A Perfect Math Curriculum
Mathematics is art. The journey is as important as the destination.
A crucial difference between English and math curricula is that in English the books come first and the curriculum is then based on these, whereas in math, the curriculum comes first and then the books are based on that. In the first case, the books are essentially artistic; in the second case, the art is lost.
Do these words resonate with you as they do with me?
In British Columbia, the students headed to post-secondary mathematics take precalculus. The pre irks me. Twelve years of maths study and still in the pre stage. As if calculus is the real math.
I would love to teach a high school maths class where I have full rein of the curriculum. When the students arrive, they see this on the board:
That is my precalculus curriculum. Over the next several weeks, the students learn the notation. They learn about infinite series and partial sums. They learn the factorization of polynomials. Rational expressions. Trigonometry and the unit circle. Even complex numbers. These are all standards in a precalculus education.
You may recognize the above as the famous Basel Problem. The curriculum I describe is necessary to understand Euler’s solution. The students finish the course with something to show for it. They are able to articulate a famous proof.
Most importantly, the students get to play. They get to struggle with problems. They brainstorm together at the whiteboard. Homework isn’t about getting the right answer.
It’s about the journey.
Recent MathAdam articles
- Euler’s Solution to the Basel Problem
- Minkowski Spacetime: Geometry of Special Relativity
- Fibonacci Numbers and Generating Functions
- Binomial Theorem: Proof by Mathematical Induction
- Mathematical Induction: A Gentle Introduction
- The Unattainable Speed of Light
- The Andromeda Paradox Explained
- Are We Creating Mathematical Illiterates?
- SOH-CAH-TOA: Ravings of a Quarantined Mathematician — a dozen Medium articles in print or Kindle format.
- When Am I Ever Gonna Use This Stuff?: A Playful Romp Through the Artform Disparagingly Known as Precalculus — My attempt to remedy some of the misfires of high-school maths education. Kindle edition available for preorder.
- Short Readings in Conics A taste of the geometry you should have had in high school. Kindle edition available for preorder
Until next time!