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Monday, July 30. 2012
It's too hard for the kids, he says.
What a great idea! Get rid of languages, too. They're too hard. That way, the division between the smart kids and the less-talented and lower-IQ kids will be even more obvious to colleges and employers.
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Algebra is for most students the first course in school when they face the intellectual challenge of abstraction. Some students may not put the math itself into actual use later in life, but they all benefit from the struggle with the concepts and methodology of algebra. This learning process helps to expand their intellect from the particular to the abstract, taking them one step farther along from infantile thinking to thinking like a functioning adult. It is what education should be all about.
My take, having 'taught' Algebra ( for one day to my peers ) is that it's the WORD PROBLEMS that stop 95% of the students COLD.
After High School, there's a tendency to forget just what a show stopper Word Problems were in Algebra.
So, it's not abstraction, per se -- it's linking the real world to the abstractions they've been scribbling all along for years.
That counting ones change is a direct application of arithmetic is patent.
Reducing real world hard numbers into physics formulas like velocity, distance after a time -- and point of origination -- killer tough.
For myself, I never found them challenging.
When confronted with an actual class of High School students -- the chorus piped up: "Do the word problems! ( If you're so smart... )"
This is the cognitive gap that shows up later in life as the proles can't figure out:
That Obamacare is a brutal, uneconomic, compelled wage increase that must cause the vast bulk of employees 'on the bubble' to be let go... ( think African Americans and other AA hires )
That Obamacare must cripple our export industries -- famed for having more than 50 employees...
That getting Federal subsidies does not stop solar schemes from being economically ruinous across the national economy...
And most of modern technical and scientific politics....
I was a math idiot in high school. I have discovered the joys of mathematics in watching Samir Khan's videos at Khan Academy.
As a former math teacher, I am ambivalent about this. Teach to the maximum, yes. There has long been a push to have EVERYONE take Algebra. IMHO, it is a waste of time to try to teach some students Algebra. Having tried it, I do not see the point of teaching Algebra to students who have not yet mastered 6th grade decimals and fractions. Perhaps a better teacher than I could have better results.
Blert's point about word problems being the killer is well taken.
I attended a highly ranked high school. Ten percent of the class were either Merit Finalists or Merit Letter of Commendation winners - a profile which describes two percent nationwide. Yet there was a General Math class for about 1/6 of the class. They went on to productive lives, even without Algebra.
High school courses on consumer math and on analyzing statistics would be more useful than Algebra for a lot of students. As statistics are bandied about a lot in political give and take and in the newspapers, it is a good idea for citizens to have some knowledge of statistics.
How to Lie With Statistics, a book published nearly 60 years ago, would be a good place to start statistics instruction for high school students.
One issue supporting algebra for students who do not want to go to college is that many skilled tradesmen, such as welders or machinists, will need a good knowledge of math.
I would also suggest math instruction in high school coupled with teaching skilled trades - which help square the circle of high school instruction: "When am I going to need this?" Well, we are showing you how you need math to do this well paying job.
I went to highschool where you could take "intro to calculus and analytical geometry" your senior year. Algebra, geometry and trigonometry were prerequisits. Six of us signed up for the course. Now it would probably be considered way to hard for the kids.
Gringo is correct about trying to teach some kids algebra. Algebra uses abstract symbols to represent mathematical objects. Some are unable to work with mathematical abstractions.
The problem such people have, IMO, is not with "mathematical abstractions" but with abstractions in general. And if you don't "get" algebra, you'll never "get" probability and statistics, which from the perspective of someone who has had years of frustration and agony actually using it is a much harder topic to truly understand (easy to misapply, however). Indeed, I can state with zero fear of contradiction that to vast numbers of working scientists who have their algebra down cold advanced statistics might as well be Comanche or Yupik.
Yep, statistics is a subtle subject. The math part isn't that difficult if you have some math talent, but the application and interpretation is much trickier. It beats me why statistics is considered an a low brow replacement for ordinary algebra.
“Up in the mornin' and out to school
“The teacher is teachin' the Golden Rule
“American history and practical math
“You study' em hard and hopin' to pass.”
--Charles Edward Anderson Berry
It meant something then.
And the dumbing down continues. Now the left has become very overt in its efforts to keep the masses ignorant.
Algebra becomes far easier when you master arithmetic. In fact it follows intuitively.
Get any kid to master addition, and he'll soon be asking questions like, "What plus seven equals ten?"
Guess what, he just did subtraction, AND algebra. (I call it arithmetic exploration).
Today there is too much rush to move on to the next subject before many young minds get the topic, all under the guise of "educating." Not only is that unproductive, it's counterproductive.
A little kid just begins to get the whole "4+3" thing, and suddenly it's "4-3". The answer is they'll review it next year and he'll get it then...but he wont. He'll just be frustrated and embarrassed by math, and give up on it.
Spend a few more weeks on addition and you'll find that subtraction and multiplication "What is 3+3+3?" become easier...almost intuitive.
I saw that issue of not keeping on a topic long enough with the math textbook I had to teach at a low-achieving middle school. The problem sets went too quickly into more complex iterations of a concept for the comfort of the students. I spent a lot of time writing out simpler problems.
IMHO, there are at least three problems with math instruction in the lower grades. First, math was the worst subject for many elementary school teachers, which means they are not comfortable teaching it.
Second, there has long been a trend towards increasing the number of topics to be covered, which means that some - or many- will not be covered thoroughly.
Third, a lot of the familiarity with learning addition, subtraction, multiplication, and division comes with repetition. A lot of educators look at repetition and drill as "drill and kill"- a bad thing. While adults do not like repetitive drill, and therefore assume that children do not like repetitive drill, they are in error. Repetitive drill reinforces things for children.
You also see this repetitive drill issue in learning reading- phonics versus whole language. Whole language proponents assume that like adults, children do not like the drills used in phonics. Au contraire.
I am not saying that all should be drill. Questions like your "What plus seven equals ten?" should be interjected into instruction. A sixth grader neither needs repetitive drill as much as a first grader, nor likes repetitive drill as much as a first grader.
From a 9th grade math course that emphasized proofs of number principles, such as the distributive principle, I used these principles to become a good number estimator. I can often calculate faster in my head than on a calculator. But I couldn't have done this if I didn't already know the basics of addition, subtraction, multiplication, and division.
I went back to school in 1995, when I was in my 40s. I have a lot different take on this and agree with a lot that is in the article. None of the math classes were taught with any practical use. It was all theoretical, including a pre Calc class that was supposedly for biz/nursing majors. This is at community college, mind you. Math instructors expected students to fail the course and have to retake it. Remember, we are talking about classes that the student pays for, that are not tied in to any real-life use. With all the required math, you had to take exactly ONE English class. Is it any wonder that we have people that can't string together a sentence that makes sense?
My husband tutored shop math. His father taught him out of WWII Navy manuals, so both his English and Math skills were very common sense. Shop math is always tied directly into things you will use on the job. By contrast, I have yet to use any of the math skills that I learned in Algebra. We would do well to restructure education to focus more on skills you can actually use and leave the theoretical stuff for advanced college. The article talks about folks that do not get degrees because they can't pass the math, yet they are getting degrees in fields that do not require advanced math.
"By contrast, I have yet to use any of the math skills that I learned in Algebra."
So you have never calculated the price of shoes after a 15% discount? Or tried to figure out which of two sizes of detergent is the better value?
It's not the formula but the structured reasoning that one retains. Reasoning that is not debatable, any fallacy is revealed in the answer. Unlike the reasoning and logic taught outside of math where the mind can fool itself for decades.
The solution is ready and available for use. The Khan Academy with the kid self pacing with class time labs for individualized help. No whole grade/age group progression. If a kid gets hung up, he's not left behind like the current group instruction does. If he's in the groove, he can race ahead without enduring months of boring repetition for group speed progression.
Apologies to anyone who may be offended, but I scraped through H.S. Algebra, just as I did H.S. Geometry.
In the real world, I've found myself seriously wishing I'd paid more attention in Geometry class. I actually had to learn that to be able to do my job. (And Trig., but I managed.) I also have to do Industrial grade Stat for work. A lot of it. I've managed to learn to do basic squares and square roots in my head, and know enough of the Trig tables to get by on. I discovered later in life that a lot of the Math they were teaching me actually did have a point.
Algebra, though? I've never noticed much of any lack for not having paid attention to that.
Solve that one for "X".
I barely passed Algebra and Geometry in High School. In fact, I think my D+ grade in Algebra 2 was a pity grade just so I could graduate on time with my class. However, languages, both foreign and domestic, came to me like breathing. I was fully fluent in French by the time I graduated, to the point where dreaming and thinking in French was not unusual. Alas, that skill has gone rusty with age and disuse. Now, I'm attempting to learn Ecclesiastical Latin. Having a ball!
I was quite amused recently when my husband pointed out that I do use Algebra and Geometry every time I begin a sewing project or when I am drafting/grading patterns. Too bad these math skills couldn't find a place in a Home Ec class.
Home Ec? Guess I'm dating myself!
I had an interview for a job recently where I had to take a two-hour test online before the interview. Half the test was word problems: if it costs $x/month to rent a copy machine and $y to buy and the depreciation is z, which is the better option? If you earn $x/hour and take certain breaks plus PTO, what should your paycheck be after a week? If you want to fill in a depression in your lawn that is x ft by y ft by z inches, how many cubic yards of soil do you buy and what will the total cost be after delivery?
You do use algebra in real life. And sometimes, you can't get a job unless you can do algebra.
BTW, I was applying for a job as a software trainer, not as a coder or a math teacher.
Except for the vaunted few at the top of the intellectual heap, all your life your work will be repetition, repetition, repetition. Our brains are wired for finding berries in the forest, recognizing good/bad plants, and seeing the tiger hiding in the grass, all visual pattern recognition. Yet we of technological civilization must train our brains for other things. Those other things require math.
Math is hard. Math requires patience and persistence. To learn math you must practice, practice, practice doing something your brain is not naturally wired to do, every day until the abstract patterns finally become lodged in your brain. And it trains you to become repetitively persistent in doing things you may not like to do, i.e. a successful and productive adult. So kwitcher bellyaching kids and dig into those fifty math problems the teacher assigns you every day.
And who says kids don't need to learn algebra?