# The Four Stages of Floating-Point Competence

The four stages of competence model describes the phases you go through when acquiring a skill:

1. Unconscious incompetence: You don’t know what you don’t know.
2. Conscious incompetence: You know what you don’t know.
3. Conscious competence: You know what you know.
4. Unconscious competence: You don’t know what you know.

I’ve applied this model to assess competence in binary floating-point arithmetic; let’s see where you stand:

# 1,073,741,823 Grains of Rice

In the children’s book “One Grain of Rice: A Mathematical Folktale” a girl uses her knowledge of exponential growth to trick a greedy king into turning over his stockpile of rice. Hidden in the story are mathematical concepts related to doubling: powers of two, geometric sequences, geometric series, and exponents. I will analyze the story from this perspective, and then discuss my experience reading it to first and third grade students.

Front Cover of the Book “One Grain of Rice”