Listen to this PodcastMore 60-Second Science
“I disagree that algebra doesn’t do anything for our lives.”
Evelyn Lamb, math PhD and Scientific American writer, on the WNYC radio program the Takeaway. She’s responding to political science professor Andrew Hacker. In The New York Times, he suggests that, although all students should attain what he calls quantitative literacy, most do not need the rigors of an algebra class.
But “it’s in all sorts of fields, not just STEM fields (science, technology, engineering and math). But, also, real estate agents use algebra and geometry every day. Anyone in finance. Budgeting in your own home. Understanding loan terms and mortgages. All of these are applications of algebra.”
You can listen to the full interview with Lamb and a previous one with Hacker at thetakeaway.org. An article by Lamb about the need for algebra is at www.scientificamerican.com.
Lamb also noted that another mathematical discipline comes in handy when she sews: “There is topology—the number of holes in your garment matters, or else you can’t put on your pants.”
—Steve Mirsky
[The above text is a transcript of this podcast.]
[Interested in science and the Olympics? Check out the new Scientific American e-book, the Science of Sports: Winning at the Olympics. Available in most popular e-book formats including for the Kindle and the Nook. Just $3.99 wherever fine electrons flow or electromagnetic waves pass.]
See what we're tweeting about
29 Comments
Add CommentWay to go doc. Any one trying to lower standards of education in our country is either an idiot or traitor.Most likely the latter. So are people demoralizing our children.Shoot them because hanging is no longer an option!
Reply | Report Abuse | Link to thisaj1350,
Reply | Report Abuse | Link to thisIt's possible you would be the exception. A little less algebra and a little more anger management might be called for in your case.
(kind of extreme but I like aj1350's "Any one trying to lower standards of education in our country is either an idiot or traitor")
Reply | Report Abuse | Link to thisHacker words were the worst I ever read in a long time of people against mathematics, specially when comparing to other countries with a conformist "But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs."
The problem is "how do you measure the effect of teaching not teaching math?". It must be obvious that the way we grew up have consequences in our personality as adults. Math has the same effect: It has consequences, in the way that you think, process ideas. If you grew up with or without a father has consequences, not always evident.
Thanks.
"political science hacker Andrew Professor" - oh, did I get that wrong? It is true, the Luddites of the world do indeed not need Algebra, or flush toilets or accurate property boundaries, or Twitter, for that matter.
Reply | Report Abuse | Link to thisAlgebra should of course be taught; however, it would be best introduced with geometry by using it to argue the general case of, say, all triangles, rather than just one specific triangle. Similarly, grammar should be taught not for its own sake, but as a way to explain how sentences work for readers and writers.
Reply | Report Abuse | Link to thisAlgebra can be a bit dry, when it is just tought for its own sake, only when you bring it into a relation with life, technology or commerce, does it become meaningful. Unfortunately too many teachers can or will not do this.
Reply | Report Abuse | Link to thisMake sense from the political science prof's point of view. After all, when a precinct reports that there was a 120% turnout, the people won't even think something may be a bit odd about the number.
Reply | Report Abuse | Link to thisalgebra is philosophy's twin
Reply | Report Abuse | Link to thiswho needs twins?
well, you're brain is one.
<g>
Hacker is mostly correct that our current junior high through high school math curriculum spends too much time on algebra (often the same material repeatedly over and over again over multiple years), leading to calculus or at least pre-calculus. Our current math curriculum is a relic of a bygone era, based on 19th Century ideal of the education a landed gentleman should have, notably algebra and trig in order to do land surveying and architecture. A modern, rigourous, scientific and nationally useful curriculum would spend much more time on logic, probabilty and statisics, which are not universally (or even often) taught as part of the mandatory universal curriculum. And insofar as something has to be reduced to make room, then advanced algebra should proably be it. This is not dumbing down. It is moving from 19th century to 21st century.
Reply | Report Abuse | Link to thisAs a Mathematics Department head for 30 years, as well as an instructor in Human Development, I often explained to my students that a major reason for learning Algebra and higher level math, is that it teaches us how to think logically, to solve problems, which leads to being able to make good decisions. (This is in addition to the obvious fact that algebra and other advanced maths, are prerequisites for a large number of careers that students may decide to choose at a later time).
Reply | Report Abuse | Link to thisTeenage brains are not yet developed in the judgement, and related logical, areas. (as you may have noticed!) This has to be developed in the late teens and early twenties. This type of thinking is essential for all of us to be successful.
Learning math makes physical changes in the brain that are important for everyone living in an advanced technological society.
I do agree with DrSteveA that the specific curriculum in Algebra needs to be reworked and made more relevant to today.
Reply | Report Abuse | Link to thisAlso, a good teacher will combine the logical with the intuitive and help students develop their creative abilities as well.
RE: "learning algebra to think logically" is an illogical argument. How about acutally teaching Logic, symbolic logic, probability, statistics, and basic research methods?
Reply | Report Abuse | Link to thisCurrent math curriculum is profoundly absurd, repeating the same basic algebra over and over again, topics of no relevance, whose incusion in the curriculum is a 19th Century artifact.
I read A. Hacker's article as an Engineer. I have greatly benefited from algebra, personally. It's my bread and butter, so to speak.
Reply | Report Abuse | Link to thisThe two main arguments for continuing to teach algebra are that it is used in every day life and that it teaches people problem solving/logic skills.
1) Algebra is used as often as plumbing, electric wiring, and cars. We should not all be plumbers, electricians, auto-mechanics, and mathematicians.
2) Even if you do need to use Algebra for a living, the fact is that there exist a plethora of tools available to automate the math and eliminate human error.
3) Andrew Hacker's argument is not to eliminate algebra from our education-- that would be like trying to eliminate gravity on earth. There is nuance to his argument. He wants to eliminate the requirement of SO MUCH Algebra, however, I think one must be familiar with the fact that we require roughly 3 years of Algebra in a pre-college (at least NC does) track. Alg. I, Alg. II, and Pre-cal (the latter being extremely algebra heavy) to understand this nuance. This would not be the end of children learning logic, it would just be the end of my hairdresser telling me how smart I am and how dumb she is because I did math. Let's stop telling the general population that they are idiots because they didn't apply themselves to learning algebra in high school.
4) High school algebra is not math. High school algebra is algorithms. Present A, follow B. Present red stop light, stop car. Present 2-variable linear equation, solve for x by moving all other terms to the opposite side of the equals sign. Real math is perhaps done in high school in Geometry class when students prove mathematical theorems. That is logic, that should never be eliminated. Many teachers skim through this part of Geometry because it's hard to teach and hard to learn. Testing on algorithms and memorizing facts is much easier.
5) Teaching statistics, logic, and applied economics in place of algebra in high school would be more useful and just as rigorous.
6) Logic and problem solving is not the domain of math alone. Programming (that's where I learned it), the scientific method, and research papers also require these skills when executed well. Come to think of it, so does grocery shopping on a budget.
7) What I learned in college, where I truly learned problem solving and logic, is that I had to teach these things to myself and so did all my peers. No one will learn logic or problem solving who does not want to. It's hard for most of us, and it never stops being hard.
One minor adjustment, I should have said "continuing to require algebra be taught to every student for 3 years in order to graduate high school" not "continuing to teach algebra" in the second paragraph.
Reply | Report Abuse | Link to thisThe problem with trying to teach everyone algebra is that not everyone can actually do algebra, and those who cannot get an inordinate amount of attention, which displaces the teaching effort onto those who will not benefit from it. Better to spend the time and effort teaching those who are able to grasp the concepts and teach the rest how to balance their checkbooks and read a ruler. I've been a math teacher for forty years, and I have seen just how destructive the egalitarian approach that "anyone can learn algebra" really is. We wind up teaching for a standardized test and have to gloss over deeper concepts so that we can teach people who will never use it the point-slope determination of a line.
Reply | Report Abuse | Link to thisPolitical Science ? The idiot apparently fails to realize half or more of his field is nothing but statistical analysis of raw data - isn't the math of statistics dependent upon algebra and other math tools ? Damn Liberals! Always telling others what to do, and they themselves are totally clueless.
Reply | Report Abuse | Link to thisMy (the baby boomer's generation) was encouraged to enter the STEM fields by the post-sputnik scare in the US. This provided the impetus for massive federal investments in modernizing public education. The first obvious improvement to encourage/prepare students for possible STEM careers was a massive enrichment in the math curriculum throughout the educational system.
Reply | Report Abuse | Link to thisWe are better off following the logic of DrSteve A above, in looking at what the best math curriculum is to prepare for both possible STEM careers, and as others have noted, to be able to participate in modern decision making - both in private life and as a public citizen. An earlier stress on statistics/data analysis is probably correct. For actual problem solving skills, basic understanding in this area is sorely lacking in US education. Whether sacrificing algebra is the route is open to debate & discussion.
But as a retired physicist currently mentoring in H.S. science classes, the deterioration of basic math skills is obvious & Hacker's direction will not help.
RDH is correct. Statistics uses some Algebra from time to time and it's pretty obvious most journalists, even business oriented journalists have little or no comprehension of the most important branch of math every citizen needs to understand. When I was in college 30+ years ago, they had "dumbed down" statistics for social scientists. It still require some basic algebra.
Reply | Report Abuse | Link to thisMy ninth grade English teacher made grammar fun by creating teams of each row and having the teams diagram sentences as relay races - one sentence part per student. I know grammar now because of this. Unfortunately, I never learned Algebra until I had to use it for calculus. Oh, if only my algebra teachers had used examples from the real world, it might have made sense and been fun to learn!
Reply | Report Abuse | Link to thisSeveral commenters advocate increased study of statistics in high school; I agree completely--it's perhaps the most useful field of math for the majority of people. I have always hated statistics, and was not taught it in school, and have had to force myself to learn it in order to understand the world--mainly social but also physical--around me.
Reply | Report Abuse | Link to thisThe glaring failure of Hacker's letter is that 9/10 of it is devoted to establishing that algebra is hard. Zounds! Who knew? Maybe Archimedes, telling his tyrant boss that 'there is no royal road to mathematics.' Yes, algebra is hard, but algebra is necessary.
We eliminated vocational arts from our schools and then expected kids to understand math without ever showing it to them in real life. Consequently we also eliminated job training. http://abcnews.go.com/WNT/video/us-bridges-roads-built-chinese-firms-14594513?tab=9482930?ion=1206853&playlist=14594944
Reply | Report Abuse | Link to thisWe need welders.
Perhaps if Those of Prof Hacker's inclination insisted on more maths then maybe no GFC. GFC did see maths on the Dark Side. Of course, how maths is taught depends on the teacher. Does he/she have a maths major ofr an education major with maths as an add-on? In Oz about 50% high school maths teachers do not have maths majors. And i understand science fares similarly here. Good luck, Dr Lamb.
Reply | Report Abuse | Link to thisAlgebra is fun! It concisely reminds us mere mortals that we do *not* know every dam thing.
Reply | Report Abuse | Link to thisSo Quadratic that!
Algebra is more than math. It is also a form of symbolic logic, an essential element in critical thinking. Politics and media reporting would all be very different if we were all trained to recognize the empty emotional arguments that pour out of the mouths of politicians and political pundits. We live in a quantitative world. Algebra is not only essential it should be extended to include symbolic logic and the ability to recognize an unsubstantiated premise and illogical conclusions.
Reply | Report Abuse | Link to this"Current math curriculum is profoundly absurd, repeating the same basic algebra over and over again, topics of no relevance, whose incusion in the curriculum is a 19th Century artifact."
Reply | Report Abuse | Link to this------------------------------------------------
People who think that you can understand and do statistics without a thorough knowledge of algebra (two years of it) are nuts! Algebra is in the very roots of statistics. Also, where are they getting their fantasies from?
I agree with VernAuthor 100 percent:
Reply | Report Abuse | Link to this"Algebra is more than math. It is also a form of symbolic logic, an essential element in critical thinking. Politics and media reporting would all be very different if we were all trained to recognize the empty emotional arguments that pour out of the mouths of politicians and political pundits."
Most politicians, journalists, etc., nowadays just present us with vapid tales and arguments that do not hold any water.
In the past, as I have read, we go much better than vapid arguments from Eisenhower and John F. Kennedy. Bill Clinton also knew how to examine problems from their roots and to solve them from there, rather than always looking for the easy way out (to nowhere). The latter is what we got from the Reagans, the Bushes, and from most of the "modern" Senators and Representatives on Capitol Hill.
None of these have ever presented a detailed analysis of anything, including all the numbers. No, they just spout off with wishful thinking, and especially the ones who come from Virginia south to Florida and west to New Nexico, via Kentucky and Arkansas.
D.A.W.
When VernAuthor typed "Algebra is more than math," he made a typographical error.
Reply | Report Abuse | Link to thisWhat he should have said was "Algebra is more than arithmetic."
Furthermore, Algebra II has a good deal of analytic geometry in it. For more information on all of this, look up the math textbooks that were written by Mary P. Dolciant and her associates. Dr. Dolciani has an article in the Wikipedia, too. I used the books from this series all through high school in the late '60s through 1973. A piece of good news is that I have read that these textbooks have been having a resurgence in popularity in recent years.
I don't know in which states, but I did read about that. Those books can probably be found at www.Amazon.com, also.
D.A.W.
It is great that someone somewhere within the mathematics community stands up to defend sanity from the innumerates over in the polysci department but the examples given are not properly illustrative. The examples given of bluejeans and land survey are better thought of as topology rather than algebra.
Reply | Report Abuse | Link to thisWe need to point out that Political Science has given us Socialist paradises with high suicide rates and gas chambers while Mathematics have given us civilization.
It seems like some of the posters with the strongest feelings did not actually read Professor Hacker's article.
Reply | Report Abuse | Link to thisHe emphasized the importance of math in everyone's life and the potential benefits and pleasure that arise from it. What he questioned was the assumption that an ability or desire to competently function in advanced mathematics should be an absolute requirement to even graduate high school with the intention of going on to get more education. One of the examples he gave of such foolishness is the exclusion of students from a university path to becoming a poet unless they were willing and able to complete three years of algebra, geometry and calculus.
When I went to school (admittedly a long time ago) the region where I lived required competency in a second language to graduate from university. Consequently, high schools required two years exposure to foreign language studies as a condition of graduation from the university entrance program. I should mention that the population of the region where I lived was 85% English speaking and none of the languages of the minorities in the area were available for study in the school system.
The rationale for such a requirement was much the same as that currently used to impose mathematics on the general student body as a condition for advancement. A positive set of attributes was arbitrarily cast as essential to being an educated man and a productive citizen. Of course whatever foreign language was selected might not actually be used in adult life but the associated benefits of a second language are not limited to its actual employment by an individual life in everyday life.
It didn't make much sense to then nor does it now if one substitutes math for foreign language.
A region I know of imposes a two year study of spirituality on students as a condition of graduating. These spiritual studies include all the mainstream religions, a group of aboriginal belief systems plus some of the major cults including a tiny one, local to their area, centered around space aliens having designated a local resident as their representative here on earth.
Can anyone seriously argue that understanding much of the basis for the world's value and belief systems, or a second language or math wouldn't be beneficial for everyone even if they personally never explicitly used such skills in their everyday life?
But the problem is you can't or shouldn't make every thing mandatory. Choosing one over the other or some else entirely is completely arbitrary.