true... and make the little darlings learn to use a slide rule too!!!
Posted on 03/15/2008 1:58:58 AM PDT by neverdem
American students’ math achievement is “at a mediocre level” compared with that of their peers worldwide, according to a new report by a federal panel, which recommended that schools focus on key skills that prepare students to learn algebra.
“The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins,” said the report of the National Mathematics Advisory Panel, appointed two years ago by President Bush. “Students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation.”
The report, adopted unanimously by the panel on Thursday and presented to Education Secretary Margaret Spellings, said that prekindergarten-to-eighth-grade math curriculums should be streamlined and put focused attention on skills like the handling of whole numbers and fractions and certain aspects of geometry and measurement.
It offers specific goals for students in different grades. For example, it said that by the end of the third grade, students should be proficient in adding and subtracting whole numbers. Two years later, they should be proficient in multiplying and dividing them. By the end of the sixth grade, the report said, students should have mastered the multiplication and division of fractions and decimals.
The report tries to put to rest the long, heated debate over math teaching methods. Parents and teachers have fought passionately in school districts around the country over the relative merits of traditional, or teacher-directed, instruction, in which students are told how to do problems and then drilled on them, versus reform or child-centered instruction, emphasizing student exploration and conceptual understanding. It said both methods had a role.
“There is no basis in research for favoring teacher-based or student-centered instruction,” Dr..
(Excerpt) Read more at nytimes.com ...
My kids would have been able to do this using a pencil and paper, and with some quick review I would be able to do it as well.
Also, I believe that you are throwing out a red herring, hoping that those of us who defend the memorization of math facts will chase it.
By the way, are you a government teacher? ( just wondering)
If not, what do you do for a living?
Whether you’re researching or creating, you shouldn’t have to count all the fingers and toes in the room because you didn’t memorize the multiplication table.
Obviously what’s needed is a series of math videos by hip-hop artists.
WhatÂ’s the square root of 12345678987654321 ? No paper or calculators, please.I said pencil and paper should be allowed :-) Well,
12345678987654321 = 1.2345678987654321 * 1016,
which is not very different from
1.21 * 1016,
and the square root of that is
1.1 * 108 = 110000000.
If that is not exact enough for you, you should first tell me why you need this result so hard ;-) Then one might be tempted to use the symmetry of that number, for example…
1111 1111 1
Cartan, are you a government teacher? ( Just wondering.) If not, what do you do for a living?Nah ;-) although I used to teach mathematics at the university for a while. But I got bored and now I am a software developer.
true... and make the little darlings learn to use a slide rule too!!!
i guess it's just selfishness on my part too cause all i care is about that they know how to make change.
“Whether you’re researching or creating, you shouldn’t have to count all the fingers and toes in the room because you didn’t memorize the multiplication table.”
I agree.
But a lot of people who do technical work are more enamored with the concepts and the analysis and investigation than in actually producing something. They aren’t usually that successful in their field because they aggravate everyone around them when they get stuck on re-deriving some algorithm just for fun or belaboring some minor point.
The more successful people have realized that part of innovation is using rote memorization where it makes sense so that they can improve the overall efficiency of their efforts.
“I used to teach mathematics at the university”
Did you know lots of guys in the math department who stubbornly refused to learn the multiplication tables because it was more interesting, challenging, and fun to just go through solving the problem again each time they needed to muliply two numbers?
That is precisely correct. I happened to be about two years ahead of "new math" while my younger brother caught the first wave, and I still remember my parents' disgust with it. "New math" was a disaster for my brother.
Did you know lots of guys in the math department who stubbornly refused to learn the multiplication tables because it was more interesting, challenging, and fun to just go through solving the problem again each time they needed to muliply two numbers?No, guess what: Everybody (including me) knew the multiplication tables by heart, as well as every formula that was interesting for their particular field (even really, really big ones ;-). But absolutely nobody kept little sheets of paper full of formulæ to memorize. The only people who put any effort into memorizing formulæ were students who were hopelessly bad at mathematics and eventually dropped out. Or perhaps they learned in highschool that you can learn mathematics by memorizing formulæ…;-)
I am not saying that it is bad to know a formula (or what 5*3 is) by heart. I am saying that if you do the right kind of work, i.e., if you try to understand the stuff, then memorizing it comes automatically. Doing memorization first is a waste of time and effort.
Of course, things may be different in grade school: We would like even stupid children to be able to compute 5*3 without a calculator. So, perhaps having kids memorize the tables might be a good idea, after all. But the important thing is that the kids also have to learn to think, and what we see instead is ever more dumbing down.
Here's my opinion, as an engineer:
5x5? Sure, memorize that.
Sine of π/2 ? Well, to be honest, when I look at that term:
Mind you, I'm an engineer that deals all day long right now with optics and with spherical coordinate systems. The key thing with most trig calculations is to recognize how things relate to each other -- visualization is key, rather than rote memorization.
Sure, it may take 3 seconds longer to visualize things, but it takes you to the real nature of the problem, and saves you from disastrous "sin vs. cos vs. tan" mistakes. I always have Big Chief Sohcahtoa review my analysis before committing to an answer!
All you are saying is that memorization is the key to learning; and repetition (practice) is the key to memorization.
I agree with both.
The “Terms & Tools” of any field involve mastery of (familiarity with) a huge new vocabulary of labels, phrases, scientific laws (often arbitrarily named after the individual discoverer) etc.
As a college teacher, I spend time emphasizing the importance of memorization of a vast & brand new language when one decides to enter a new field.
Any educator who denies this critical aspect of skill building is an idiot.
Even math involves memorization, - of the ARBITRARY NAMES of the numbers, (one, two, three), the ARBITRARY decision to use ‘base 10,’ the ARBITRARY rules for using parentheses and other symbols, etc.
I think you forgot the sarcasm tag.
Preparation in K-6 is more than adequate. The problems appear in High School. By the time of College most should be able to factor polynomials easily and know the difference between sine and cosine.
I have to tell you that, for some reason, memorizing math facts doesn’t work the same as memorizing words. I have a bit of a photographic memory, but it doesn’t work for math, or numbers. I could memorize formulas and theorems. Geometry was actually fun, but I can still remember my algebra teacher writing across the top of my paper, “You’re algebra is great, too bad you can’t add or subtract.”
By the times you get up to 11 or 12 on the times table you’ve already learned up to 10 so it’s just a matter of learning four more. That was drilled into us by the 3rd grade.
I’d be happy if the kids could learn decimals by the time they leave high school. You would be shocked at the number of college kids who can’t answer the following question:
Which if the following is the largest:
a. .1
b. .01
c. .019
Many kids will say .019 and when you ask them why they say “Because everything works backwards to the right of the decimal.” Huh???
My students revolted when I required them to do square roots without a calculator. I won.
On the contrary, Saxon explains things very clearly so that you can understand not only what you are doing but WHY. I learned a lot as I taught my kids; things that I knew how to do but never really understood before. Math makes way more sense to me now.
The school district we used to live in switched over to Saxon Math for it’s elementary grades after seeing how well all the homeschoolers did using it. No surprise that the school district saw its standardized test scores improve after the switch.
My kids have all excelled in math and were raised on Saxon. Engineers who my husband works with who are familiar with Saxon Math say the it is hands down the best math curriculum for preparing for the real world, practical use of math.
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