A report at the Washington Post delineates the debate going on as to whether to make Algebra II a mandatory course in high schools nationwide:
Of all of the classes offered in high school, Algebra II is the leading predictor of college and work success, according to research that has launched a growing national movement to require it of graduates...If you're going to comment, you need to tell us how many of those three questions you got right. I was only able to do the first one.
One of the key studies supporting the Algebra II focus was conducted by Anthony Carnevale and Alice Desrochers, then both at the Educational Testing Service. They used a data set that followed a group of students from 1988 to 2000, from eighth grade to a time when most were working.
The study showed that of those who held top-tier jobs, 84 percent had taken Algebra II or a higher class as their last high school math course. Only 50 percent of employees in the bottom tier had taken Algebra II. “Algebra II does increase the likelihood of being employed in a good job,” they reported, although warning that many factors come into play.
To check the Algebra II findings against the “real world,” the Achieve researchers then asked college professors and employers to identify which skills are necessary to succeed. Somewhat to their surprise, they found that whether students were going into work or college, they needed the skills taught in Algebra II. Other independent studies backed them up...
But not everyone is convinced that Algebra II is the answer.
Among the skeptics is Carnevale, one of the researchers who reported the link between Algebra II and good jobs. He warns against thinking of Algebra II as a cause of students getting good jobs merely because it is correlated with success.
“The causal relationship is very, very weak,” he said. “Most people don’t use Algebra II in college, let alone in real life. The state governments need to be careful with this.” The danger, he said, is leaving some kids behind by “getting locked into a one-size-fits-all curriculum.”..
Acxiom, a database company that employs 2,100 in the town, hires software and database developers, most of whom have bachelor’s degrees in technical fields. For them, Algebra II skills are a prerequisite. Similarly, at Snap-on Equipment, a plant that employs 170 making the sophisticated gears that garages use to align and balance tires, most production jobs require associate’s degrees in electronics.
By contrast, at the Kimberly-Clark plant, which makes feminine hygiene and adult incontinence products, production workers need only a high school education. The jobs pay 11 to $20 an hour, and when 70 spots recently came open during an expansion, about 2,000 people applied.
“We’re looking for people with the ability to think critically,” said Jeremy Cannady, until recently a manufacturing efficiency coordinator at the plant. But “not the ability to do exponential functions or logarithms.”
Q1: Cube root of 8 = 2, 2^5 = 32
ReplyDeleteQ2: Multiply both numerator and denomintor by complex conjugate of (-2-4i), which is (-2+4i). Expand and simplify to get answer.
Q3: Reflection on y-axis... f(x):- f(-x).
3^(-x) = (3^(-1))^x = (1/3)^x.
I took algebra 2 my freshman year of high school.
ReplyDeleteI'm not shocked to learn people who never took it at all work in a tampon factory.
First one, and of course, high school algebra was a long time back and dulled by years of studying arts and law.
ReplyDeleteHowever, I think it was useful to learn just for the sake of learning to think mathematically. If we start cutting out subjects just because some people don't use them as adults will be selling kids short. It's not the actual content that you need to learn, it's the ability to learn different subjects in different ways. The intellectual flexibility to go from writing a research paper on history to doing math equations is what will benefit kids in the long run.
It's ironic to find such a glaring flaw in mathematical reasoning in this article: “Algebra II does increase the likelihood of being employed in a good job”
ReplyDeleteWell, based on the cited statistics, you can't make that claim.
Just imagine that case:
- There are 100 people with top-tier jobs, 84 of which took algebra II.
- There are 500 people with top-tier jobs, 250 of which took algebra II.
So, in this sample, of all the people who did take algebra II, 25% got top-tier jobs, and 75% got bottom-tier jobs.
By the way, I'm not trying to say anything about taking algebra II, I just want to point out that statistics made by people other than mathematicians shouldn't be trusted ;)
Sorry, my previous comment should read "500 people with bottom-tier jobs", obviously..
ReplyDeleteBy the way, I was able to solve the 3 questions, but being a student in engineering, it would've been worrying if I wasn't.
I know what you're trying to say, Seban, but your (revised) example isn't enough to confirm the argument. Having more people in a lower-tier job isn't a negative if most of the jobs are lower-tier.
ReplyDeleteUsing your numbers, there are 600 jobs available. There are 334 AL+ subjects, 84 of whom got top-tier jobs = 25% got a top tier job.
There are 266 AL- subjects, 16 of hwom got a top-tier job = 6%.
In your postulated universe, having Algebra II does increase the likehood that the subject lands a top-tier job.
:.)
"Algebra II is the leading predictor of college and work success" But correlation is not necessarily causation.
ReplyDeleteAlgebra II is the next step of math beyond that required in today's curriculum. Presumably the only people who take the class are those who actively choose to do so.
It's easy to imagine a scenario that goes like this: Algebra II becomes the highest required level of math in high school, and everyone starts taking it just because they have to. Math teachers throw their hands in the air and start teaching "Algebra II For People Taking the Standardized Tests" and we start getting high school graduates entering the workforce who have taken Algebra II but can't even do Algebra I. Test scores now reveal that Pre-calculus, the next class in the sequence after Algebra II, becomes the greatest predictor of college and work success.
We should focus on making sure we're effectively teaching the stuff that is currently required before upping the bar.
(Oh, and for the record, I knew how to solve all three of those, though I didn't technically 'get them right'; the answer wasn't obscured in any way...)
ReplyDeleteI agree with @cshabsin. I suspect voluntarily taking music lessons/classes is the biggest predictor of professional success in music also.
ReplyDeleteIt just so happens that technical positions are those that are most valued in our society.
Interesting. I didn't take Algebra II in HS. I did take three semesters of calculus in college, none of which helped in medical school, residency, fellowship or my academic medical career.
ReplyDeleteI hear you. :.)
ReplyDeleteI'm going to comment as a teacher and as a parent.
ReplyDeleteI agree that all should take algebra II, for all the reasons given by posters and by the author of the article. Public schools should produce a well educated public.
One of my children excelled in the subject, adored math courses in high school and is an engineer. The salary for her field is quite good.
My other child struggled with the subject. Even one on one tutoring resulted in great frustration and worksheets gray from erasures and pitted with small holes.
Tucked away in my files is a journal article- adolescents who fail math courses have a very high rate of mood disorders- depression and bipolar. I need to do more reading to discover why this impairs the brain processes needed to do algebra problems properly, but the authors of the journal article stated that students failing math could be a red flag for identifying serious mental health issues.
I do think we need quality training for skilled labor- electricians, HVAC, plumbing, etc. Starting trade school while in high school would give students not attending college an opportunity to leave high school with the skills to earn a decent living. A quality two tier system is needed.
Algebra and Calculus are of great value in many technical fields, and I believe that successful completion of Algebra II is a good indicator of critical thinking skills. I do not believe that it should be required of all HS students. A great many careers, in every socioeconomic level, have no need for it.
ReplyDeleteI would rather see students achieve higher reading skills. As an engineer and educator, I am saddened by the number of people with college degrees that are unable to read and comprehend even minimally complex instructions or text. Reading skills are vital for being able to function in a rapidly changing world, and I would expect that higher-level reading ability is a more accurate predictor of economic and career success.
I got them all right, but then, I'm a math tutor.
ReplyDeleteI suspect the researchers are getting the cart before the horse. It may well be that the people who take algebra II are smarter, more ambitious, better educated, and almost certainly more often college-bound. The fact that they end up better and more lucratively employed is probably due to that, not to taking algebra.
Algebra can, however, make you better looking.
I'm an engineer and got all three answers. However, I'm sure that the correlation is caused by smart people first, who happen to do well in all their classes, including Algebra II.
ReplyDeleteI was valedictorian of my high school and got a 4.0 GPA at one of the most competitive universities in the world. This was not caused by hard work. I was just naturally talented at doing well at school. I was also naturally untalented at nearly everything else (so it all balances out:) Intellectual capacity is largely just the luck of the draw.
Coworkers of mine were actually talking about the fact that we feel unjustly lucky; we were born smart and there is a demand for smart people in the 21st century economy. Due to the lack of supply and high demand, that turns into salaries that are 10x more than the average. However, we don't do 10x more work than the average person. It's just luck.
Going back to Seban678's point: In his sample, of those that took Algebra II, 25% got top tier jobs, while in the entire population, 16.7% got top tier jobs (100 out of 600). Likewise, if you did not take Algebra II, then the ratio of good jobs is 16:250, or only 6.4%!
Btw, the second problem is most easily solved (without pencil and paper) if you notice that all of the answers appear in different quadrants of complex space (I,II,III,IV). If you picture the polar coordinates of the numerator and denominator, you can see that the numerator is roughly more than 270 degrees and less than 270+45, and the, and the denominator is between 270-45 and 270. That means that the difference in angles is about 45 degrees (plus or minus a bit), so the answer (being a division) should be in the first quadrant. So you just look at the signs of the real and imaginary parts of all 4 answers and find the only answer that works.
ReplyDeleteTo Mark and Minnesotastan:
ReplyDeleteAh yes, sorry about that! As I said, you can't trust statistics done by people who aren't mathematicians, and you didn't ;-)
But in any case, my main point was that the claim SEEMS to match the statistics, but the statistics don't imply the claim. So I think it is misleading.
A more accurate claim could be "landing a top job increases the probability that you have taken algebra II in high school"
im in differential equations, but i work at a fast food joint??? wheres my top tier job?? what about including the statistics of people who never took algebra, but also landed a top tier job in a different field. i mean, there are two sides to an argument right???
ReplyDelete