I’ve been living with this question for a long time – starting with my own son when he attended Middle School (he is now 45, a Managing Director in Greenwich Capital, with his own Middle School aged children).
On Sunday, July 29, the question got a renewed focus with an article titled “Is Algebra Necessary?” in the cover Op-Ed of the New York Times, written by Prof. Andrew Hacker, a colleague of mine from the City University of New York.
I am spending my time trying to democratize the issue of Climate Change by writing a book that I have designated as a textbook for the general public; writing this weekly blog; teaching General Education courses on the topic and founding an undergraduate program designed to lower the communication barriers between the Natural Sciences and the Social Sciences.
The common thread in all these activities is an attempt to democratize the necessary decision making process required to address these climate issues that are so essential to continued human existence. I make the point that the main stumbling block we face is the need to expand science education to the general public, so that decisions that are based on interactions between humans and the physical environment will adhere to a common set of principles.
Suddenly, Professor Hacker tells me in his opinion piece that I must do this without algebra. Here are his arguments:
My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.
This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.
According to the data in the article, one quarter of ninth graders fail to finish high school. In South Carolina, it is 34% and in Nevada 45%. Algebra, according to this account (based on chats with educators) is the main culprit. Furthermore, he states:
Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: ‘failing math at all levels affects retention more than any other academic factor.’ A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.
The article makes an argument that not teaching algebra to everybody does not mean not teaching quantitative reasoning:
Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.
He suggests that we replace algebra with “citizen statistics” that will include topics such as personal finance and how to compute the “Consumer Price Index.” The notion is that we should teach skills to students that will be useful in the job market and should not teach difficult abstract concepts that make them want to drop out of school.
Hacker is talking about the heart of elementary algebra: variables that represent numbers and the rules that apply to these variables. To use a relevant example – any estimate of environmental impact requires an estimate of future growth of quantities such as population and economic activities. With a constant growth rate, this is calculated as exponential growth, and involves calculation with exponential functions related to logarithmic functions. These functions are usually taught in schools in pre-calculus, a level that is more advanced than elementary algebra and only selectively required, depending on the track that students are taking. Many students that take environmental courses have never taken pre-calculus. One can teach exponential growth without relying on exponential functions by instead using the concept of doubling time. However, one needs to manipulate simple one variable equations in order to be able to estimate the needed information. The simplest graphing requires ability to work with slopes, intercept and scale – you cannot do that without elementary algebra.
Even simple things such as unit conversion and percentage calculations need elementary algebra.
Political decisions will need to be made based on interactions with the physical environment. These will require a kind of literacy test for the ability to understand the data on which the decisions are being made. To exclude anybody from mastery of these skills means to give up on them. We don’t want to go in this direction.
There is no question that the teaching of mathematics, perhaps more than any other subject, can be improved. But the “improvement” cannot be done by excluding students that have difficulties. No, we have to redouble our efforts so as to reach these students.
well in terms of algebra, if you ask a current student of algebra whether or not they need it, they would tell you: “No! We don’t need algebra; this is useless. Why would we need algebra if we weren’t going to implement it?” That’s what I used to say, but it all depends on whether you plan to major in mathematics. Possibly not a major in math, but it will be useful to you as you transition from high school to college.
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Of course algebra is necessary!
As you correctly stated, algebraic thinking goes hand in hand with proportional reasoning. One cannot master percentages, ratios, proportions, or statistics without some measure of algebraic thinking.
If students are removed from algebra, what math would they take? In my school the students take algebra in either 7th, 8th, or 9th grade. They then take geometry and algebra 2… and most go on to take trig and pre-calc or calculus.
Not only is algebra a prerequisite course for college, algebraic thinking is a prerequisite for adult level decision making. How many years can a student possibly take a general math class? Surely they would not be equipped for life having never taken a high school algebra class.
Thanks for the reply. I used to play bridge a long time ago in another life, our regular foursome used a Precision club convention, and much fun was had by all. I understand exactly what you say about rejecting distributions that do not allow the contract. I did not mean my comment to be taken as explicitly denying that the contract is makeable. Rather, I think that making the contract will be quite difficult, and we are in for a long rubber.
I agree that a generation is not a long time in the larger view. May I also clarify that my comment speaks exclusively to the situation in the USA. The world is larger than this country, and there are many forces on the carbon mitigation side without its borders. And, of course, many forces opposing. But on the whole I think that the USA is the last bastion of the denialist camp, and I do think they are losing in the USA as well.
Nevertheless, the need is pressing and the hour is late, and we must all do what we can.
sidd
Thanks Sidd for your thoughtful comment,
When I learned how to play bridge, one of the first lessons was to discard distributional possibilities of hands that will not allow me to make my contract.
In my opinion, your description is one such hand. Whatever our collective knowledge and the educational level are, it is our collective job to make them better. Those of us that earn our living in the educational system have to be in the front line, but every aspect of society needs to be involved – this includes family, community, workplace, media, and government on every level. We have the time to do it, now we have to mobilize our collective will to do it – giving up is giving up on all of us – it is a collective suicide with immediate consequences – it is not an option.
You say in your comment that the needed time could be a full generation. It sounds like a long time to us, but in the context of climate change – it is not a very long time. If we can see significant improvements within a generation we will have a decent chance of learning how to live in equilibrium with our environment.
First, thanks for your writing.
Second, let me apologize in advance for what is going to be a long comment.
1)I think the situation with school education is the USA is worse than you imagine. I am pleasantly surprised when I come across a youth who can compose a single paragraph in correct english, or to read and comprehend a passage out of, say, Gibbon, not to speak of one who has any idea how to take a square root without a calculator. The country has raised a generation that cannot count and will not read, thus, to paraphrase Voltaire, they believe in absurdities and thus they commit atrocities.
2)This detirioration in what used to be a standard skillset imparted in schools has greatly harmed the national dialogue. This has a direct effect on the controversy in the USA regarding the fact of anthropogenic climate change. I quote Michael Pollan from Second Nature:
“If nature is the one necessary source of instruction for a garden ethic,culture is the other. Civilization may be part of our problem with respect to nature, but there will be no solution without it. As Wendell Berry has pointed out, it is culture, and certainly not nature, that teaches us to observe and remember, to learn from our mistakes, to share our experiences, and perhaps most important of all, to restrain ourselves. Nature does not teach its creatures to control their appetites except by the harshest of lessons–epidemics, mass death, extinctions. Nothing would be more natural than for humankind to burden the environment to the extent that it was rendered unfit for human life. Nature in that event would not be the loser, nor would it disturb her laws in the least–operating as it has always done, natural selection would unceremoniously do us in. Should this fate be averted, it will only be because our culture–our laws and
metaphors, our science and technology, our ongoing conversation about nature and man’s place in it–pointed us in the direction of a different future. Nature will not do this for us.”
This is exactly the dialogue that is impossible today in the USA, for the majority of citizens are incapable of understanding the rape of things to come. I have no solution other than the painful process of fixing the educational systems, a task that can only bear fruit after a generation, even if it were begun now, and somehow succeeded in the face of the ardent opposition of an alliance of bigots and oligarchs. And by then, sir, we will all be in dire straits indeed.
sidd