Math has to be meaningful, or why do it?
By Murray Bourne, 26 Jan 2008
I recently received the following email from an adult reader of my Interactive Mathematics site. She has an interesting story about how she's bravely trying to figure out higher math all by herself.
Math students rarely see any connection to the real world, so it is not surprising that many believe they are learning it just to pass a test. Over to the letter...
I'm currently teaching at a Kindergarten. I like interacting with little kids, teaching them alphabets and nursery rhyme. However, the prospects are rather bleak, prompting me to reconsider my future.
I'm planning to take GCE A-level [a pre-university course]. Thing is, mathematics seems to be compulsory and I'm hopeless at it. It's the bane of my life really. Never done well and never motivated.
My past Mathematic teachers' teaching methods were rather uninspiring and I must admit that my foundation in math is pretty shaky. I took O-level Math [Grade 10 level], failed, retook it and got a B3, self studying.
Than, I ventured into an unknown territory called Calculus. I didn't take tuition because I've had enough of conventional teaching methods. I took it upon myself to research and flipped through countless reference books, including "Calculus for Dummies", "How to ace your calculus, the streetwise guide","Math student surviving guide" etc...(You have no idea how desperate I am).
On the internet, I've chanced upon 'Paul's Online Math notes', Math SOS and the like. These webmaster are well intentioned but I feel like being sucked into a black hole. Ya, I don't understand the context.
Problem is, conventional ways of teaching mathematic did nothing for me. For example, while learning differential, the opening chapter will start with "limits and continuity",then "derivative".
My usual questions will always be what is this for? Why do we need to learn this? How do we apply it? Many assessment books, reference book always start with a short and concise introduction but are usually too short for me to grasp the idea.
For two years, I've been reading up and I can understand the idea and even apply what I've learn. I can find the derivative using chain rule, quotient rule. Find integral using 'integrating by part' method and 'substitution'. Still, i didn't do well for the exam.
Now, I'm seriously doubting my ability and take the easy way out; Give up.
It was not until I discover your site that ignited my fighting spirit and retake Math. The way you explain each subject and illustrate the application in the real world is indeed eye opening and fascinating. It was then that I realise that I've been learning math in a wrong and 'disrespectful' way.
Yes, I do practices, but I'm not solving problem. I'm imitating the example given, and when they remodel the question a bit and I'm lost.
I enjoy every feature of your site especially mini lectures. Have you consider mini lecture for differential equation? Also, incorperating games is another delightful idea, though I can't say so for your choice of music. Haha. Just kidding.
I really appreciate your effort and other webmasters who dedicate their time in ending my Math drought. Thank you.
I'm glad that she found some meaning in the applications. A large part of her positive reaction to the site is her 'readiness' to learn at the time she found my site. She already had a lot of questions in her head and fortunately, she found many of the answers that she was looking for. And those answers were as much about finding the meaning behind the math as they were about understanding the math.
And I'm especially glad that the site has resulted in this outcome:
"...ignited my fighting spirit [to] retake Math."
About the music - it is supplied by Last.fm on a random basis. Mostly it's good, but sometimes the tracks they choose are iffy. π
In a later mail, she went on to say:
I forgot to mention, your newsletter is another great help. It further enhances and enriches my experience.
I thank the reader for sharing her story.
You may be interested in other comments about Interactive Mathematics.
See the 7 Comments below.
29 Jan 2008 at 12:23 pm [Comment permalink]
Great letter, Zac. I liked
>> what is this for? Why do we need to learn this? How do we apply it?
The search for meaning in math goes on and on.
Question: Do the teachers know the answers to these questions?
29 Jan 2008 at 3:40 pm [Comment permalink]
My teacher in senior school never told us why we were doing things. It was "learn it for your exam" and that was the best we could get from her.
Even the applications she couldn't do (she kept messing up).
I now enjoy playing around with math, but I didn't when I was at school. Maybe I can see what it is for, now.
30 Jan 2008 at 2:55 am [Comment permalink]
Thanks for the comment on students2.0! To hear you say that "For most people (post-school), mathematics is no more than a tool for problem-solving" is quite disheartening, because I now have such a passion for it, but I do agree with you. Most people never get past the "why?"s of it all. and what are my views of technology in mathematics? I believe strongly in the rule of "too much of a good thing..." especially in this context. As a teaching tool, I'm all for it. I believe that students must be engaged so they may understand completely, and teachers do their best to incorporate that in a variety of ways. (My current math teacher just sent me on a quest to discover various mathematical concepts utilized in the Great Pyramids, and it has given rise to wonderful discussions.)
Thank you for this post. I'm glad to see many relate to it.
15 Mar 2008 at 4:01 pm [Comment permalink]
I really agree with the student who said she could not understand why we study certain things in mathematics; talk less of their applications to real world problems. Even at university level many do not see the possibility of applying maths in life. Actually your way of introducing mathematical problems really helps to situate someone reading the article. Atleast when someone knows why we have to do certain things in the problem he/she can follow to end even if he/she hates maths. It is really interesting in this site. Thanks alot.
21 Mar 2008 at 8:36 am [Comment permalink]
Hi Laurent and thanks for your kind comments.
I often comment on the evils of teaching 'math for math's sake". Sure, there are lots of people who enjoy dabbling in algebra and they don't worry about whether it has application or not. But that is a small proportion of the community. There is a much bigger proportion who need to see why they are learning a thing - or they will immediately forget it.
All the best with your studies.
10 Nov 2010 at 3:42 am [Comment permalink]
There's a book I have called the Manga Guide to Calculus which aims at the applications of calculus as well as the study of it. I was fascinated how calculus is so very much incorporated into our day to day life as the book shows. I mean, the main character was to start work at a newsagents and the first thing the director asked was if she had done any calculus before.Calculus I think is a fundalmental tool to understanding all aspects of our world since our world essentially is a multitude of functions (some natural, some models made artificially), whether it's the typical roller coaster calculus or the relationship between Tv advertising time and profits or the life span of a human being with relation to their mathematical coordinate in the world. A lecturer then said that because of this, calculus is not a niche subject but a very broad and overwhelmingly significant tool. Anyhow, other branches of maths are equally interesting, maybe you can try Hardy's A Mathematician's Apology, which is a short book but in it Hardy, a number theorist, defends his subject as the ultimate route to truth and the pinnacle of human curiosity.
10 Nov 2010 at 5:26 am [Comment permalink]
Thanks Denhen. And here's another view about the most useful field of math.