KinderCalculus
KinderCalculus is an experimental K-6 curriculum intended to teach kids Calculus before leaving Elementary School. It is not intended to cover the equivalent high school materials thoroughly, but provides enough instructions to enable a child to manipulate equations at that level. I accomplish this goal with these strategies
- drop the outdated obsession with large number arithmetic
- simplify the vocabulary (explained below)
- unify algebraic concepts (explained throughout)
- introduce Non-Standard Calculus
In the typical American K-6 curriculum, large number arithmetic typically takes 5 years to complete. I propose to spend that time on algebra and calculus. Focus on manipulating equations -- not number sense, not reading tables and charts, or other topics in the American curriculum.
Vocabulary
Because of its unconventional goal, KinderCalculus uses an unconventional approach. I propose to replace much of the arcane vocabulary with simpler more relatable kid-friendly terms. It is my personal belief that the choice of vocabulary plays a substantive role in the subject's difficulty. Ask yourself: would I start teaching my child to read with a sentence like "observe the blotchly decorated canine as it executes a rapid gait", or would I start with "See Spot run"? Should we teach kindergarteners to practice the "collaborative consumption" business model, or just teach them "sharing"? Let's face it, we force cumbersome language on children with words like "distributive property", "operators", and "indefinite integrals". These difficult words place a substantive cognitive load on a child and distracts the child from the concept at hand.
KinderCalculus replaces this polysyllabic abuse with significantly shorter words like "verbs" for "operators" and "nouns" for "operands". Other simplified terms are "layers" for "order of operation", "evert" for "distributive property", and "peers" for "commutative and associative operands". The terms are chosen based on its mnemonic value, descriptiveness, relatability, and their appeal to a child's sense of subversion. For example, with K-2 children, "potty humor" is an endless source of amusement so I use the term "blunderwear" to describe certain algebraic layering pitfalls similar to the inner and outer layers of clothing. With children, the silly becomes memorable and the subversive offers an illusion of empowerment. See the Glossary for more terms.
Remark
At this stage, this content is only a teacher's guide. As such, the focus is on alternate ways to explain concepts to children, so I don't cover a particular concept from the beginning to end. I only highlight areas where this approach diverge from the standard exposition. The reader is assumed to have mastered high school mathematics. Except for fractions which we need early on, I do not offer any changes to teaching arithmetic because that subject has been refined through the centuries. This material has only been tested in my own family and we seem to have moderate success at an effort level of 2hrs/week.
Table of contents
| Grade 1-2 | Grade 2-3 | Grade 3-4 | Grade 4-5 | Grade 5-6 | Appendix |
|---|---|---|---|---|---|
|
Grammar & Syntax |
Algebra |
Calculus |
Calculus |
