Math is boring?
There was a recent editorial in the New York Times called "Who Says Math Has to Be Boring?"
One of the arguments in the article is that abstract math is too hard and boring and that if school curriculum was focused more on "real-world" problems and applications of math, more people would be interested in mathematics. What do you think? Is there any problem with "school math"? Would it be better if there were more real-world/applied problems in math class?
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Arron Kau
7 years, 5 months ago
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Personally, I prefer abstract math more over "real-world" application problems. They have easier numbers to work with, and give more practice focusing on the problem-solving technique (journey) rather than just the answer (destination). And I appreciate the quotes around "real-world" problems, because abstract problems are the basis of all other kinds of problems.
As a student in the USA's ever-changing education system, there have recently been a curriculum implemented called "Common Core" trying to unify the country's education. Among this, in the math curriculum, there is more focus on real-world application problems (although they have existed in most textbooks before this). To me, these questions are of much lower quality. Here are 2 example problems from the same lesson:
These are both from a lesson about solving radical equations, but the first one just involves plugging in numbers. I'd like to hear input from other students about this debate too.
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Strangely for me, it is rather the "real-world" problems that are keeping me motivated to learn more and more about maths. More specifically, it is combinatorics where the skills are used to find probabilities, calculate # of arrangements and expected value etc. Not only do I find these topics interesting and beautiful in some of the results, but I also feel complete as I'm equipped with these tools that I could use in real life.
Justin, I think one of the problems is that to bring applied problems in, it's necessary to do most of the work ahead of time (as in your example).
Either that, or spend a lot more time on each problem. I agree completely that #2 is much more interesting than #1.
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Yup! I agree too! :) Many people in my school and I believe elsewhere prefer to be motivated or learn about concrete real-world application of Math in Science, etc. However, I seem to feel more compelled to do abstract math questions as they attract me more! I have never been able to explain this to others or to myself! Glad to know that I am not the only one who feels this way! :)
Include number theory and combinatorics in school. :D
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Unfortunately, that's not a possibility for a lot of teachers. But I agree that it would open up a lot of interesting material that most student's (at least in the U.S.) don't see.
I agree. NT is mostly absent in our curriculum and all NT problems I get on Brilliant, I solve using logic and minimal knowledge.
Combi is slightly present but NT is TOTALLY absent.. :(
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Number theory is also slightly present in Indian school curriculum.
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Slightly? Oh yes, there is Euclidean Algorithm and what else? -_-
lcm and gcd -_-
We have it already but the thing is they are not given under these names
I also have noticed such a strong distaste for anything math related from many of my colleagues. I believe one of the major issues is the "death spiral" principle. A student can get bogged down by the structured nature of math and try to avoid it. This can cause the student to get behind, and when trying to understand it, he gets handed additional material. Trying to trudge through this, the student immediately gets bored, and then proceeds to try to avoid it. This gets the student behind... You get the picture. It can force some people in a cycle that they may never get out of. It is a tragedy when most of the people you meet in college have grown a distaste for learning anything that requires a little extra effort.
Mathematics is a language. As with all languages, you must learn all the seemingly boring and mundane grammar and syntax before you get to the more interesting topics. Without a fundamental understanding of this language, it becomes massively difficult to proceed to more complicated topics, and can lead to a death spiral if not careful.
Now onto the question. If there's anything you know, it's that my class hated word problems. These are the real world problems that do not explicitly state the parameters nor do they state how to proceed to get to the solution. These types of questions are vastly more helpful to the student than just be given a formula, be asked to use it correctly, then be asked to state the result. Why? Because the world we live in rarely behaves that way. These problems, although very helpful, made my class frustrated. They liked thinking in very mechanical and precise terms, because that was most easy to do.
I think the largest problem is not in the type of problem that you ask (not to say it isn't a factor). It's the attitude of today's society. Individuals have lost a passion for learning. They avoid work as much as possible until the repercussions catch up. They only learn to gain some kind of advantage. It's almost a hedonistic approach (we're not quite there, but as a society we are getting pretty close). This attitude is extremely damaging. Learning should be about becoming a better rounded human being, not about the short-term gain that it provides.
Edit: I found a brilliant (no pun intended) video that brings up this topic quite nicely:
http://www.youtube.com/watch?v=Yexc19j3TjE
Every time I ask my friends why they think math is boring, they always say: "How are we even gonna apply it to real life anyways, except for when you study science majors?"
Personally, I think they shouldn't focus more on real world problems but more on abstract math. The real-wrold problems about math is so simple (well... most of the time) there isn't any need to learn in schools. For example, we don't need to learn about estimating groceries cause we already know the basics of how to estimate stuffz and we don't need to extend on it."
Abstract math however, do need educating. I think the problem with school math is they literally go: "Here's a problem, use the formula to solve it and you're good!" What about the concept? What led them into discovering this? What did they do to actually prove it? How can we extend it? (Well, you can argue this is done, but it's literally just applying another formula on top of that, no actual problem-solving). If they had included these things, I think there isn't any real problem.
I guess you can argue about time or they already are doing it, but what's the point in arguing if people aren't interested at ALL in the topic you're arguing about?
I've recently changed from an American international school (which ironically did not have common core, but a original standard) to a Canadian international school which uses IB. Although the curriculum themselves maybe taught in a different order (ie, American focuses on one topic such as Pre-Calc, Trig, Alg II, but IB system asks to cover bits from each topic), the content themselves are no different, I'm very impressed with the idea of Theory of Knowledge, which is a course that is required in the IB diploma (no, I do not take the IB diploma, ironically). The class covers logical reasoning, philosophy, and rationalism, in fact the topics covered are closely related to proof based math solving, at the same time the knowledge can be used in debates, and reasoning. Why did I bring the idea of logic up? Well this is what I commonly see which ever system I go to, first being the "full stack" of knowledge, or misleading ideas, you can see this in debates in which the student constantly uses facts to push an argument, just like court, the opposing side is likely to lose because they have no idea how to reason the idea is wrong, basically more facts the better your debate will be, I also see this in math, for an example when a student is given a problem with a new idea they have the tendency to forcefully throw in ideas they just studied repetitively, without backing up with reason. They also become set to the mind that s everything will work the same and becoming more frustrated in solving new problems. Another thing I tend to see is a extremely weak statistics background in the students, I believe if the common core can integrate the idea of applied statistics students can have a extremely positive effect. Statistics is not the analysis of the data, but the collection of the data, but in this case I include topics such as probability, logic, and mathematical analysis which can maybe be followed by combinatorial, statistics come out in various jobs and I have faith in the possibilities that can be harnessed through out ones life, statistics is another interpreter of math to the real world. Also because statistics is well known for mus-interpretations, and lies I believe students should be taught case examples of mistakes, not just correct methods. What I also noticed that, in tests like AMC/SAT which are multiple choice, is having written the answer on the question itself. As long as you know your methods of proof you can go around testing your answer which can pretty much guarantee you a 100%, the power of proof based math can be harnessed toward these kinds of tests, after all proof based math is what so called "actual math"/"hard math" is based upon.
Another alternative is to insert a discrete mathematics class which covers topics from logic/combinatorial/group theory, and I believe to make it work the curriculum will need to be based on pure application than mechanical solving. After all any colleges, and companies look for the idea of problem solving skills, if one is not looking to pursue math as a carrier I believe they should not take from their high school years how to mechanically solve problems but the gift of problem solving skills which can be used throughout the world.
Yeah... You know, it's funny. Maybe it's just me... but, uh, I'm pretty sure that I maybe don't want POLITICIANS creating my curriculum.
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Totally not related to this conversation but I find your levels on your various math topics impressive!
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Thanks! You're not doing too badly yourself!
Yes I do think so
this is exactly true.we were taught vectors,algebra,etc but we do not know why did we learnt that topic.we have no idea about the physical application of this concepts. For example,physics is taught to us every concept in detail and explaining its importance and focusing on the real world problems and this doesn't happen with math.
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Vectors are important. What if you choose the life dedicated to planes? The passengers generally want to know when their flight is done, what would you do then? You should be able to figure out how to apply it to real-life situations. So what if you never use it, at least you'll have it when you need it.
Many could argue so. They think it is boring and difficult. They all say its pointless! This is because in modern days people could say "I will use a calculator all my life so why the heck do I need to learn this subject in school. I don't even care if I E my teachers quiz." I see but you need to learn the functions on that calculator. Either way why would you need to do real world problems, after college you should be able to apply your skills to solve problems. But this is coming from the perspective of someone who sees math is interesting. I would like to hear the opinion of someone who is anti-math/pro-calculator with guide me through life/this is the subject of the day I dread the most.
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Math, I see, only becomes interesting when you discover the easter eggs, you can only produce a number that ends in 5 with a number that ends in 5 and another number, (x-1)(x+1)+1=x^2, square of one is the first odd number(s) added 1 square of two is the first two odd number(s) added...
The big problem that I see in math and science classes is that we will learn a formula that represents something, but we won't learn how it was derived. So what happens is that we learn different formulas for various things and just memorize them for the exams but then forget them after a while.