Posted on 12/26/2007 9:10:30 PM PST by Amelia
...Tegethoff used to teach what she called "very boring math," using worksheets of addition and subtraction problems. Now her lessons delve into algebraic thinking. By the third grade, Viers Mill Elementary students are solving equations with letter variables.
Long considered a high school staple, introductory algebra is fast becoming a standard course in middle school for college-bound students. That trend is putting new pressure on such schools as Viers Mill to insert the building blocks of algebra into math lessons in the earliest grades. Disappointing U.S. scores on international math tests have added to the urgency of a movement that is rippling into kindergarten. At stake, some politicians say, is the country's ability to produce enough scientists and engineers to compete in the global economy.
But education experts say students aren't the only ones who need more rigorous instruction. Too many elementary school teachers, they say, lack the know-how to teach math effectively.
"You can't teach what you don't know, and your students won't love the subject unless you love the subject," Kenneth I. Gross, a University of Vermont mathematics and education professor, recently told a group of college mathematicians at a conference hosted by the U.S. Education Department and the National Science Foundation. "All of mathematics depends on what kids do in the elementary grades. If you don't do it right, you're doing remedial work all the way up to college. Arithmetic, algebra and geometry are intertwined."
(Excerpt) Read more at washingtonpost.com ...
This sounds like Elroy Jetson’s school.
Another education article I found interesting. I’m trying to decide if teaching algebraic concepts in primary school is a good thing, or another instance of “new math” that no one understands.
I do agree that many elementary education majors need a better understanding and knowledge of mathematical concepts before they begin teaching arithmetic or math.
Elementary math today, at least in the district where I live, is at least a couple of years more advanced than it was when I was a student many years ago in a district with similar demographics.
I think it’s good to teach algebraic concepts in elementary school. When we lived in Virginia, our oldest four children were all exposed to basic algebra in the fourth grade. Our oldest son, who struggles with reading and writing, found something at which to excel when his teachers introduced variables. He loved it. Unfortunately, the public schools in our current area are about two years behind in EVERYTHING, so we have had to remove #5 from the area school. Our oldest boys are being homeschooled, and the curricula we are using is nearly identical to Virginia standards. A strong foundation in math makes higher level math courses so much easier!
I agree. There’s not much else you can do to learn the basic facts that simply need to be memorized.
I’m glad to see them challenging the kids, though. I’ve always contended that kids are capable of far more than most adults these days give them credit for. I’ve seen little kids learn skills at what seemed like an incredibly young age, and they catch on quickly and become proficient quickly. This applies to things I’ve witnessed like skiing, swimming, crocheting, knitting, reading, even math.
Kids are sponges and hate to be bored.
I liked algebra, but I loved calculus. It was fun to discover where the formulas for say, the volume of a sphere comes from, instead of just memorizing it.
Google Singapore Math to get an idea what I mean.
My kindergarden son knows that different things that equal the same thing also equal each other.
He's working on A2 + B2 = C2 for his intro to plane geometry
I loved math until they started substituting letters for numbers and “imaginary” numbers. I eventually got up to speed in High School, although I am still uncomfortable with logarithms.
I have 4 adult children ranging from 25 to 36 years old. I put all 4 of them thru private school where algebra came very early.
Education majors learn in college to teach subjects about which they have little knowledge.
It is all part of teaching children how to think about math rather than teaching them math. Without the boring rote addition and etc., the data banks are left empty and we raise a generation of children who can only work with calculators. They never learn how to think a thing through and are lost when there is no calculator to hand. They will continue the slide in relative performance. Math performance was hurt by a little tiny thing, teaching children to make change without a computer, not to mention all the major omissions and feel-good stuff. And teaching change-making is so small a use of time. I can teach a slow kid how to do it in 20 minutes, max. If he is smart enough to count to 100, he can learn at least that fast to count change.
My kid is in the 4th grade, the math is crazy hard for that age. I’m afraid they are going to fast, and losing kids along the way. I’m all for tough standards, but frankly I wonder if this is a bit overboard.
Same here. My 11th grader is taking calculus. Started algebra in 5th grade. Compared to the HS I graduated from in '82, all of her subjects are more advanced and challenging than anything I faced. At least twice the homework too.
“Elementary math today, at least in the district where I live, is at least a couple of years more advanced than it was when I was a student many years ago in a district with similar demographics.”
Absolutely. Our son, who is fairly smart but not a “brainiac,” is doing Algrebra 2 in 9th grade. I did it in 11th and I was a fairly bright guy.
They move much faster to more complicated concepts because of the internet.
Archimedes to Dositheus greeting
On a previous occasion I sent to you, together with the proof, so much of my investigations as I had set down in writing ... Subsequently certain theorems deserving notice occurred to me, and I have worked out the proofs. They are these: first that the surface of any sphere is four times the greatest of the circles in it ... and further, that, in the case of any sphere, the cylinder having its base equal to the diameter of the sphere, and height equal to the diameter of the sphere, is one-and-a-half times the sphere, and its surface is one-and-a-half times the surface of the sphere. Now these properties were inherent in the nature of the figures mentioned, but they were unknown to all who studied geometry before me, nor did any of them suspect such a relationship in these figures. ... I send you the proofs that I have written out, which proofs will now be open to those who are conversant in mathematics. Farewell.
- Greek Mathematical Works II, Loeb Classical Library
Amazing that they knew this stuff thousands of years ago. I always wondered about the volume of a sphere. 4/3 pi x r cubed is the volume, take the differential and you get 4 pi r squared as the surface area of a sphere, if you take the differential of that you get 8 pi x r. What is that? Volume to surface area to ???
You have to excite kids. If this doesn't intrigue them, nothing will....
If the function y = 1/x is revolved around the x-axis for x > 1,
it creates a volume as above, typically called Torricelli's trumpet
or Gabriel's Horn. More important is that
the solid has a finite volume, but infinite surface area.
In other words you can buy enough paint to paint the surface areas, but not enough to fill it!
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This means the differential increase in volume is A dr, the area times the differential increase in radius.
...if you take the differential of that [ 4 pi r^2 ] you get 8 pi x r. What is that? Volume to surface area to ???
This merely reflects Archimedes' formulation that the surface area is 4 times the area of "the greatest circle", along with the fact that the differential increase in the area of a circle is 2 pi r dr, the circumference times the differential increase in radius. So note the extra factor of 4 is "purely geometrical," and not to be found as a consequence of differential reasoning.
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