G. V. Ramanathan, emeritus professor of mathematics, statistics, and computer science, asks in the Washington Post:
How much math do you really need in everyday life? Ask yourself that — and also the next 10 people you meet, say, your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher.
Unlike literature, history, politics and music, math has little relevance to everyday life. That courses such as “Quantitative Reasoning” improve critical thinking is an unsubstantiated myth. All the mathematics one needs in real life can be learned in early years without much fuss. Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.
Those who do love math and science have been doing very well. Our graduate schools are the best in the world. This “nation at risk” has produced about 140 Nobel laureates since 1983 (about as many as before 1983).
As for the rest, there is no obligation to love math any more than grammar, composition, curfew or washing up after dinner.
[Can we add cursive handwriting to the list in his last paragraph?!]
This is an interesting argument. Your plumber, lawyer, grocer, mechanic, physician, and/or math teacher also might say that literature, history, or even politics or music has little place in his or her life right now. That may not mean, however, that there’s little worth in having learned about the discipline.
How much math (or any subject) do folks need in everyday life? And how much math (or any subject) should students take in school beyond whatever that is (and why)?
[hat tip to Tim Stahmer]
Image credit: Deep down inside we all love math T-shirt
Actually, I think that the better question is “Why are we teaching the math that we are teaching [that is not relevant to many people]?” Most people graduate from high school without a single class in statistics or finance. Everyone will have to deal with compound interest, mortgage payments, taxes, budgeting, and most people will be required to analyze trends in data. Geometry literally means measuring the Earth [Geo=Earth, Metry=measurement] yet the course is more often about proofs over measurement.
One of my serious peeves in education is that we pretend to give everyone a College Preparatory education. #1 for most students it’s too watered down to actually prepare them for college (see the growth in Remedial non-credit Math course at many colleges, especially community or junior colleges) and #2 that curriculum is often completely irrelevant to the mathematics that they will use in their lives.
This is something that needs to be yelled from the rooftops. It is foolishness that we are teaching Calculus to so many high schoolers instead of real-life uses of math.
Calculus is one of the most applicable disciplines to “real-life” when it is understood. Everthing we do or that happens can be more quantitatively understood and prediticed using calculus. The problem may not be what we teach but how we apply it in our classrooms.
Funny. It’s not a matter of whether math provides essential advanced problem solving tools, anyone who does science or engineering for a living uses it every day. Even in business, consultants use it all the time. Ramanathan makes the point by saying the math and science elite are doing very well in the third paragraph quoted above.
The argument is that *most* people don’t need math: your plumber, your electrician, your grocer, your doctor (unless he actually reads medical research, then he needs to understand statistics).
Ask yourself why a few bright people need advanced problem solving tools and most of us don’t. That’s the part that bothers me. I benefit from it because I get to use tools that other people don’t understand in order to help them solve their problems, and I get paid well for it. But I wonder whether this is really best for everyone in the long run.
Is it because most of us are too stupid to use these tools? That’s the argument from folks who don’t think most of us should bother with college. I don’t buy that.
Or is it because we think base level intellectual ability is good enough to sustain life and let us thrive? I think most people fall into that trap. I suspect they’re wrong, that we will need more advanced intellectual abilities rather than less in the future. At least I hope we are moving that way rather than the alternative.
Hmmm. Maybe I should go rent Idiocracy again just in case.
Sorry, that’s a strawman, and a very common one at that. Many countries have excellent vocational learning tracks, and have economies and societies that are doing quite well (many with a higher standard of living than the US). As I said, a watered down “College Prep” is neither sufficient for college, nor useful for anything else. Many people struggled academically with abstract instruction, yet flourished at much more difficult tasks when they saw the application (including higher level mathematics)
As I noted in my post, I find it hard to disagree with the professor’s logic, despite having taught math for twenty years. However, this is all part of a larger issue about the curriculum, and about school in general. We don’t seem to want to have a serious discussion about what is school for and what should students be learning in that relatively limited amount of time.
Instead, we just assume that the traditional subjects should be taught in the traditional manner. Kids need to learn some math but do they need it to be the huge part of the K12 curriculum (as measured by the amount the subject is tested) as it is? Does every high school student really need four years of math beginning with Algebra? Society says yes to both without even considering other options.
@Bill: You may well have been talking about college prep, and I apologize if I missed an important point of yours, but you may notice upon re-reading that I didn’t mention college prep anywhere. I was making a different point.
So your dismissal of my response seems irrelevant to me and maybe a little rude. By rude I mean specifically dismissing my comments in toto as a “strawman” while not really demonstrating an honest attempt to understand what I was saying. I sincerely hope you don’t teach for a living, taking the time to understand what other people are saying is critical to that endeavor in my opinion.
As I understood it, the article was about how much math we need and I argued from personal experience that the better we learn it the more of it we can use. That’s an argument about problem solving. Are you arguing against that point?
The place I dipped into the politics of educational reform is when I opined that more of us can be smarter, and to me this implies that more of us can learn to use math better. Maybe you are arguing against that point?
Just to be clear, I don’t really care that much about the arbitrary politics of educational reform, I care more about learning and I care about the future of human intelligence. But I realize political arguments are often a neccessary evil.
I hope that makes my thoughts clearer and hopefully a little less like a “strawman” to you?
Since I am probably coming off as contentious let me disclose a little more about my situation.
I didn’t rely on school for most of what I learned, I was blessed to have great parents who encouraged reading and learning outside of school and I was always surrounded by books and engaging problem solving opportunities. I learned things in school, but only a small fraction of what I eventually would use, including learning how to actually use math. My father loved to solve math problems and I learned a lot more from him than from formal math classes about actually applying math to real problems.
So yes I’m sure it is naive for me to apply my experience to other people, but to me learning and thriving is about a lot more than school or college prep or college. “Alternatives” should be about learning, not about the business of running schools.
My teenage daughter asked me the other day why anyone would go to college if they had a good trust fund. I sadly had to admit that I wouldn’t have gone to college if I didn’t need it to get the kinds of jobs I wanted to work in. I would have wanted an education, but I would have acquired it myself through books and by finding mentors.
Todd in Philly, USA
It just occurred to me (duh) that there I was not distinguishing two different questions: (1) how much math do we need, and (2) how well are schools teaching math. That probably caused some confusion, which I regret.
Sorry if I misread you Todd. In most discussions of mathematics education “Problem solving skills” is code for “Higher Math Classes”, and for good reason. Lower (and often general) level math students are taught “skills” in a void. They are required to do algebraic manipulations and geometry proofs without any application (or in Pseudocontext as the topic at Dan Meyer’s Blog) That’s the one-the-ground reality, which anyone who does teach is well away of, and anyone who was never in a lower track course is blissfully unaware. Critics outside of education often argue from their own experience, not realizing that their own experience is atypical, or at least privileged.
As for not bothering with college, I know many friends and former students who left with degrees that they can do nothing with, and are employed in jobs and fields that require none of their training. I also know many people who apprenticed, studied independently, and acquired the skills that have made them highly successful. Oh, and they started their careers or their own businesses without tens of thousands of dollars of debt, and now have years of work experience over their peers. Would you rather hire a self-taught programmer with 4 years of experience who stays current with industry use software, or someone fresh out of a CS or IT program at most Universities?
Consider the person whose terminal formal education is a High School Diploma. Would that person be better served by a non-application based Algebra course, or by a Finance, or a Data Analysis and Statistics course? Which one would actually teach problem solving? Which is not to say that Algebra can not be taught as problem solving, but it currently is not, especially for lower levels.
Sadly, this problem is hardly restricted to Math. Our general education students often avoid or are directed away from studying foreign languages, which is also amazingly damaging to their futures.
@Bill: Thanks for the useful clarification, and I apologize for my part in the misunderstanding and for my thin skin. I don’t know why math should get me so fired up. 🙂
The closest I’ve found to the way I envision problem solving is David Perkins approach of learning to navigate the various domains and building “reflective intelligence.” I’ll leave it to educators to figure out how school can make that happen, but I think it’ the right idea whether in school or otherwise. kind regards, Todd.
You’ve just hit on one of the major frustrations of teaching. We are often asked to teach problem solving, life-long learning skills, communications and the catch all “Higher Order Thinking”, then our students are assessed with bubble sheets and our administrators want to know we’re doing to bring up those scores.
To give you an idea of the disconnect: the school that I work at is Title 1 (over 75% of the students are economically disadvantaged) only 23% of our students were ranked “Proficient or better” in science, yet we had more students advance to the finals in Junior Academy of Science than any other school in the state. I would like to think that that is more reflective of research, analysis, and communications skills than a multiple choice test.
Ken Robinson argues that if we are going to make math compulsory throughout secondary school (and English for that matter) then we should also have compulsory dance, art, IT, building, sport, etc.
This is simply because everyone is different. Some people will become professionals who need a high level of maths, while some will become professional dancers.
If it is difficult for complex art or dance techniques to be compulsory, it should be just as difficult to argue that we should have compulsory high levels of maths at school.
Some will say that it’s good to give students a wide range of options in case they change their career. I believe better skills are self-discipline and curiosity, which enables you to change your occupation as often as you please. The only way I’ve found, so far, to teach these skills is not to teach them, but to let the students discover their passions for themselves and have us teachers as their guide.
Through this the students will understand what it takes to become an expert at something, and above all they will be happy. Is this not what every parent wants for their child, and what should be the measure of a good society?
@James: If I understand you, there is something of the spirit of “learning to learn” in that approach and I think that make a tremendous amount of sense. We can’t become experts in everything, but we should each have the experience of being very engaged in *something* as part of our early learning.
I suspect that many of the metacognitive skills and strategies that go along with the process of becoming an expert probably transfer to learning in other domains. I further suspect that they can also provide a good start to learning to navigate problem solving and decision making as a different kind of domain of its own.
I’m not sure what is the counter-proposal that is being offered. Are you suggesting that less math should be required in high school? Are you suggesting that no math should be required in high school? Are you suggesting a different curriculum?
I do have a few problems with the quote in the post:
1) I do not believe that high school education is little more than job training or college prep. You need to explore to see your strengths and weaknesses. You can’t do that by opting out of hard classes.
2) What kind of math are we talking about that a plumber does need to use any? I have a picture in my mind of a guy cutting a piece of pipe to progressively shorter lengths until it fits. Seriously, a lot of plumbers are small business owners, which requires plenty of math to make solid decisions.
3) I don’t believe looking at the Nobel Prize winners is any indication of how our nation is performing as a whole. That would be making the argument that because North Korea has 140 millionaires, it is a wealthy nation.
4) Since when is a quantitative analysis course not helpful to critical thinking? I do pose this as a question. Do you have evidence that such courses are not helpful? If so, please share. If not, we should substantiate the myth.
I think there’s a confusion of ideas that the comments are elucidating: there’s a disconnect between what most people are taught in maths and what most people need to use in daily life. In the UK we have a numeracy curriculum for adults that aims to address the latter, but we still teach maths that is not the same at school.
But there is another, social, disconnect too. Maths is just about the only subject people boast that they can’t do. (Some will honestly admit they don’t understand much science, but that’s slightly different.) Since “we can’t do maths” then anything mathematical we can do, can’t be maths. Lots of people do a lot of maths, looking at percentages, means, ranges, arithmetic manipulations with non-integer numbers. They do a lot of manipulations with fractions, non-base-10 arithmetic and so on. Of course none of that is “maths” because we expect to be able to tell the time, calculate a tip, work out our change and so on and we can’t do maths can we?
As for reforming the US school system – that’s a step too far for my comments. As you might guess from all my maths, I’m based in the UK. We have our own problems and I wouldn’t claim to know enough of yours to really comment in detail. However, I do think in both countries a reassessment of the use of school could be usefully made. A system that teaches core life skills (some maths, reading, writing, computer use, history, some science, citizenship etc.) and then adds college training to those likely to use it, more vocational training for others and mixtures for yet others would surely be a step in the right direction?
I teach the adult numeracy curriculum that Eloise refers to and the most frequent comment from my learners is “Why didn’t they do it like this in school!”
The ‘school maths’ curriculum (and a depressing number of school maths teachers absolutely exel at putting people off the subject for life and convincing them that a)it’s useless and b)they’re rubbish at it, when neither is the case.
I think it is changing slowly. Looking at recent primary age maths work it’s a lot more focussed on the ‘why’ than the learning rules by rote that most adults remember.
Listening to other people’s experiences of maths I’m always acutely aware how lucky I was to have a maths teacher who ‘pretended’ not to teach us differential equations and instead taught us how to get cannonballs on target 😉
John Dewey has been saying this re-focusing of curriculum is needed for several decades. The best learning comes from needing it to solve a problem. The problem must be real and it must have consequences. I self-taught myself many basics of computer hardware (and some software) because my computer crashed and I didn’t want to pay someone to do something that I could have done. I taught myself carpentry because, again, I didn’t want to pay someone for something I could have done. (Hmmm…seems to be a common thread for my learning quests…) The problem comes in finding out what problems motivate our students. How about a problem-solving curriculum that is real and not some arcane pseudo-contextual. Dan Meyers Blog is excellent reading for all subjects! Get rid of the crap and do real problem solving. How about focusing on a few concepts deeply? (and not as they say in America “teaching a curriculum “a mile wide and an inch deep”. I did some problem solving this week and hurt my students brains by “making them think”. (actual quote from a student…made me laugh.)But, the discussions that were made were much better and deeper than when I lectured, practiced, and tested, but took longer to develop. It will require many of us, to move outside our comfort zone, and re-evaluate why we do what we do. Forums like this has be true professional development! Thanks to people who take the time to post their thoughts and open themselves up to honest debate (even if the medium is poor for picking up nuances and mis-cues in the above posts. 🙂 )
@Dan Mott: I agree. And I wish schools were set up to encourage this rather than focusing so much on testing. Problem-solving as the basis of learning (rather than top-down curriculum) seems to be a popular topic of discussion these days. I struggle with how much curriculum should be imposed.
For more on Dewey, see Carl Anderson’s guest post on this blog, which also discusses Freire:
I’d encourage people who are interested to study Freire, who says the curriculum should be generated by listening to the students (“generative themes”) in a class.
Another take on this is the “essential question.” History teachers use this in my town, but the entire school year is based on one at the Parker Charter Essential School in Massachusetts.
@Bill: True, in U.S. society, it’s somehow “acceptable” to not be good at math or foreign languages because “they’re just too hard.” Just wondering why you think avoiding the study of foreign languages is “damaging.”
Angela Maiers is a reading specialist. I love this post, especially where the 5th-grade students say they want to choose material to read because they like it, not be forced to read something because it’s in a specific reading level:
My son is in the 6th grade. He has a lot of talents, but reading and writing have always been a bit of a challenge for him. Now, he’s reading in depth on subjects he enjoys, even books that are published for adults.
Personally, I’d like to see technology enable individualized learning, but I don’t see it happening in the current paradigm with the teacher:student ratios that are out there (at my last school, each teacher in my dept had ~200 students). With tighter and tighter budgets and the advent of technology (though I love it), teacher:student ratios will probably get worse.
The problem is that the maths we DO need, or COULD help us in real life is not taught, or it’s only taught to us by rote. We’re taught to dislike it, not to explore it or play with it, or how to use it effectively in our real lives. So we don’t really know what Maths could do for us, because we avoid it where we can. And forget all the irrelevant things we were taught.
All education needs relevancy.
I am a community college graduate with credit for college algebra, business math, and math related to my trade. I happened to look at one of my son’s calculus books that he took in college. He went on to become a social worker, yet the college required him to take the course. He says he has never used any math beyond what he had in H.S. I have used most of the math I took in my education. However, most of my math was PRACTICAL, not abstract. Yes, scientist, engineers, Etc. would have use for higher level math. My engineer friend says that most of the math he uses everyday is done by computer. He rarely ever uses it in his head or on paper. I would say that the math most REGULAR everyday people would need would be what they teach in H.S. minus the calculus, Business math, Technical Math, and a math related to what you would use in your non-scientific job.
I think in practical life we just need numeracy skills rather than mathematics. Even schools should just keep two separate subjects for kids – Numeracy and Mathematics. Numeracy should involve all math we learn till 8th Standard (Indian) because it involves all the things we are every going to use in Math like type of numbers (whole, integer, rational, etc.). In addition to that, there should be a subject about reading and understanding statistics and calculating probability. If you ask where are you going to use probability, well all your games like poker, blackjack, etc or if you are going in some analytics field, you need knowledge of probability.
And there should be a second subject called Math which should be taken by ONLY those who are actually interested in learning the subject. This should involve all the concepts of mathematical thinking like why do we need the concept of numbers, algebra (some of it is useful in daily life but not things like quadratic equation, or binomial theorem), complex numbers, trig, etc. And this should NOT be taught the way it is taught in school right now, but the way it was interpreted before the invention of these fields, as thought experiments. Do you think we always had the concept of x and if it did not exist, how do you think people would have invented the concept of placeholder for unknown quantity? Why do we need to know an unknown quantity? These are the questions that Math should be answering.
And yes, geometry is such an interesting subject. It should be the favorite of everyone because it involves shapes n all. How can someone not like parallelogram, mid-point theorem of triangles, properties of circles. Circles was the hardest and my favorite lesson in school. It had so many properties.
You can inscribe so many shapes inside a circle and create so many complicated problems.