If you’ve ever been a student you may have asked the question, “Why do I have to study this?” Our good friend Vanilla, the man with the string shortage, has retired after a career in education. He told me that this was the most frequently asked question in the math classes that he taught.
I recently helped the granddaughter of a friend with trigonometry. Her first question was, “Why do I have to study trigonometry?” I didn’t have a ready answer. Later, I searched online for an answer. That turned into an exercise in disappointment! Who would be satisfied with answers like these?
1. It’s the next unit in the book.
2. The curriculum committee says you have to.
3. It’s on the SAT.
4. Mathematicians find it “elegant.”
5. In case you ever need to know the height of a flag pole.
The “Why” question is one that I had wrestled with as a student. It was never satisfactorily answered. Those five responses are all poor responses to the question IMHO. They are true, at least the first four are true, but they are not designed to satisfy the questioner.
In our most recent session I had a paper sack sitting on the table. A folder clip held the top closed and a post it note on the side had “Why?” written in large flowing script. Inside on separate strips of folded paper I had printed reasons 1 through 5 from the list above. From time to time the girl would glance at the sack, but she never said anything about it. I answered the questions that she had brought with her and we discussed the effects of crosswinds on an airplane’s flight path and related topics.
She looked at sack again. I asked if she remembered her first question. She did with a tiny prompt and I confessed that I hadn’t given her a good answer to that question. Now it is was time to talk about the question.
I shook the sack and she reached in and pulled out #1, then #3, #2 and #4. As she read the first three answers, she would say, “That’s true.” I would respond, “But not satisfying.” Her response? “Right!” As she read #4, her dad (an accountant) said, “Hey, that what they told me.”
When she pulled out #5 and read it, she reacted with scoffing laughter. (I was pleased that the ridiculous answer came out last.)
After that I explained that you can divide reasons to study a given topic or subject into at least two reasons:
1. You need to know this. Reading, writing and arithmetic are needful to function in our society, for example. An engineer will use trig and calculus on the job.
2. You will enrich your world if you know this. These are topics that are not entirely essential, but they give you deeper insight into the world around you and how it works.
There is yet another reason why we read about and study topics. That is when something is interesting or fun for us. Would you have given a different answer?
@Sharkbytes – even emotions and beliefs have been found to be mathematical in nature, just a bit more chaotic than we are used to in the sciences.
Brain mathematics, f.ex. Neural Networks, can be used to replicate natural processes in the brain. I really think it's only a matter of time before synthetic intelligence a) becomes sentient and
b) discovers emotion (whether spontaneous or intended).
It's very good exercise for logic and having a sense of how the world works, which can give you more intuitive ability to judge things concerned with tasks from driving to cooking.
Truth is, since I found trig fascinating, I don't understand those who just feel it's useless. Everything in the world that isn't emotions or beliefs operate according to math.
I love what you did with your little student – taking the time and effort to make learning interesting and to encourage an enquiring mind – bravo!
Like most of life studing is an adventure, you must endure the mondane, work past the usuall, and strugle with the rediculas before you can be supprised by the logicaly obvious. As an engineer the math is esential, obviously learning grameer and spelling were my usless studies.
Rebecca – I like your "train the brain" answer. It is valid and is and should be satisfying when accompanied with an explanation. Don't worry about sentence fragments. You make yourself understood.
Vanilla – IMHO, a good teacher will try to make learning desirable to students.
Pricilla – Advanced math isn't for everyone. As my student said, "If I need to know the height of a flag pole, I'll climb up it with a ruler in my hand." No argument from me.
I never got as far as trigonometry. I stopped at Algebra II, math not being my strong suit. Science, barring physics which is really math wrapped in a science blanket was more interesting. I HATE physics, don't understand physics but never fail to recognize physics in action.
I was always told – because you have to. And that was that.
Rebecca's answer makes sense. Yes, let's get the neurons and synapses going here! Chuck, your final answer, could we make it so for our students, would be the ultimate solution; for if a topic is "interesting or fun," the student will never ask, "Why do I have to study this?
Oh dear, I think I need more algebra. I see that some of my sentences are a bit unfinished. Sorry– I haven't had my coffee yet this morning! I trust you know what I meant. LOL
As a homeschooling mom,. my kids have wondered such things… and so have I! I've had to endure elementary and high school FOUR TIMES again since I finished mine.
The best reason I came up with was that this kind of math "trains your brain." Neurons need pathways. When we think a certain way over a period of time, brain activity is heightened in certain pathways. I always noticed that after a period of very intense period of algebra or reading far beyond their comfortable reading levels, my kids thought a little deeper and their comprehension — even in matters seemingly unrelated to math or reading.
So that's my contribution to the sack. lol