Mathimatics has been always a horrow subject to me. My brain blocks when I only see numbers and formulas… It’s a wonder how I could have survived so far with such an attitute towards maths!
Renecetly I came across an amazing article on mathematics, which literary has blown my mind. A Mathematician’s Lament, is written by Paul Lockhart in 2002. Paul is a mathematics teacher at Saint Ann’s School in Brooklyn, New York. His article has been circulating through parts of the mathematics and math ed communities ever since. His point is that much mathematics education is hijacked by people who know nothing about it.
Here are some quotes:
“The first thing to understand is that mathematics is an art. The difference between math and
the other arts, such as music and painting, is that our culture does not recognize it as such.
Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound.
In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?
Part of the problem is that nobody has the faintest idea what it is that mathematicians do.
The common perception seems to be that mathematicians are somehow connected with
science– perhaps they help the scientists with their formulas, or feed big numbers into
computers for some reason or other. There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical,
subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or
physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
So let me try to explain what mathematics is, and what mathematicians do. I can hardly do
better than to begin with G.H. Hardy’s excellent description:
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas.
So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of
ideas? Ideas about the rhinoceros? No, those we leave to the biologists. Ideas about language and culture? No, not usually. These things are all far too complicated for most mathematicians’ taste. If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary. . . .”
Or this one:
“Sadly, our present system of mathematics education is precisely this kind of nightmare. In
fact, if I had to design a mechanism for the express purpose of destroying a child’s natural
curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being
done– I simply wouldn’t have the imagination to come up with the kind of senseless, soul-
crushing ideas that constitute contemporary mathematics education.
Everyone knows that something is wrong.
The politicians say, “we need higher standards.” The schools say, “we need more money and equipment”.
Educators say one thing, and teachers say another. They are all wrong.
The only qustion that arises after that article: “Why hasn’t anybody talked about math like this before???”
P.S: waht about a solution? does the author suggest soemthing worthy? Oh, yes! Check this dialog out!
Paul Lockhart created a dialogue between two made-up characters.
SIMPLICIO: Are you really trying to claim that mathematics offers no useful or practical applications to society?
SALVIATI: Of course not. I’m merely suggesting that just because something happens to have practical consequences, doesn’t mean that’s what it is about. Music can lead armies into battle, but that’s not why people write symphonies. Michelangelo decorated a ceiling, but I’m sure he had loftier things on his mind.
SIMPLICIO: But don’t we need people to learn those useful consequences of math?
Don’t we need accountants and carpenters and such?
SALVIATI: How many people actually use any of this “practical math” they supposedly learn in school? Do you think carpenters are out there using trigonometry? How many adults remember how to divide fractions, or solve a quadratic equation? Obviously the current practical training program isn’t working, and for good reason: it is excruciatingly boring, and nobody ever uses it anyway. So why do people think it’s so important? I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them. It might do some good, though, to show them something beautiful and give them an opportunity to enjoy being creative, flexible, open-minded thinkers— the kind of thing a real mathematical education might provide.
SIMPLICIO: But people need to be able to balance their checkbooks, don’t they?
SALVIATI: I’m sure most people use a calculator for everyday arithmetic. And why not? It’s certainly easier and more reliable. But my point is not just that the current system is so terribly bad, it’s that what it’s missing is so wonderfully good! Mathematics should be taught as art for art’s sake. These mundane “useful” aspects would follow naturally as a trivial by-product. Beethoven could easily write an advertising jingle, but his motivation for learning music was to create something beautiful.
SIMPLICIO: But not everyone is cut out to be an artist. What about the kids who aren’t “math people?” How would they fit into your scheme?
SALVIATI: If everyone were exposed to mathematics in its natural state, with all the challenging fun and surprises that that entails, I think we would see a dramatic change both in the attitude of students toward mathematics, and in our conception of what it means to be “good at math.” We are losing so many potentially gifted mathematicians—creative, intelligent people who rightly reject what appears to be a meaningless and sterile subject. They are simply too smart to waste their time on such piffle.
SIMPLICIO: But don’t you think that if math class were made more like art class that a lot of kids just wouldn’t learn anything?
SALVIATI: They’re not learning anything now! Better to not have math classes at all than to do what is currently being done. At least some people might have a chance to discover something beautiful on their own.
Ih this article I found an answer to a question why most of the children just hate maths…again, as with many other (all?) things in life, it is the wrong way of teaching, the lack of understanding of the subject’s nature.
Alas, as in every other profession a doog talented teacher is a rare dimond.
I just used to LOVE mathematics at school (and university, too) – it was always my favourite subject anyday! 🙂
Being a very lazy fellow, I never spent much time in reading text books. With that kind of attitude, it wasn’t a surprise that I couldn’t score very well in the examinations in other subjects. But maths was always a different story. There are no volumes and volumes of boring, complicated stuff to read, no complex formulae to learn (mathematical formulae are fairly simple, logical and easy to understand compared to chemical formulae, for instance), no need for any kind of “rote learning” at all.
All it requires is careful understanding of what is being taught, and paying close attention to the finer points. After that, a simple exercice that involves solving a few problems to put the theory into practice – all that can be done right in the mathematics class itself. And before the day of the examination, just a glance at the all the topics and formulae and maybe solving a couple of tough problems. That is more than enough to score a perfect 100/100 in the examination. As simple as that! 🙂
Mathematics requires barely 20% to 25% of the effort put into learning other subjects. And one can always score a perfect score in maths, something that’s quite impossible with other subjects – even if you put in hours and hours of mind-breaking effort, poring over textbooks, notes and reference books. At the end of the day, though a lazy undesirable like me never thought much about my score cards, they always showed a big disparity between maths and (almost) math-subjects on one hand, and the “rest” on the other.
It was no magic, it was mathemagic! 😉
Mathematics is cool, useful, interesting, creative, very practical and loads and loads of fun!!! 🙂
I’m saddened to hear that Western students and teachers (especially Americans) are having a very tough time with teaching and learning mathematics 😦
I guess it’s a part of the deliberate dumbing down 👿 of the Western education system, all part of the diabolical plan to turd worldise the civilised societies 😡 With the people of the civilised societies being forcibly dumbed down, they can easily be turned into arse-licking morons like the uncouth hordes of the lowly turd world.
There is also this crazy thing that’s being propagated in the civilised societies of the West – that girls and women are “naturally less capable” of understanding and teaching mathematics (and to a lesser extent, science). All that is sheer crap and pure filth! 😡 The ones who taught me the basics of mathematics (and did a fabulous job of it) all happened to be women! 🙂 Though women were outnumbered by men later on, they were equal in maths proficiency in every way to their male counterparts.
While it’s true that women can have a natural affinity to doing well in the humanities-related stuff (and men in science-related stuff), to suggest that girls and women are naturally less capable of doing maths and science is a BIG LIE! 👿 It makes my blood boil to hear that girls and women in the civilised societies are being turned away from mathematics in this crude and disgusting manner 😡
On a lighter note, there is this unproven (even bordeing on the ridiculous) myth that is often heard in my place. There is a vegetable called “lady’s fingers” (or okra/gumbo). Apparently eating this vegetable greatly increases one’s mathematical ability.
I guess parents in the civilised societies of the West need to feed lots and lots of “lady’s fingers” to their kids according to this myth 😉 😀
Math was one of my fav and it s becoz my teacher was the best. evrytime she explained something she wud put so much heart, we just loved her brilliant class, there was always a special feeling, a magical atmosphere during each lessons…
you had great luck, radha!
It is finally the teacher who makes the difference.
I was also extremely lucky with my math teachers – all of them were fascinated with their subject and their mood was truly contagious. Middle school math teacher read us wondrefull children’s books about math by Vladimir Levshin , that made our lessons magical. High school teacher (who I believe is a genious in teaching) made his lessons a true adventure. “People, look, isn’t this beatiful” – he exclaimed sometimes when seeing a beautiful solution. He did show us math as an art. We were always encouraged to look for the most beatiful and simple solution, we even had a festival of theorems, where for two month we had to look for most beatiful theorem in math magazines, libraries – everywhere, and present it to the class. I remember friends coming to my house for a cup of tea and whole evening discussing – yes, right – math homework- this is how much we loved it! Marks never mattered, he was equally generous with “2”-s and “5”-s, freeng us from being dependent on them (I remember laughing aloud, looking at my first ever “2” at math) – and at the same time everyone could make his final mark better by making a presentation about something that interested him or her.
Another teacher from different school, wrote a book “Alice in Math Land” and came to our school to read it while he was writing it – before it was printed, we were his first listeners! If you ever see this book, please read it – it’s a great reading for adults too.
wow, Alenok, that’s an amazing experience! “I remember friends coming to my house for a cup of tea and whole evening discussing – yes, right – math homework- this is how much we loved it! ” that is a true sign of interest…
I had same fascination for Literature and mostly because my teacher was so keen on the subject too: she would invite me to her place and we would read and discuss the new things (at that time, in later 1990s many earlier “forbidden” works came out)…
Somehow or rather, we all need a really good teacher at every time of our life. Till the point when we ourselves become the teachers/masters….
A kid writes a letter to maths….
“Maths, why don’t you grow up and solve your problems yourself ??”
hahahhaha! a great one! :))
I can understand and score same marks in maths like any other subjects but I don’t know why I don’t likes maths ,numbers and their relations,logic and their race , who is going ahead. I think I am not competitive person. I remember When I left maths in 12th My teacher personally requested me for not to leave maths and I can do maths well but any how I left it behind. I remember in 11th I have scored same marks in maths with scholar batch students of our college ( as not even in/ or allowed by teacher for scholar batch) and even having 80% absenteeism in regular class ( at that time really I was not a good student). In that period only I first time heard about mother when her program was in kolhapur (1984) (actually Brhmapuri is nearer to my village and we used to visit for festivals) and exactly after 8 years i enter in sahajayoga. mothers karad program also I missed even being having present in karad in 1988. we (myself and wife and children) got realization in April 2002 and first time we attend seminar at ganpatipule in desember. I mean to say If I would have Sy in 84 then scene would have different I think so .I am not sure because now also whatever I do, I do from bottom of heart otherwise not.( sorry for change of subject)
interesting, mahesh…you know we all find our destination at the right time, right place…2002 was obviously better for you than 1984 🙂
from 2002 i feel i have got my destination. now i dont have any complains regarding anything and with any body I try to accept and enjoy the things / relations as it is and remain cool many times if things goes wrong and not in my hands I try to check with vibratory awareness and if that is also not at the of undersandable level then I literally leave it on mother but goes on doing the things as i wish furgetting about what is right and what is wrong. some where in another blog you said about outcome ( outcome is important) but in nursing we learn and we teach also that all the time reasult may not be faverable and still we have to do with our best till last breath and then forget every thing what isright and what is wrong and this would have done and that would have done. no. I leave everything there only and try to start new with new moment ( it may be battle of survival) feeling of loosing something which may be one of the best of mine, many times painfull. I try to overcome it any how. and try to remain cool .no bleams to any body and any thing at all.
even at this stage I will not blame to teachers. ( any how my tendency was to neglect to maths I used to do for exams only ( take care not to fail in exams) ( either I have not properly encouraged by teacher from fifth or we have not got regular one teacher in that period every year, our maths teacher were changed and unfortunately I was not a teacher fave orate student specially for maths) still they have done very good job i my life always
hi mahesh, noone is blaming teachers here!
Most of them are good-hearted people and try to do their job well. But – as everywhere else – in the teaching there are only few people who are really gifted and capable to inspire. This is kind of normal. Same with doctors, hair-dresseres, scinetis, etc. I have reised this topic ealier if you may remember: for a reason unknown most of the people are doing theri job on a very mediocre level…
[…] A Mathematician’s Lament – or why I hated math at school […]
How is it an art? Show the expression of constants and numbers sir. Geometri is closest to art in existance because it measures to the length art can go. Math is a limiter it is our attempt to make sense of the chaos that hides the true pattern, the true art, creation, an art we will never achieve in over thirty millenia (and this existance is only about seven.) Like all other forms of anything people do it is just mimicry of either evil or good, and all theological stuff is up for your debate.
Math is behind (or in the front) of all arts. Colors seem to match and creat harmony because they follow mathematical patterns, objects are proportional because of their mathematical relations (golden ratio), music sounds beatiful because of mathematical patterns and relations in its structure, language is a mathematical language just made of 26 “digits” instead of the 10 we are used to. It´s all around us, including the size of the screen you are looking at, the proportion of the rectangles in which you read what I wrote, the order in ehich the snow flaxes are running on this screen,sometimes I wonder, is there anything that is not related to math or based on it? Love maybe? but it seems that no one knows what is it.
By the way, I am a math teacher, English is not my first language.