This is a nice sentiment, but the fact is that it is not in itself sufficient. Kids, many kids, like to learn for the sake of learning, but their time is finite, like anyones, and so some sort of heirarchy has to be set up. For instance, a kid may well think that learning to playthe gitaur is worth learning, and in fdact may thinik it is so worth learning that theyt go home and practice 4 hours a day and don’t ever crck thier math book, even though they agree in the abstract that it is important. I myself thought that history was much more worthwhile than math–although I enjoyed math–so that is what I devoted my time to. So even a child that loves to learn needs to have help prioritizing things in such a way that they are prepared for adult life.
I, myself, fall into the “math is important becuse it teaches you precision and logic” catagory. Hell, I am a liberal arts major, but I think my math skills help me write as much as my english skills. It was in my math classes that I learned to brreak problems (or arguements) down into logical pieces, and to systematically work through things; THe Ryan’s remark on “hand-waving” is dead on—at least on the high school level it is in math class, not english class, that you learn that you can’t skip steps, and that what is obvious to you is not always obvious to everyone else, and even that (most importatly) that when you explore that which is obvious to you in detail, it sometimes turns out to be wrong.
Good motto. Also a good point about defending math with specific applications.
It may just be easier, and more effective, to say “look around - - all our technology required an understanding of math - - and all of nature can be better understood using math.”
sorry for interjecting a different attitude, but i LOVED math. in grammar school it was almost the only interesting thing they taught and not enough of it. i really liked what they called word problems. they were verbal descriptions of something in the REAL WORLD and i had to figure out for myself what equations to use, then do the arithmatic. to me straight math problems were just plug and crank, boring. i noticed most of the other kids seemed to hate the word problems.
i think the problem with teaching math is that it is disconnected from reality too much. the teachers should show the kids something REAL that needs to be solved, then teach the math of how to solve it. a few years ago a had one of my apartments carpeted and had measured the area and knew it was 80 sq yds. the salesman came and measured it and told me i needed 82 lineal feet. what’s a lineal foot?
i looked it up on the internet and found carpeting comes on 12 foot rolls and 82 lineal feet is 82 feet long, 12 feet wide. 109 SQUARE YARDS. people are using specialized jargon and math to rip other people off every day. gotta have the math but you have to UNDERSTAND how it relates to REALITY. that is where the schools are failing.
I really like the idea of story problems, with no fixed solution. Just ask the students the question and have them try to figure out how to do it. Obviously, for a new topic they don’t have the tools, but with a skilled teacher there to keep them pointed in the right direction, you can sort of get the effect of redeveloping the math. A lot of intervening steps will have to be left out, but that’s okay.
Confronting the student who wonders what is the use of it all is sometimes hard. I think story problems also help here. I don’t think story problems should be watered down at all, with extraneous data trimmed out. Leave the extraneous data in. E.g.
Fake story problem:
Farmer Brown has 3 potatoes, a Farmer Jones has 5. How many do they have together?
Real story problem:
Farmer Brown has grown potatoes on three patches of land. In August, he harvests 21 potatoes, of which, six are inedible. He harvests 12 more in September.
How many edible potatoes does he have at the end of August?
What is the mean number of potatoes produced by Brown’s patches in each month?
While there may be advantages to learning certain parts of math; certainly basic arithmatic and certain parts of algebra, much of it is pointless and irrelevent. Certainly there’s little or no need for anyone to learn Trigonometry or advanced Geometry (and I don’t mean very advanced, either). And any perceived benefits that they may have must be balanced against the enormous harm that is done by forcing kids to learn subjects that they regard as boring and irrelevent. This has the potential to turn them off to learning in general.
Much of algebra can be accomplished through geomtetry (factoring for example). I’d draw you a picture if I had a good way to do it. Learning the geomtetry was a great help to me in being able to visualize what was going on with the algebra rather than just memorizing techniques. I remember my algebra now largely by my memories of the geometric visualizations. Trigonometry may be fairly irrelevant for many careers but it’s the first exposure I had to functions that couldn’t be described algebraicly. Without this exposure to functions, I would have had no clue what was going on when I learned about computers.
I am a writer, I don’t need to know much about computers, but I thought I wanted to be a programmer when I was little and by learning about functions I discovered a lot of what computers were about. Now I’m a writer. My degree is in English.
My point about Trig is that it exposes you to a whole bunch of stuff about where math can get you. I think that this gives you a chance to see if you like that. IMO, Algebra doesn’t get far enough to make a good judgement. Trig does. The careers which require Trig are generally in high demand and lucrative. I would be upset as a parent if my children were not given every opportunity to understand those careers. I found english class boring and irrelevant in junior high. I had poor teachers. Upon getting good teachers, I found it to be the most stimulating and relevant subject I ever studied. My Trig teacher, the first time, was so bad I nearly failed the class. I was generally a straight A student. Later, in a pre-calc class I finally learned Trig and was fascinated by it. I think that, in many cases, it’s not the subject that’s boring. It’s the instructor.
In my experience, people who learn the subjects of the year before well, generally don’t have too difficult a time with the next year. But if one teacher does a poor job (and it may just be a lack of connecting with that one student), it becomes very difficult to catch up in that subject. So, I think teachers have a huge influence on their students. I was lucky in that when I had trouble with anything I had a mother and friends of parents who were good at helping me. My dad, a very smart man, was not a good teacher. He was the only one around who could help me with Trig, thus I struggled and it took an exceptional teacher to bring me back on track. That teacher, Dr. Kirwin, is, last I heard, president of Ohio State University.
IzzyR, it sounds to me like you had some lousy math teachers. A not uncommon occurrance.
One of the things kids should learn is that not everything is fun and IRL you have to work and do things you do not always like. The last 30 years of “learning should be fun” have been a disaster, not only because kids know less stuff but also because they have not learnt self discipline and an ethic of work and effort. Many kids have been spoiled by unrealistic expectations. Math is good for you. Just do it.
There isn’t? Trig is awfully fundamental. Let’s forget for a moment all the things in the real world you just won’t be able to analyze without using trig. Without it, you’re going to have a difficult time learning calculus, and without calculus, pretty much any technical career that requires a BS or better is off limits, not to mention just understanding how things work to satisfy your own curiosity.
I’ve used the math you call “pointless and irrelevant” to a considerable extent in my job, without which a bunch of stuff you take for granted wouldn’t exist. But aside from making a living, I can’t begin to recall how many times I’ve just been curious about how something worked, and learning the answer ended up requiring a good working knowledge of some higher level of math. Do people no longer learn things as an end unto itself? I hope they do, and I believe schools should equip children to that end.
If math turns kids off to learning, then there is a problem that needs fixing. But the solution to this problem is not simply to avoid teaching it! Let’s not throw the baby out with the bathwater, eh?
I’d like to concur with the poster who earlier opined that seeing real world applications for math problems is vital in teaching students to enjoy the subject. This past year I had probably the worst teacher that I’ve ever seen for my geometry class. In her defense, it was her first year teaching the subject. We did absolutely no problems pertaining to real world situations, and she was for the most part unable to motivate anyone. Most of the class did well below their potential.
I was one of those, and as I look back on the year now, I wish I had put a little more effort into it. The reason I didn’t was because at the time I saw no practical application for anything I was doing, and it’s only now that I am starting to see how the subject could have been useful. When students get into high school, they stop learning things just because they’re told to; they instead look for why they should learn them. If they don’t see why, then the subject looks pointless and dull and they respond accordingly. The best way to not foster this attitude is to clearly show where the skills you are learning can be applied in a real world situation.
Just to clarify my earlier post, I do not mean to imply that high school math is irrelevent to higher level learning and subsequent career opportunities. Clearly it is not. My point relates only to the relevence of this math for the general public, the vast majority of whom will have no possible application of it to their lives. I believe this sort of learning fosters in children negative attitudes towards learning in general.
Obviously there are some people who like math, and these people should be encouraged to take this subject.
I agree with sailor that it is a good lesson for kids to learn that not everything is fun. But it should at least be relevent. There are many subjects which kids study which are not fun, but which at least have a clear purpose. Studying these teaches the proper lesson - you have to work hard and do things that you might not enjoy, in order to accomplish things. Teaching subjects which are irrelevent, which have no application to people’s lives, and which they will completely forget as soon as they graduate, just teaches cynicism.
For the record, I think high school chemistry is even more pointless and irrelevent than math.
VileOrb has slandered my math teacher, a nice man who I liked. It was the material.
phouka - did your teacher’s training courses have to justify all these subjects too?
not to sound too extreme, but humans will either acquire knowledge & wisdom - and survive - or not - and perish.
there are countless examples of the benefits of math, it’s almost ridiculous to question its value, but I understand the difficulty in expressing its importance to children who do not see the big picture.
I think the root of the problem is that it can be a difficult subject so many people just write it off rather than make the effort to learn it. And our society (society is to blame! :)) will still support those who do not learn.
I don’t know of a simple Golden Reason that will convince all teenagers to like math, but it may be something like… “sure, you can live your life without learning math, but your life will be better if you do”
“sure, you can live your life without learning math, but your life will be better if you do”
Good one Phouka.
IzzyR - I’m still convinced that some teachers would be able to make math interesting for you. The only classes that I think are inherently boring are the ones involving nothing but memorization. Some Actuary math would fit in that category. Trig is a lot more than that. It is probably too late for you. You already have an opinion and in other threads I have commented in detail how hard it is to change someones opinion. However, as nice a man as your math teacher may have been, I believe someone could have made your trig class more interesting.
More for IzzyR - If you are not interested in higher learning, drop out after 9th grade and go to a trade school. You won’t be forced to take Trig (unless you choose one of the many trades which require it) and you can start paying taxes that much quicker. I’m not sure what you mean by “general public” in this context, clearly the millions of tech workers in america are a part of the general public and they need trig. Iwas thinking about this last night and I asked a friend who is in a school learning to be a car mechanic. He dropped out of high school 10 years ago and has been working as a mechanic since but wanted to go get a certificate so that he would have more opportunities for higher pay. Guess what? He’s taking Trigonometry this term. He hates it. I told him I would tutor him if he needs it and he was a little startled since he knows I’m an English Major.
History was the subject that I always wanted someone to explain the purpose for. I see it now but I avoided history classes as much as possible throughout my education. I learned most of my history through literature so my concept of how things happened is a bit confused. I am convinced that if I had had a good history teacher back in elementary school, I’d be a lot more knowedgeable and better off for it.
I’m in the same boat as you: hated math and didn’t see the relevance of it, and am now learnng math for it’s own sake.
I agree with most of the reasons that others have given about uses for math and relevance thereof, however…
When I was younger, none of 'em would have convinced me. What finally got me to shut up and just do the work, rather than bitching about it was one math teacher (Geometry, 10th grade) who, when faced with me whining for the thousandth time “But why do I have to learrrrn this? I’ll never haveta use it in real life!” finally (justifiably) blew her stack and, instead of giving me the sort of responses others have suggested said “Because in ‘real life’ you are going to have an employer, and the employer is going to expect you to do dull, repetitive and ostentably useless things. Whining to him or her will get you fired. Therefore, if nothing else, you’re learning to deal with doing a job, even if it’s boring. Consider this practice for any job you’ll ever get. I don’t care if you like math and I don’t care if you’re having fun. Currently your job is to be a student. Now sit down, quit griping and get back to your job!”
I was pretty shocked at the time, but, after some serious thought (and given that when I told my folks about it, they gave her a standing ovation)I decided she was right.
This was some of the best advice I was ever given as a student. I don’t suggest that it should be your first answer to students (others in this thread have come up with far better answers), but it’s something you may want to consider for a last resort.
I appreciate your concern for me personally. However, you will be relieved to hear that it is not needed. Actually, I had reason to learn quite alot of math post-high school, and currently work in a job which is extremely math oriented. I do not dislike math. It has relevence to me and to my ability to make a living, and I accept it like I would any job. In high school, I disliked math because I was convinced that it was completely irrelevent. Looking back at the stuff that I learned in high school, I realize how right I was. Of course, most of the stuff that I despised in HS was stuff that I would have had to learn anyway for my career. But I maintain that it should be taught post high school to those intrested in pursuing a career which requires it. High school should emphasize more those subjects which actually give a person a greater awareness of, and understanding of, the world around them. Such as physics, biology, psychology and the like.
If most people do not use math in their daily lives, it’s simply because we’ve been lousy at teaching them the usefulness of math. I use all kinds of mathematics in my daily life (and even more in my profession). People don’t use math to figure out how much soil they’ll need to pot their plants, but if they DID they would get the job done better and faster. Instead they go buy a bag of soil, and either have some left over or have to make a second trip. it never occurs to them to actually calculate the volume of the pot and then buy the appropriate size. People don’t optimize their use of resources, because they either don’t know how or don’t have the mental discipline to use what they’ve learned. The mundane uses of mathematics are all around us, if only we’d take the time to use it.
When I read the newspaper, my mind is often doing mathematical background checks on what I read. If someone writes an article about an issue I care about and says something like, “Every day, the rate of AIDS infections increases by 3%” I know there is something wrong, because my mind is engaged. I’ll get a pencil and paper, and doing some quick checks to see if the numbers make sense. If it looks wrong, I’ll go to my computer and look up some other information. I’ll apply my knowledge of statistics to figure out confidence intervals and whether or not this ‘new data’ is simply some reporter writing about something he doesn’t understand.
You’re right that many people are completely detached from mathematics. And that’s a shame.
OK, IzzyR, your last post clarified you position substantially and I can sympathize with that position. However, as I understand it, the current high school curriculum is designed to prepare the student for college, not to provide an understanding of the world around them. I am not saying that this is the best idea. I only am saying that this is the stated goal. Trig is a good course to prepare you for college. As I remember, to get even a little into physics you need trig, and calculus crops up not long after that. Biology beyond the elementary level requires some statistics and chemistry helps too. Psychology is such a poorly understood subject (by the experts even) I would hesitate to teach it at a low level. Knowledge of history, literature, biology, sociology, and statistics would be prerequisites if I was creating the curriculum.
I think my high school physics class could have been better titled ‘ballistics’. And, I learned more of that in trig class than I did in the physics class. I used my trig to solve the physics problems much more quickly than the way we were being taught, and the teacher praised me for it (thank god he didn’t insist I do it the clunky way).
My thought is that these sort of brushing the surface classes that get taught at the high school level are more a waste of time than learning something useful, even if you never use it.
As far as teaching the students to understand the world around them instead of preparing them for college, that seems a worthy goal. I hesitate to make a that choice at such an early age but I believe they do that in many places in Europe. It could work.
He hates it. 
I told him I would tutor him if he needs it and he was a little startled since he knows I’m an English Major.