Teaching Math, USA Style
I am no expert but, from my teaching experience in the USA, I was wondering why Mathematics is broken down into a series of fragmented courses, each with a hefty hardcover book to bend the backs of students forced to carry them? Here is one high school course structure:
Algebra
Geometry or Integrated Alg/Geometry
Advanced Algebra A or Advanced Algebra
Pre-Calculus or Discrete Math
AP Calculus AB or AP Statistics
AP Calculus BC
Calculus 3
When teaching math in New Zealand, we combined Algebra and Geometry and Trigonometry. Calculus was part of senior Mathematics. I wonder if students see each “branch” of Mathematics as discrete when they are taught in separate courses? Would it not be more powerful to link these major topics? After all, Geometry is simply visual Algebra and Calculus is Algebra in Motion? When I was a high school student, we integrated the math topics and I am sure these gave me a more global view of the subject. To test the idea, I taught “An Introduction to Calculus” to a class of 14 year olds as an end-of-year fun activity. Successful? I believe so, but only because they viewed it as an “extra” and a challenge, rather than a course to be feared for its difficulty and the weight of the textbook to support it.
[Wikipedia notes: Before the Renaissance, mathematics was divided into two main areas: arithmetic — regarding the manipulation of numbers, and geometry — regarding the study of shapes.
During the Renaissance, two more areas appeared. Mathematical notation led to algebra, which, roughly speaking, consists of the study and the manipulation of formulas and Calculus, consisting of the two subfields infinitesimal calculus and integral calculus. This division into four main areas — arithmetic, geometry, algebra, calculus — endured until the end of the 19th century.
Today, the Mathematics Subject Classification contains no less than sixty-four first-level areas. Other first-level areas emerged during the 20th century (for example category theory; homological algebra, and computer science) or had not previously been considered as mathematics, such as Mathematical logic and foundations (including model theory, computability theory, set theory, proof theory, and algebraic logic).]
