A few days ago, Andrew Hacker, an author and former professor of political science at Queens College in New York City, created quite a stir with a New York Times op-ed entitled Is Algebra Necessary?, in which he argues that it is no longer necessary to expect the vast majority of K-12 students to study algebra, geometry or calculus.
Hacker argues that the teaching of mathematics takes a toll beginning with students in junior high or middle school. "Algebra is an onerous stumbling block for all kinds of students," ranging from the disadvantaged to the affluent. Hacker acknowledges that basic "quantitative literacy" is important for everyone, but he asserts that "there's no evidence that being able to prove (x2 + y2)2 = (x2 - y2)2 + (2xy)2 leads to more credible political opinions or social analysis." He further argues that even in jobs that require science-technology-engineering-math (STEM) credentials, considerable training occurs after hiring, and (by implication) mathematics training in school is not that important. He concludes:
Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven't found a compelling answer.
The present authors (DHB from USA, and JMB from Australia) fully acknowledge that there are many problems with present-day K-12 mathematics education worldwide, not the least of which is the relatively poor training of teachers. As William Schmidt and Curtis McKnight note in their book Inequality for All, only 35% to 40% of the 7th and 8th grade teachers they surveyed in Michigan and Ohio had either a major or minor in mathematics, and only half of teachers in the 9th and 10th grade.
Other nations outside the U.S. are not standing still. Finland for example, has ranked at (or near) the top of the OECD nations in educational performance for more than ten straight years, due in large part to its strict requirements for teacher training (all teachers must have at least a masters degree). See also our recent articles School maths is failing children and Yes, there's a numeracy crisis -- so what's the solution? in the Conversation. Along this line, in Australia the New South Wales provincial government has just ruled that all aspiring teachers must specifically study mathematics and science, and further must meet minimum entry scores to even qualify for educational programs at state-operated universities.
One fallacy in Hacker's reasoning is clear: Why single out mathematics? Yes, a knowledge of calculus may or may not help one negotiate through traffic or connect one's computer to the Internet, but the same could be said for many other disciplines. How does knowing whom Hamlet killed accidentally help one be a better consumer? Does knowing the history of the Spanish-American War help one complete one's tax return? Many other examples could be listed.
With regards to Hacker's article, while we agree with many of his specific points, we respectfully disagree that one can be a well-functioning adult in the 21st century world without at least the rudiments of algebra. Consider a very common, simple question: You bought an item at a store, and although you didn't keep the receipt, a charge of $173.15 was posted to your credit card account. The sales tax (or VAT) rate is 8.25%. What was the pre-sales-tax price of the item? With algebra, it is easy: x + 0.0825x = x(1 + 0.0825) = 173.15, so x = 173.15/1.0825 = 159.95. How can you possibly solve such a problem without at least a rudimentary mastery of algebra? As another example, if you get a 20% pay cut, followed by a 20% pay increase, will you be better off, worse off, or the same? (Answer: worse off).
We also agree with Hacker that specific topics taught in a typical K-12 mathematics curriculum need to be rethought in a 21st century economy. Detailed calculus-based graphing techniques (which can now be done better by computer) could give way to a greater emphasis on "discrete mathematics," including aspects of probability and statistics, which might better be termed "reasoning and reckoning."
But a basic facility with algebra is essential to do justice to such material, even at the high school level. And then there is the indisputable fact that a good facility for algebra, geometry and yes even calculus is absolutely essential for that subset of students who aspire to careers in STEMÂ fields. Yes, it is true that even those who major in STEM fields in college and/or graduate school still have significant skills to learn once on the job. But without a strong background in the topics that Hacker derides, they will be hopelessly lost.
As mentioned above, one of Hacker's points is, in effect, that the requirements for algebra and the like serve as an "onerous stumbling block" for disadvantaged students. But we argue the opposite: a system that "tracks" students into mathematically less challenging courses early in junior or middle school, or even in high school, runs a very serious risk of derailing talented young minds from disadvantaged environments. One of us (DHB) has a daughter with several years experience teaching at a very disadvantaged high school in Southern California. She agrees that a "tracking" scheme of the sort implicitly proposed by Hacker would lose a large number of poor black and Hispanic students -- these students need "more opportunities in later grades than other students."
Yes, many disadvantaged students score less well than others, but in many cases this may be due to the fact that they lived in a foster home, or in no home at all, for a year or two. And "dumbing down" the program does not do these students a favor either -- it only places them further behind and deeper in discouragement at the prospect of ever catching up with their more privileged peers. But with dedicated teachers, numerous such students from this daughter's high school and others in the area have gone on to major and excel in mathematics, science and engineering. Some have even received scholarships to institutions such as Stanford University and U.C. Berkeley. None of this would have happened if Hacker's proposed changes had been implemented.
Finally, we must add a personal note. DHB still recalls that his fifth grade teacher reported to his parents that he was a "good B student," and even after he exhibited significant precocity in mathematics, was told in the ninth grade by a well-meaning school counselor that "he didn't really have the aptitude" to be a professional mathematician. If DHB had taken this advice, this article would never have been written!
Similarly, JMB recalls the terror of the British eleven-plus test that he took at the tender age of 10, which would irrevocably decide whether he would be assigned to a precollege track or a vocational track. Introduced as part of the well-intended Butler educational reforms after WW2, the eleven-plus had the effect of consigning 75% of students to a non-academic stream, thereby determining much of their future life. JMB did pass the exam, but what if he had a bad day (say due to a toothache or recent family trauma)? Again, this article would never have been written! Incidentally, his wife, who has a hard time with numbers, thrived mathematically after algebra was introduced in high school.
While we generally agree with Hacker that significant improvements must be made, dumbing down the curriculum, or tracking students at an early age into college-prep or non-college-prep mathematics is not the answer. Hacker may well be right that only 5% of the workforce needs rigorous STEM training, but there is no way to know which 5%. We also know that making all mathematics seem applicable has been a pedagogical disaster. In the 1990s the Dutch did just that (as part of a larger battles over Realistic Mathematics Education): mathematics was to balance checkbooks and understand mortgages. No wonder the university mathematics cohort was cut by two thirds when such miseducated students reached college. To misquote Peggy Lee, "if that is all there is then keep on dancing."
Mathematics really does matter in the 21st century, and better mathematics teaching is desperately needed. Our decision-makers need to acknowledge that some things that need to be fixed are costly. There are no quick smarter-and-cheaper alternatives to investing in training and in paying specialist teachers better.
Simple. 173.15/108.25% = 159.95.
High schools, students, parents, teachers and the public at large need to know about this placement testing as it puts up a surprising barrier to entry for many students. We may be able to, as Mr. Hacker, suggests to change the curriculum to reflect more citizen Math, but until that happens, it is critical that students learn and know the Math expected of them.
While many will not major in science or engineering in college, all students benefit from the challenge and discipline of Math. The study of Math including Algebra broadens career choice, inspires critical thinking, and enhances problem-solving abilities while building confidence and persistence for academic, professional and personal success. In addition to content, Math has other benefits: instilling values of discipline and excellence, improving memory and focus plus preparation for the ‘knowledge economy’.
Robin A. Schwartz
Author Build Math Confidence e-newsletter
www.mathconfidence.com
I would say every form of math whether it is Algebra, Mensuration, Geometry, Trigonometry or Calculus is useful in today's world.
But I sure as hell won't say we need to ditch algebra. I think it's very useful, especially when you're doing any kind of financial planning, building anything, working with electricity, or doing stats. Also, having a sense of how things change over time, whether things grow linearly, geometrically, or logarithmically, is useful in this computerized world. It's not just the math itself, but a sense of how quantities relate to each other that's so useful.
Also, what's with the focus on algebra. That's an 8th or 9th grade subject. The classes that follow are geometry, another algebra, pre-calculus, and calculus. Is Hacker suggesting that math education ends at 9th grade?
And sorry, by the time kids are in the 9th grade their path is pretty well set. They are either achievers and are going to college, or they are not and will either try to go to college and fail, or finish HS, or even drop out. Forcing someone to take algebra who sees no need for it and has no plan to use it is a waste and counterproductive.
I am a Computer Science major at a well respected university. According to your statement, I must have been an A or B student eagerly trying to learn as much as possible in high-school. Quite the contrary, I was barely passing most of my classes, mostly due to a lack of interest. Math was the one subject that could keep my interest. I had no interest in history, english/literature, and even a few of the science classes. I even had to repeat a class and go to summer school. Throughout grade school, I kept that same attitude. Once I got to college, I recognized the freedom and responsibility I was given, and quickly thrived.
The only thing that kept me going through high-school was my interest and involvement in the FIRST Robotics program(http://www.usfirst.org). If you haven't heard of it, I strongly recommend you check it out. This program isn't just about STEM, it promotes the coordination and co-existence between STEM and non-STEM people. Everyone is encouraged to learn from everyone else, no matter the topic.
My life may not fit the mold for the average student, but if things worked the way you described, I would've been lost in the system, and would probably be flipping burgers and asking if "you'd like fries with that." Nobody has a "destiny" set in stone. With enough motivation and the right environment, anyone can change their future.
Great article,
Mike Byster
http://www.mikebyster.com
Inventor of Brainetics, Educator, Author of Genius, Mathematician
But shopping is easy as I can calculate the per unit price in a few moments and to get the best deal on anything I buy. I can calculate what time we will be somewhere (in my head) usually within a minute or 2 by calculating distance divided by the speed the cruise control is set at. So truly understanding mathematics does have many useful everyday applications.
The whole purpose of algebra to me is getting your mind to think of numbers as an abstraction rather than as discrete. If we lose power for a prolonged period of time, your computer won't work. But my mind will always be able to calculate any problem that comes up.
2. Hacker does not single out math; he singles out algebra and above.
3. Your examples of why algebra is necessary are moot because they can be solved with basic math.
4. Hacker is addressing people who won't be going into STEM fields.
The only part of your argument for algebra which holds is that you use some algebra in statistics. In fact, the only time I have used algebra in my adult life has been in grad school and the GRE prerequisite. I agree with you that people need to be taught basic algebra, but not for but one of your examples.
That said, there are certainly a number of algebra courses that DO tie a boulder around students' necks and command them to drag it up hill.
Resolve for that variable, don't just make the whole equation null.
Pat Lovett
Do you want this gap to increase?
I am a scientist. I know when algebra is required and when it is not. And frankly, unless you are going to be a scientist or engineer, it is not.