Grades 1-3: Introducing Relations
- What are relations?
- What are operators?
- What are numbers?*
- Numbers in real life
- Telling Time, Counting Money
- Relations Between Numbers
- Operators Symbolize Relations
- Simple Arithmetical Operations
- Add and Subtract any Pair of Numbers
- Simple Multiplication and Division (to 10)
- Geometry and Ratios
- Plato's Meno
- Archimedes and the Method of Exhaustion
- Multiplying and Dividing Larger Numbers
- Multiplying and Dividing Fractions
- Decimals, Zeros, Negative Numbers
- How to Use an Abacus
- Pythagorean Theorem
Grade 8: Algebra. The Compendious Book. al-Khwarizmi.
Grade 9: Analytic Geometry. La géométrie, Descartes.
Grade 10a: Trigonometry.
Grade 10b: Calculus.
Grade 11: Discrete Math.
Grade 12: Elective (if so chosen)
- Boolean algebras (logic, set theory, etc.)
- Linear algebra
- Multivariable calculus
- Graph theory
*Note order. The relations are more important than the numbers. For example, a first-grade project could be to make a family tree (create a statement of relations), and then a way to link any two members of the tree together without long text block or, well, the tree (that is, create operations). We then introduce the standard operators (perhaps in the context of the family tree project). Numbers also have to be introduced early, but teaching relations and operations needs to be separate than numbers for a while because (1) we want students to have a major aha! moment when we merge the two together, and (2) by teaching the relational/operational aspects separately from numbers, we can focus students' attention on the fact that mathematics is really relational in nature.