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"

Also:

"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!

What's Wrong With U.S. Secondary Education? Just About Everything!

Aug. 1978, giving an astronomy workshop to teachers in St. Lucia.  Such workshops were given in all subject areas at regular intervals and followed by teacher tests.

The appearance of educator Deborah Kenny on 'Morning Joe' was sobering as she described an educational system in crisis. Not only is the U.S. now ranked 17th in science vis-a-vis other nations, but 25th in math. And we won't even go into the latest economics test issued to U.S. students in which they performed deplorably - most not even aware of basic financial indicators or issues.

Kenny, when pressed by Scarborough, went on to list ways the whole system can be improved, first and foremost adopting the "team" concept in which each school sees itself as a team dedicated to solid advancement. She also appealed to "innovation" - allowing teachers to be creative in their classrooms in terms of inquiry, and cautioned that the system needed to drop the gov't gimmicks for easy handouts (based on testing alone) and having administrators in every classroom checking off teacher violations.

All of these are fine, but she barely scratched the surface. (Understandable given she was allotted maybe only one third the time to do justice to the issue).  But how and why is the U.S. secondary education system so terrible? What factors contribute to undermining it, especially in areas of math and science where our nation continually flounders? Below I explore some of the reasons that occur to me, since I myself taught more than 20 years overseas (in Barbados at secondary and tertiary level) before teaching in the U.S. at tertiary level (Univ. of Alaska-Fairbanks, in space physics, physics and at a Maryland community college in calculus physics).

1.  Too much interference by School Boards- low level politicos:

This was the first factor that struck me on return to the U.S.: the degree of interference in all manner of school policies, even choice of textbooks and curricula. School boards, often highly politicized, sought to imprint their schools with their own biased marks, agendas and beliefs. Obviously, such micro-managed oversight will kill innovation and creativity in its tracks. Both of those are predicated on a spirit of free inquiry which absolutely cannot be pursued if hack politicians are looking over teachers' shoulders at every turn.

Thus, a teacher of biology who seeks to examine hominid evolution may be called on the carpet, just as one (say in Texas) who teaches American history and wishes to investigate more at a deep politics level the basis of the JFK assassination. Perhaps he even wishes to use a book ('The Untold History of the United States') that will be more amenable to inquiry as opposed to vanilla regurgitation of oversold myths and bogus factoids. In either case, most politicized school boards will cut the teachers off at the knees.

Innovation? Dead and buried!

2. Being Hostage to Government 'Carrot & Stick' Gimmicks:

Another vast killer of inquiry and creativity are the two government educational gimmick programs: 'No Child Left Behind' and "Race to the Top". In either of these, students and teachers become hostage to test taking for the sake of "making the cut" and not losing out on government largesse, benefits - which will be withheld if schools fail in standarized tests.

Time spent to actually teach is thereby usurped in the interest of making students excellent test takers, as opposed to educated Americans. Not even mentioned by those who push this fetish, is that many students are allowed to opt out especially in "elite" districts. So exactly how is that fair? The test hostages are then being screwed over twice! They're losing time for actual education while also not getting anywhere near the funding those students in the elite districts benefit from. (The ones afforded the privilege of opting out of standardized tests - thereby gaining an even greater time advantage for real teaching).

More pernicious is that the test taking obsession drives educators to step over the line to meet the test standards, even if it means cheating.  Look no further than the Atlanta cheating scandal. True, the cheaters are still accountable, but when the two main gov't gimmick programs put so much at stake in terms of benefits, one can understand how such desperation manifests, even if it can't be accepted.

3. The problem with math teaching in the U.S.

I actually went over this in two prior blogs and readers can reference that content here:

http://www.brane-space.blogspot.com/2011/03/mis-education-of-mathematics-teachers.html

and

http://www.brane-space.blogspot.com/2013/01/college-math-prof-and-why-us-education.html

Additionally, I presented a Caribbean Math test geared to secondary (CXC, or Caribbean Examination Council) students, and noted that it would probably give most U.S. students grief - probably even college students. That link is:

http://www.brane-space.blogspot.com/2011/04/could-us-high-schoolers-pass-basic.html

Perhaps the best insight into U.S. math travails is in Darryl Yong's blog which I cited in the second link above.

4. Science defects:

I highlighted these in a blog to do with why U.S. students have so much difficulty achieving good results in physics, see e.g.
http://brane-space.blogspot.com/2011/07/sad-state-of-us-high-school-physics.html

And what applies in this subject area also applies to a large degree in the other main science areas of chemistry and biology.  Chemistry, of course,should have a heavy emphasis on experimentation - and the biology to be worthwhile must address Darwinian evolution and not run from it. However, in too many districts school boards have interfered, as well as the state (e.g. Texas) to dumb down exposure.


5. History teaching defects.

This is very well known and author James Loewen has discussed U.S. history failings at length in his excellent book, Lies My Teacher Told Me.   The gist of it is that 95% of American students who take hsitory are sold a bill of folderol and gibberish that leaves out all the warts and blotches while it extols the 'good stuff'. Some history book are so pathetic they don't even acknowledge the role of other nations (e.g. Britain) in WWII but make it appear the U.S. won it single-handedly!  Other books totally avoid the false origin of the Vietnam War (in the Gulf of Tonkin Resolution) and avoid (like the plague) how early white settlers butchered Native Americans to grab their land.

With crap like this being taught, it's little wonder too many Americans don't know diddly or squat about even recent history.


6. Economics teaching deficits:

The recent revelations about secondary students' deplorable lack of financial acumen and economics exposure is also tragic. But again, with so much teaching to the test, what else would you expect? Certainly any student worth his salt ought to be able to identify the main reasons for the 2008 credit crisis and financial meltdown. He (or she) ought to be at least able to identify the derivatives known as 'credit default swaps' even if not the Gaussian Copula formula that was employed to integrate them into otherwise decent bond products.

Any H.S. student ought to also be able to answer questions such as:

a) Jeans are on sale at a big box store for 15% less than the original (marked) price of $24.99. If the sales tax is 5% what will you end up paying for the jeans?

b) You put $1,000 into a new bank account for which the interest is 0.2%. per annum.  If holding any account below $5,000 incurs a $10 per month fee, do you see any gain at the end of the first year? How much? If a loss, how much?

c) Joe and Mary are within 6 years of desired retirement. They estimate they need at least a $300,000 nest egg along with their Social Security. In order to ramp up their savings they put $100,000 of their $200,000 so far saved into equity and bond funds in their 401ks. After three years, their total loss is $30,000. Assuming average 5% gains per year afterward, how long will it take them to make back their original investment?

7. Anti-intellectual culture:

Briefly touched on with Deborah Kenny's appearance this morning, although critical, is that we seem to inhabit an anti-intellectual culture. This is also a big reason why secondary school teachers are accorded little respect. (One former teacher sitting at the table and part of the discussion, noted spitballs being hurled at him each time he entered a classroom)

Altered, higher pay scales will change some of this: making teachers the professionals they should be. But it can't solve an endemic problem in the culture itself. Indeed, Benjamin Barber in his book 'Consumed' points out how the intellectual basis of the nation has been eroded over time by a culture of infantile consumerism. Susan Jacoby ('The Age of American Unreason') meanwhile notes that crass, anti-intellectual religiosity, as embodied in fundamentalism, is also part of the problem.

Whatever, the solution is long term and requires intense education to show how we've all been victimized by the capitalist purveyors of shlock.

Lastly, fixing the educational system in the country is a monumental task. But at least addressing the problem areas I identified above will make it function more in concert with our higher expectations. As opposed to at the lowest level!