense he was 2. We work many hours on that as well but he gravitates towrds math because he does well in it so I say lets build on his strengh.

What Dr. Wildberger is on to may provide insight but it also makes me think about how to teach fundimental math skill to kids. You can have them count their figers and so forth or try to visualize the number of objects and count up or take away or they can just memorize that 3+3 = 6. Not sure what the best way is. I do all sorts of these with Max and he seems to catch on each way. Multiplication will be interesting. I took 3 years of calc and diffy Q's in college - the concepts were tough to memorize than the "tricks" and equations. I wish I spent more time understanding math and how to truely apply it rather than the ol plug n chug.

Oh, how I loathed trigonometry. Loved most math classes, hated trig. Maybe now I know why.

If that works, it sounds pretty cool. I have to use trig everyday in my engineering classes, sometimes it's a struggle to remember all the laws and tricks involved.

I'm really curious about this myself. My first instinct is that it's a crock, but I'm willing to give it the benefit of a doubt. It's always possible to come up with a new way of doing things if you are creative and have an open mind that is not bounded by prior knowledge. Trig is/was a pain in the butt, Geometry was really easy, Algebra, not too bad, and calc was actually not too bad.

LubeMaster, you may want to look into teaching your son to use an abacus. I've always been more into math and science than the other subjects. I've recently begun to teach myself to use an abacus (actually a soroban which is the Japanese version). I wish I had learned it years ago. I'd recommend it to anyone with kids. It teaches a new way to look at addition/subtraction and multiplication/division. You can even takes square and cube roots with them.

Here are several links with info.
http://www.hellgate.k12.mt.us/bldg1/grade5/cooper/abacus/page1.htm
http://www.abacusbrainstudy.com/link.php
http://www.ee.ryerson.ca:8080/~elf/abacus/
http://search.stores.ebay.com/search/search.dll?query=soroban&srchdesc=y&sid=175299227& store=ZakkaNik+Japanese+wholesale+Japan&colorid=-1&fp=0&st=2&fsoo=1&fsop=1&submit=Search
http://www.aph.org/products/abacus_cranmer.html
https://v396.securesites.net/deal_eng.html

I'll have to learn myself. As kids we used to race my Dad in math problems. My twin would call out the equation, my older brother would use pen/paper, I would ue the calc and my Dad would use his head. He won about 99% of the time. In college I took a semister of Logic. Had a book called "the Lady or the Tiger", it was all logic word puzzles. He would get them immediately where it took the prof and best in the class at least 1/2 hour to work them out. I asked how he ever got so good at math and logic and he said, "what do you mean good, either its right or wrong."

Mike - My son is the flip of yours. Sucks at Math and does great with spelling reading and writing.

If frustrates me because I am good at math but I have a hard time teaching it. I just know it from studying.

Thanks Steve for the Abacus tip I am going to look into it.


What frustrates me with Trig is the fact that you will almost never use it in life. If you need to use it, you will use a computer to figure it out. I agree that you should understand what you are doing but I have seen persons with no math background do very well in Land Surveying (Trig at its finest in every aspect) as well as someone who has a strong math background.

I know it needs to be taught but in all honesty I have forgotten a lot of what I knew from not needing to use it anymore. I have computers and software to do the job for me and its a lot faster and more accurate too.

Mike - we signed our son up at an afterschool tutor. It was to develop cognative skills though. Something schools use to teach and have moved away from. The school was called Learning RX

http://www.learningrx.com/center2/

It made a world of difference in my son. I highly recomend it. It was very expensive but worth every penny as far as I am concerned.

My daughter is fairly sharp and likes math. Unfortunately, sometimes she gets a poor score on a problem she has solved because her solution is not the same as the method the teacher and the text uses. In other words, she gets to the same result often times by a different path.

I dismiss the poor test score and praise her with a broad smile, for her understanding of math, and her understanding of the problem to be solved. Score schmore. The kids knows her math.

That's too bad Supe. The teacher probably grades from a sheet that came with the textbook, and doesn't understand enough math to figure out that your daughter used another, but equally acceptable method of problem solving.

That's almost certainly the case. A sharp teacher would recognize her talent and reward her for it. Too bad the teacher is eclipsed by the student.

"sometimes she gets a poor score on a problem she has solved because her solution is not the same as the method the teacher and the text uses"

Unless she's just guessing and not showing any working, that's just lazy and dumb marking. You've got a case to present the work to the teacher or faculty head and ask for a justification. At the very least, your daughter should be asking the teacher why she lost the marks & challenging the marking. It may not have an impact now but next time the work is marked you may see a difference.

i seem to agree with steve. sounds like a crock. the trig identities sucked to memorize, but other than that, it is simple.

i would like to see an example before making any assumptions.

I don't think it's a crock but will wait until I've read the book. Won't be out for a few weeks. But any hope of not having to worry about identities/formulae is shattered:
"Divine Proportions: Rational Trigonometry to Universal Geometry contains dozens of new and important formulas, and almost a hundred theorems. The formulas are mostly polynomial or rational, and the basic ones, such as the Triple Quad formula, the Spread Law, the Cross law and the Triple Spread formula are quadratic in any variable. The theorems are often based on existing results, but they hold in much greater generality, and their formulations are sometimes unusual. For example the new Spread polynomials replace the closely related Chebyshev polynomials of the first kind, but extend to arbitrary fields."

So it sounds like an alternative method of calculating ratios & trig functions. He does make a good point that calculators will only ever give approximations to trig ratios & that his methods give more accurate answers but we will see. I don't see how normal trig is that complex to begin with but I'm coming from a biased pov.

Jim - thanks for the lead. Max is getting special stuff at school and I work with him for about an hour every night then we read a few books. The last thing we do is the computor which consists of this board. He is with us right now. He likes the spider thread that I have. What boy or girl wouldn't until they are taught to fear them? I must have bored him because now he's fast asleep sawing logs.

Time to watch the C-bpys whoop on the skins with Mommy...

I'd definitely recommend the abacus for not only people that excel in math, but especially for people/kids who have a hard time with math. Using the abacus teaches a new way of thinking about math. I only wish I had known about the abacus when I first met my wife and her kids were younger. I think it would have made a huge difference to my stepson who isn't a math natural as he went through school.