*Essays and activities to exercise your mind.*

## Put 100 Marbles in a Bucket

The coin flip is a basic example of probability that most people are familiar with. Heads or tails. Fifty-fifty. Even Steven. If you flip a fair coin many-many times, half the flips will come up heads.

## What Teachers Study

Most small children haven’t internalized ideas like “can’t carry a tune in a bucket,” so singing comes easily to them. Some children learn melodies more readily than sentences.

## The First Inquiry Pack is IN!

An Inquiry Pack is a collection of activities and ideas that invite you to think as a mathematician, an engineer and an artist. It’s not a pack of stuff. It’s a pack of ideas, suggestions and challenges.

## Make It, Dress It

Many people think that the people who play with dolls and the people who use mathematics are two different kinds of people. If you think that way, think some more.

## Connecting the Dots

If I tell someone that my favorite branch of math is graph theory, communication seldom occurs.

## What is the Same?

What should you take into consideration when you say that two triangles are the same? Should color matter? What about size?

## A Book for Your Birthday

Imagine that you are writing a book called “Life Story So Far.” This book is divided into chapters, and each chapter covers the same number of years.

## Starting the Day

“The day doesn’t really start with the discussion, does it?” I ask Ms. K. “Everyone starts their own day before the little bell rings.”

## Taking Notes in Room 103

“I wish there was a way for me to just sit and watch what is going on,” Ms. K told me. “It is so important to see it all. You have to learn everything you can about each one of them.”

## Reading About Teaching

During the time I was visiting Room 103, two books offered valuable insights that helped me interpret what I was observing:

## The Biggest Problem

At the beginning of the school year, the most pressing problem the students face is how to navigate their classroom.

## Teaching to the Top

“I teach to the top. I think it is very frustrating for them when you start in the middle and keep raising the bar.”

## In Room 103

Each day, for the first hour of the day, for the first two months of the school year, I parked myself in a corner of this elementary school classroom and took notes.

## Story Problem

Once upon a time there was a little old lady who lived in a little old house in a little old wood, not too far from a field…

## Hilbert’s Hotel

This is a famous story in math circles, said to have been invented in the 19th century by David Hilbert.

## Learning by Writing?

Writing can help you learn new things faster and better. This has more to do with how your mind works than how writing works.

## 2 + 2 and Math

If you get to 2 + 2 in your thinking, you might also get to ideas like counting, long division, prime numbers, and Sudoku puzzles.

## Turing Test

The British mathematician and logician Alan Turing formulated an idea which has come to be known as the Turing Test: If, in every “conversation,” the machine responds in the same way as a human would, we can say that the machine thinks.

## Critical At Any Age

Throughout my career as an educator I have worked alongside students, teachers, scientists, artists, and engineers. Critical At Any Age is my unfolding effort to share what I have enjoyed learning in these collaborations.