Thursday, August 22, 2013
Kids Hate Algebra II? WHY?
Quick! Do the following in 10 minutes or less!
If (3x + 1)/3 - (x - 3)/2 = 2 + (2x - 3)/3
find the value of x
(b) Factorize completely:
(i) 15 x2 - 20 xy2
(ii) 3 - 12b2
2) f and g are functions defined as follows:
f: x -> 3x - 5
g: x -> ½ x
a) Calculate the value of f(-3)
b) Write expressions for (i) f -1 (x) and (ii) g-1 (x)
3) Solve the quadratic equation:
x 2 - 3x + 2= 0
Plot the graph, indicating the coordinates of any maximum (or minimum), and also of any x-, y- axis intercepts.
If you were able to complete the above problems, even if not necessarily in the time, then you likely took Algebra II. If not, then well, you obviously stopped at Algebra I, assuming you took Algebra at all.
Now, however, it's come to light that kids HATE Algebra II! They are sick and tired of it and want out. This according to the article 'Wrong Answer!' in Harpers (Sept., p. 31) by Nicholson Baker. The author provides a number of examples of Algebra II hate he encountered on the Web with comments such as:
"Algebra needs to die!"
"Is poking myself in the eye an acceptable substitute for my algebra homework?"
"Algebra is the huge fucking dam that prevents me from flowing, and being a better person!"
"I have to take 11 algebra tests in 2 hours. It's six in the morning and I've got to pass 'em all or I fail!"
"I really hate Algebra 2! I wish I was dead! I want to kill myself!"
Woah! Can it be THAT bad? What's going on? Why are all these kids so miserable and some, evidently, to the point of phoning it in (though granted we must make allowances for teen hyperbole!) The author, Baker, believes he has the answer: It's the Algebra 2 Common Core, stupid! Egged on by the ridiculous 'race to the top' baloney (which only rewards a few schools anyway), schools across the nation have evidently adopted a new, common core Algebra text by Pearson which:
"is very new and very heavy"
"The federal Race to the Top grants have encouraged your school to buy many copies of this new, expensive textbook along with the associated workbooks and software licenses."
For what? Well, evidently in order to follow the injunctions of the "Common Core" standards developed by a non-profit outfit called Achieve, "and paid for by grants from the Bill and Melinda Gates Foundation". Baker then quotes Melinda Gates:
"High standards mean more than just teaching all students Algebra II. It means teaching all students the skills necessary for success in Algebra II so they can apply them in different areas throughout their lives and careers."
In other words, Melinda - and likely Bill too- are convinced that a high standard of performance in Algebra II will translate to major useful life-career skills. But I dispute this, and so does Baker, and so does a high profile mathematician, Underwood Dudley - a number theorist who for many years has been a sharp critic of required math courses. As Dudley put it in an issue of The American Mathematical Monthly in 1987:
"The vast majority of the human race and the vast majority of the college educated human race never need any mathematics beyond arithmetic to survive successfully."
Wow! What a transgressive statement! It basically turns the entire Common Core Algebra II standards idiocy on its head. He's saying that not only will the college -educated barely use the math embodied in Algebra II, but for sure neither will those with just high school degrees. I mean hell, you don't need Algebra II to work out how much interest you will have to pay on your 4.5% mortgage on a $150,000 home (for which you paid $20,000 down) over thirty years. You don't need it to figure out a 20% saving on a pair of jeans that normally costs $19.99 - and factoring in a 5% tax.
Obviously, having said all that, it doesn't apply if a kid plans to go into engineering or astrophysics. Then, he will need not only Algebra II but plenty of calculus, as well as differential equations, numerical analysis and complex analysis. But how many college grads will go that STEM route? Better, how many graduating with a STEM degree will actually find a STEM job?
The author also makes the cogent case that if thinking skills are really what's required, Algebra II isn't essential to specifically fulfill the need. Many alternatives can be found, e.g. a basic logic or critical thinking course. So, why in hell expose so many kids to stuff like rational functions, as defined e.g. in Chapter 8 of Algebra 2, Common Core:
"A rational function is a function that you can write in the form: f(x) = P(x)/Q(x) where P(x) and Q(x) are polynomial functions. The domain of f(x) is all real numbers except those for which Q(x) = 0"
The author adds: "Not only that but rational functions can be continuous or discontinuous, and a continuous rational function is one that 'has no jumps, breaks or holes'"
To make his point further, on how the average non-math oriented kid can be confused:
"Next you're presented with a salient feature of discontinuous functions: If a is a real number for which the denominator of a rational function f(x) is zero, then a is not in the domain of f(x). The graph of f(x) is not continuous at x = a and the function has a point of discontinuity at x = 1.
Then you learn something more about points of discontinuity: they can be either removable or non-removable."
Got that? If you don't, then imagine some kid who isn't math savvy sitting for endless hours a week in a classroom and getting more frustrated with each succeeding lesson. Imagine the frustrated teacher that has to teach this to a class, to whom it comes over as Greek, literally. Then you get the picture of why forced Algebra II for a mass audience, a mass captive high school audience, is a bad idea.
As for the textbook:
"Algebra 2 Common Core is, in other words... a highly efficient engine for the creation of math rage: a dead scrap heap of repellent terminology, a collection of spiky, decontextualized, multi-step mathematical black box techniques that you must practice over and over..."
As it is, all our schools are going under the spell of this 'Common Core' BS - and it's creating mass hatred of math. We have kids actually talking of killing themselves over it, or else expressing such manifest hate that they will be math detractors for the rest of their lives. This is not the way to move the nation forward educationally.
We can do better and have to do better. It's time to rethink the standardization of high school math and realize we can't fit 22 million square pegs into 22 million round holes. In the words of Underwood Dudley, in his math article (ibid.)
"We cannot justify teaching mathematics to 17, 18-year olds by asserting they will find it useful. We cannot claim we are presenting beauty either. We are, of course, but what percentage of our students can see that, however dimly?"
He thereby pigeonholes the problem in a nutshell. As Nicholson Baker puts it:
"If Algebra II were an elective and colleges didn't ubiquitously demand it, fewer people would learn it. But fewer people would fail it too, and fewer people might drop out of high school, and the level of cheating would go down, and the sum total of student misery would be reduced."
Words to consider!