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Teaching, Mathematics and Teaching Math.

Archive for January, 2011


Posted by forumjoe on January 10, 2011

To go along with the class discussion on why we study maths, the first lesson needs to discuss expectations. I believe this will help clarify in the students’ minds what they can expect from the course, what they can expect from their teacher, and what the teacher expects from them. If we make this explicit at the beginning of the course, I hope to reduce student misunderstandings about what is required of them.

Here’s the list I’m working on, but I’m sure it’ll grow over the next month.


What can you expect from this course?

  • This course will hopefully teach you what you need to know to pass the course, to survive subsequent years of mathematical study.
  • Does not teach you how to be a good mathematician!

What can you expect from your teacher?

  • I will always attempt to be prompt and reliable.
  • I will always be available to help; before school, after school, at lunch and recess.
  • I will always do my best to help you learn the content and to get the best results you can.

What do I expect from you?

  • I expect you to be polite.  You should show respect to your fellow students and your teacher.
  • I expect you to not waste my time. This sounds selfish, but if you waste my school time, you’re not taking it from me, you’re taking it from other students who need it.
  • I expect you to not disrupt the learning of others.  Everyone has the right to a hassle-free environment.
  • I expect you to use the feedback on tests and homeworks effectively.  This is what I do it for.
  • I expect you to take advantage of my availability.
  • I expect you to do work at home above and beyond what is called for by the homework*.

Homework is a bit of a separate issue, and I’ll be making my expectations of homework submission clear at another time.


Does this sound fair to the students?  Would you have liked it if a teacher made this clear when you were at school?  Should there be more expectations in any category?


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Why is Mathematics a core subject in school?

Posted by forumjoe on January 1, 2011

Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

– B. Mencken, 1715

In order to get my students to think a bit more about what they’re studying and why they’re studying it, I’m going to ask them the above question… Why do we study mathematics?

And I’m going to get them to really think about this. First individually, then in groups, but not in the way that can be brushed of with “Because its important”. However, if I’m going to ask my kids this question, I’d better have some idea about what the answer is, so I decided to do some research and discuss the results here.

It is my belief (though I can find no factual evidence of this) that 90% of careers and occupations use no maths higher than Year 8 level. Beyond addition and subtraction (which cash registers and calculators can do anyway) how much maths do you really need to survive in society these days? Why do we force students to study maths beyond this level? Sure, there should be maths classes covering calculus and algebra and trigonometry in highschool for those students who WANT TO BE THERE, and these should be wonderful, happy places where students creatively solve problems and learn about the world, like Lockhart envisioned.

Mathematics is looked at by society at large as a “necessary evil”. Why is it necessary? Do schools make Mathematics a compulsory subject because society sees it as necessary? Or does society see it as necessary simply because “everyone has to do their dues” in the mathematics classroom as a child. Parents expect their children to study maths because they themselves studied maths as a child. But if they’re not going into a career that requires maths, why do they need to study it?

The SIN rule
The Mode of a dataset
The Volume of a right prism

When will people ever need to use these things unless they get a job in a field that requires it? The only reason to understand these concepts in maths is because they’ll need to build on their understanding next year. It’s a repeating cycle. “You need to learn [x] because it will help you learn [y] next year”

Cut The Knot’s manifesto – – has a great collection of quotes on this issue from throughout the ages, for both sides of the argument. Here are some interesting ones that I’ll be showing my kids to start discussion on this:

J. B. Mencken, De Chralataneria eruditorium, 1715 (quoted in C. Fadiman, The Mathematical Magpie, p. 256):
Mathematics contains much that will neither hurt one if one does not know it nor help one if one does know it.

Has anything changed since 1715? I think many people would agree with this statement today.

Fran Lebowitz (b. 1951), Social Studies, “Tips for Teens”, 1981.
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.

Phwoar, no such thing as Algebra!? But what about… oh. How about… hmmm. Surely… no, ok. Maybe you’re right.
Algebra is a great mathematical tool. It’s great for solving mathematical problems and it is a fundamental building block for many subsequent mathematical concepts. But if someone doesn’t learn it, or doesn’t understand it, will it affect their ability to contribute to society?

R. P. Boas, Jr., If This Be Treason…, Amer Math Monthly, 64(1957), 247-249.
When I was teaching mathematics to future naval officers during the war, I was told that the Navy had found that the men who had studied calculus made better line officers than men who had not studied calculus. Nothing is clearer (it was clear even to the Navy) than that a line officer never has the slightest use for calculus.

So now, perhaps, we are approaching the crux of the problem. Why is this so? Why does studying calculus help in an occupation that has no use for calculus? I can think of a whole bunch of possible reasons, but I don’t really know. Hopefully this is where my research will lead next.

There are lots of great quotes in Cut The Knot’s manifesto, and I encourage you to check them out. Many have anecdotal evidence about how studying mathematics helps develop the mind in ways useful for many careers. I shall leave you with one of my favourites. Benjamin Franklin, in 1787:

It seems to me, that if statesmen had a little more arithmetic, or were more accustomed to calculation, wars would be much less frequent.

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