How The Number Garden began

Growing up with rigorous play

I was lucky enough to grow up in a household rich with rigorous play. The chessboard offered a powerful hook, which gave me an opportunity to build complex problem-solving skills from a young age. Participation in chess tournaments and chess clubs pushed me to develop focus, time management, and decision-making.

Aside from chess, my dad was constantly sharing puzzles and games of various sorts with me and my siblings, for the joy of it. He was a card player at heart, and a passionate problem solver. Backgammon, Rummikub, and brainteasers were our bread and butter.

Advancement without enrichment

As I grew up, the learning I was doing outside the classroom put me in a position where I was ahead of grade level and bored out of my mind. The schools I attended offered some element of advancement, but very little enrichment, aside from extracurricular activities like theater and debate.

I loved both theater and debate, and I managed to mostly keep my mouth shut while I performed the learning tasks set before me in order to earn my gold stars.

Discovering mathematics as mathematicians do it

When I got to university, I encountered mathematics in the way mathematicians do mathematics, which blew my mind. I was upset. Why had no one shown me this when I was younger?

The way mathematicians use definitions, conjectures, and proofs is the most fun game I can possibly imagine. Mathematicians are playful, curious, and joyful in a way that I had never seen before. If you have not declared a math major, you have likely never encountered this version of mathematics.

What changed my view of what children can do

While I was in university, Vi Hart published several amazing videos that pointed me toward the idea that this elegant version of mathematics does not need to be limited to the ivory tower. My work with Math for Love made it clear that this version of mathematics is accessible to everyone, at all ages.

Children as young as 5 are perfectly capable of noticing patterns and forming conjectures in order to interrogate those patterns in a rich social environment. Through careful curation and intentional pedagogy, we can teach in a way that invites children into the beautiful world of mathematical thinking.

Pedagogical lineage

Over time, I found myself drawn into a tradition of mathematical and educational thought that gave shape to this work. The Number Garden's pedagogy is shaped by Math for Love, Don Finkel, Paul Lockhart, Vi Hart, James Tanton, Peter Liljedahl, and Neil Postman.

Math for Love has been an especially important influence. Its work demonstrates, in practice, that rich mathematics can be accessible, joyful, and socially alive for learners of all ages. I have also benefited immensely from mentorship from Dan Finkel, whose teaching and writing have deeply shaped the way I think about mathematical culture. His talk Five Principles of Extraordinary Math Teaching is one clear window into that vision.

Don Finkel's masterful book Teaching With Your Mouth Shut offers a rich methodology for inquiry-based learning. Paul Lockhart's work, especially A Mathematician's Lament and Arithmetic, demonstrates what it looks like to invite children into deep mathematics without any hint of force or coercion.

Vi Hart helped open up the possibility that beautiful, playful, elegant mathematics could live far outside the ivory tower. James Tanton's Thinking Mathematics series offers an endless well of rich mathematics: surprising, joyful, and genuinely worth thinking about.

Peter Liljedahl's work provides scientific credibility to the power of vertical non-permanent writing surfaces and to the broader conditions that help real thinking happen in a room. Neil Postman's writing remains an important influence in thinking about education, culture, and what kinds of human beings our institutions are helping to form.