Math is the most common subject that I tutor. Most of my students are between Grade 11 and first-year university so I really am talking about mathematics here, not elementary school arithmetic. Those who come to me for help differ wildly in their abilities. Some are years ahead of their classmates and simply want enrichment. At the other extreme are those who are just hoping to pass that one last required math course so that they can put the subject behind them for the rest of their lives. Most are getting ‘B’s but striving for ‘A’s.
All of this is pretty much what one might expect. What baffles me, though, is how someone can be in Pre-calculus 11 and still not know how to divide fractions. When I asked one of my most dedicated students about this she looked at me as if I deserved pity for my naïvité. “They get ‘C’s” she said, as if that explained everything. Rarely one for tact when away from teachers, she then added “That’s what happens to the ones who never do any work. They just keep on passing.”
In the grand scheme of human history, the widespread use of mathematics is a relatively recent phenomenon. We don’t just “pick it up” the way we do our native languages. It has to be studied. Math requires knowledge, skills, and thought processes that our distant ancestors had little use for.
In the 20’th century it became fashionable for educators to insist that the way to teach mathematics was to make it fun and easy. I see no harm in enjoying math and learning anything is a process of bringing ease to that which was once difficult. However, the idea seems to have been taken too far. A common attitude among students and even some parents seems to be that there is no point in learning anything if it cannot be made fun and easy.
Was cracking the Enigma code easy?
Was discovering the structure of DNA easy?
Was landing humans on the Moon easy?
Is brain surgery easy?
Will dealing with climate change be easy?
Just for fun, see how many million Google search results you get for the phrase “math fun” or “math easy”. Then see if you get more than 2,000 results for the phrase “math hard work”.
Learning Math and Learning Music
Sometimes I wonder if I expect to much of my students. At other times I wonder if my expectations are too low. Becoming adept at mathematics has a lot in common with learning music. In this Wall Street Journal article that challenges conventional wisdom, Joanne Lipman reflects upon lessons that she and others learned from an orchestra conductor.
1. A little pain is good for you.
2. Drill, baby, drill.
3. Failure is an option.
4. Strict is better than nice.
5. Creativity can be learned.
6. Grit trumps talent.
7. Praise makes you weak…
8.…while stress makes you strong.