As an x-mathematician (or maybe once a mathematician, always a mathematician?), I always cringe when my students complain about having to take math throughout high school. Sure, they believe they’ll never use it in their future endeavors (wrong!) and have no intention of studying anything remotely related to it in college (hmmmm, logical thinking in any academic discipline – and in life! – requires the brain of a good mathematician). I can’t help but wonder: Don’t they see the beauty in math? Don’t they get a rush when they solve a challenging problem? Ok, maybe it’s just me, the math nerd who thinks that way (and who majored in mathematics in college because she thought all the cute, smart guys would be in her advanced math classes – wrong!). But I was elated when Bill Morse, my friend and educational consulting colleague from Connecticut, shared his thoughts on mathematics with me…
I hope my math-phobic students will read this and perhaps come away a bit more optimistic about studying mathematics for all the future benefits it will surely reap, especially in college. As Bill says, math is beautiful! Math is poetry!
I “abandoned” math 50 years ago, but I did start college as a math major. In high school I took pre calculus and calculus, and as a college freshman I took, upon advice of my science advisor, freshman calculus. I got one of the highest grades in the class, even though I could hardly understand a word the teacher said. He had a heavy accent. I took differential equations for engineers in a state univ. in the summer, then as a sophomore I was placed in a theoretical or advanced calculus course taught by a famous professor.
Which course was more difficult? It depended on the teacher, sometimes on the clarity of the teacher, but mostly on the difficulty or complexity of the material. My best math teacher ever was in high school, best in the sense of inspirational, motivational, and studying pre calculus and calculus with him was more like taking a class in poetry, more like writing poetry and understanding beautiful poetry. It was challenging, exciting, theoretical, and often required our taking an entire weekend or week to think about and solve a single problem. In college the frosh calculus course was just textbook formulaic problem solving, lots of problems, from some poorly written textbook. For math addicts (I was one at that time) it was simple, and not particularly interesting. The sophomore calculus theory course, however, used no textbook, and listening to the lecture and working on problems was like understanding and writing hieroglyphics. A few students understood it, I wasn’t one of them. I barely survived, then dropped out of math.
Math can be beautiful, it can be simple, it can be like plumbing or like poetry, it can be logical and make perfect sense, or it can be like hieroglyphics, near impossible to understand or decipher. It depends on the material, and on the teacher, on his or her talent, his or her approach or expectations. Your written solution to a math problem, where you might go through each step or calculation on your way to the solution, can be efficient or inefficient, breezy or cumbersome, neat or sloppy (I am referring to your method not your handwriting), beautiful or prosaic.
How difficult math, how difficult calculus is or isn’t also depends, let’s face it, on the student’s ability in math.
Schools and colleges often have basic, intermediate, and advanced level calculus. They offer calculus for math majors, applied calculus for engineers, calculus for business majors. Should your student take the calculus course that is offered next year? Ask the current math teacher, he/she knows what you can do. Ask students who are taking the proposed calculus course: How hard is the course, how clear, how good is the teacher?
As a educational consultant, I find it very instructive and interesting to sit in on a math class, during a school or college visit. That tells me more than just walking through the science building. One of the best math teachers I have ever observed is Ann Polina, Math Chair and Head of Westover School.
If you are still with me and my lengthy comment, let me end with a little story. Many math classes you or I visit, have a large photo of Einstein, and often a memorable, amusing quote. Let me quote Einstein on math. He was talking with my Dad one day (they were colleagues at the Institute for Advanced Study) and said the following: “I don’t understand modern mathematics. Do you?” Dad did not answer.
So you see, to answer the question, is this or that math course harder than that one, I’d say it’s all relative.
PS. Grab a bottle of Excedrin, go to Wikipedia and look up Morse Theory.
P.P.S. I, too, love to observe math classes when visiting boarding schools and colleges. I have never seen such a group of students so engaged in the study of geometry as I had years back at the Oakley School in Utah when their geometry teacher taught them about “Carla Corner,” an adorable right-angle character who helped them remember everything they needed to know about right triangles, complementary angles, and perpendicular lines! More recently, Brett Barnett, Mathematics Department Chair at Brewster Academy in New Hampshire, captivated a group of visiting educational consultants with his project-based learning competitions in geometry – which my team won! (Call me if you’d like to know about the problem that stymied all the groups but mine.) Yes, math can be such fun!