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 ...
People should be able to do something so basic.
It’s not like functions or derivatives.
Yeah, I stumbled across it in a puzzle book once, waiting for my wife at a gift shoppe.
I immediately recognized that [1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1] was the convolution of [1 1 1 1 1 1 1 1 1] with itself, i.e., (x^8 + x^7 + x^6....x^0)^2 = 1*x^16+ 2*x^15 + 3*x^14 ... 3*x^2 + 2*x + 1*x^0).
With x = 10, solution = sum (for n = 1,2,..9) {n*10^(n-1)}.
Obvious, isn’t it?
Yes! Saxon Math! I don’t know why it isn’t universally taught. It is to math what phonics is to reading.
Just to note -- I subbed a ninth grade pre-algebra first day recently. I told the kids "no calculators!" -- they immediately went into an uproar, and some actually snuck behind back to pilfer a calculator and use it while hidden under their desks. Addiction behavior!
Instead we curse our young with a drug-like crippling of mathematics education and thinking in general. We curse them with a drug called a calculator, that prevents them from learning to mentally walk, mathematically.
Calculators should be banned must of the school year, except maybe a two week overview in them.
ANY math program can be used to understand math. Some are just better than others. John Saxon convinced many people his way was the only way. I don't agree.
And, my experience in teaching 3 homeschoolers is justification for my opinion.
He didn’t convince me by anything but using his books.
Some are just better than others.
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Saxon Math is the best of any of the many math books I have used for my personal education or for the education of my children.
Make them factor polynomials and they may use calculators if they wish. If I recall Real Analysis and Complex Analysis and even Matrix Algebra there was simply no use for calculators in class.
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Very cute! (Sitting here laughing!)
That's very true. If you talk to elementary or middle school teachers, most are either forbidden from retaining students, or given a maximum number that can be retained per year, regardless of how much the students learn.
I've also seen middle school students who failed all their classes but were "administratively promoted" by the principal.
I don't totally discount the quality of teachers, however, particularly in the lower grades. Not all, but a lot, of elementary education majors seem afraid of math. I took a "Teaching Math in the Elementary School" course back in the late 70s, and too many of the prospective teachers in that class were unable to pass a math test at a 6th grade level.
Not longer after that, an English teacher friend who was rooming with a 5th grade teacher recounted how her room-mate couldn't do the problems involving fractions she was attempting to teach her students. My English-teacher friend had to make up the answer keys for the elementary teacher.
I agree. For this reason, I taught my children the basics of arithmetic using plenty of manipulatives on a daily basis. Even when they were older children we often used diagrams and manipulatives to prove or review concepts.
With children ages 5 to 9 or so their manual dexterity skills stink! It takes them **forever** to do a worksheet that and adult could finish in a few minutes. It takes great effort for them to essentially carefully "draw" each numeral. In the end, oral responses to flash cards was less frustrating for them.
I also discovered with the oldest child that (even though he understood all the concepts of addition, subtraction, multiplication, and division,) his lack of memorization of math facts made more advanced arithmetic frustratingly slow for him.
In the end, I simply insisted that each child have nearly instant recall of their math facts before I allowed them to move into Saxon Math 4/5.
Doing memorization first is a waste of time and effort.
I think you and I would both agree that pure memorization without understanding is a waste of time.
In teaching the long division and multiplication algorithms, I simply did one for the children every day. Each day the child would start a problem, when he got to the point that he could go no further, I would finish it for him. It took about 2 months with each child, but eventually they learned each step. No tears. No fuss. No frustration. No math anxiety.
Wow!
I have on occasion jokingly suggested that every government teacher pass the GED for high school drop outs.
Maybe they should be required to take it every 3 to 5 years or so. I wonder how many would be nailed on the math section?
How do you propose students retain knowledge without memorizing?
The key thing with most trig calculations is to recognize how things relate to each other -- visualization is key, rather than rote memorization.Yes, I agree totally!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!
I have no idea what that gibberish meant in your last post. Maybe you forgot to put 7 dots and only put 6, but that is still ridiculous. Maybe, you can explain the nonsense with the dots.
Of course, people could figure out 7*6 by adding 7 six times or 6 seven times, but then they would have to know their addition facts.
Plus, in your algebraic way of solving it, people would have to know their order of operations, or the distributive rule. That is assuming that they know that parenthesizes next to a number means multiplication.
It is ridiculous in the extreme to think that average people can learn math without memorizing their basic facts, procedures and rules.
But I just do that for trig. equations. To do that for simple multiplication or division - as per what you advocate - is just insane.
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