# KinderCalculus

KinderCalculus is an experimental home curriculum that teaches typical K-6 children Calculus by relieving them of the burden of large number arithmetic.

Freed from this burden, children in my family reached Calculus in their K-6 years with 2 hours/week of effort. A wider test is needed but that is difficult to do because families will rarely commit a child to a 7-year curriculum throughout K-6. Though our coverage is not as thorough as the high school materials, we've been able to manipulate equations at mid-level difficulty by using: (1) unified algebraic concepts (2) a simplified vocabulary (3) shapes to de-clutter equations (4) infinitesimal numbers. These methods are included here.

With these basic skills, we've even re-derived some of humanity's crowning intellectual achievements on reality (Einstein), infinity (Cantor), and creation (fractals). I think it's worth rethinking the burden of big arithmetic if we can replace it with these these wonders of the world.

The "kinder" part of the name KinderCalculus refers to the German term for young children and not Kindergarten. Email inquiries can be sent to numiri@yahoo.com with the subject heading of "KinderCalculus".

## Vocabulary

Because of its unconventional goal, KinderCalculus uses an unconventional approach. I propose to replace much of the arcane vocabulary with simple relatable kid-friendly terms. It is my personal belief that the choice of vocabulary plays a substantive role in a subject's difficulty -- any subject:

• in language. 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"?
• in business. Should we teach kindergardeners to practice "collaborative consumption", or just teach them to "share"?
• in physics. Most children cannot grasp what an "inertial reference frame" in Special Relativity is, but they certainly know what being "adrift" is.

Let's face it, if we force cumbersome language on children, we place a substantive cognitive load on a child and distract the child from the concept at hand. KinderCalculus replaces such poly-syllabic abuses with significantly shorter words like "verbs" for "operators", "nouns" for "operands", "speed" for "derivative", and "peers" for "commutative and associative operands". Terms are chosen based on its mnemonic value, brevity, 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 associative 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.

## Remarks

Thoroughness: at this stage, this content is only an outline of a teacher's guide -- it is NOT meant to be read by children and it is NOT a complete textbook. As such, the focus is on alternate ways to explain advanced concepts to children, so I don't cover all the concepts in the K-12 curriculum. I only cover areas where this approach diverge from the standard exposition for Algebra & Calculus. I skip non-algebra & non-calculus areas such as number sense, probabilities, proportions, reading data tables, etc.

Exercises: rather than do a wide breadth of exercises for Calculus homework, I take the lazy teacher approach of doing hard exercises over and over again, such as repeatedly doing proofs of the Fundamental Theorem, Chain Rule, Product Rule, and time dilation in Special Relativity. This stems from a lack of teaching preparation time more than anything else.

Prerequisite for teachers: the reader is assumed to have mastered high school algebra & calculus.

Prerequisite for children: fractions & 2-digit arithmetic.