If you watch an artist create, you’ll notice that they constantly move between two positions. At one moment, they will be close to their work and changing it. A painter might be adding brush strokes to a section of the painting. A sculptor might be shaving or chiseling a corner of the sculpture. A poet might be changing one word in the final line. They are close to the piece, focusing on one local region, and engaged in action. Then, all of a sudden, they will completely shift postures. They will step back and look at the piece as a whole. How does their change look in the context of the big picture? Does the change they made have the effect they thought it might? If not, does it work anyway? Does it invite new possibilities that they hadn’t thought of? How does it make them feel?
This action, this “stepping back and looking at the whole”, is a beautiful experience. It is the creator watching their creation emerge. A sonogram for their growing piece. I hoped there was a name for this, but I couldn’t find one, so I made one up. I call it wholegazing.
Anecdote from History
Seymour Papert created the mathematical programming language Logo so that learners could wholegaze their mathematical work. He told the story: he passed by a sculpting class and saw them wholegazing. They were creating soap sculptures of turtles. He watched as they would approach the sculpture, carve a few new lines, then step back and look at it from different angles. Then back in they would go, making more changes for a minute, then stepping back again. On and on it went. They were creating, he thought, going through this beautifully intimate dialogue with their creation. He wanted that for math, so he created Logo, a computer programming environment where learners could type mathematical ideas and have those ideas rendered as visual drawings. Now learners could dive in, alter part of their code, then render the whole program and see how their changes affected the whole. Even the main character of the Logo environment is inspired by the soap sculpture experience. For those who know Logo, the character responsible for making the drawings is a turtle. Logo is, to this day, one of the primary ways learners are introduced to computer programming.
Examples of People Wholegazing with Mathematics on Twitter
However… I have to point out that I am also very excited to tackle this problem.
This, to me, is the very definition of #desirabledifficulty. And I’m addicted to it.
— Matt Enlow (@CmonMattTHINK) November 22, 2018
Me thinking https://t.co/lyx4PJYzj1
— John Golden ???? (@mathhombre) November 12, 2018
I’ve never thought much about them, either. So, here’s a first go. I used the “Length vs. Time” simulation.
Here is a video of the simulation with my quick initial thinking:https://t.co/wljIfeMHtX
— Harry O’Malley (@harrytomalley) November 18, 2018
This whole thread:
— Mike Lawler (@mikeandallie) January 28, 2018
Examples of Tasks and Lessons that Facilitate Mathematical Wholegazing
The Matrix Bullet Dodge: This task asks learners to write functions that will help Neo from The Matrix dodge a bullet.
Central Park: This task asks learners to write an expression that calculates the width of a parking space in a parking lot given different constraints.
Daily Desmos: This site posts a graph every day and challenges the user to recreate it using Desmos or similar technology.
Emerge Lessons: These lessons slowly reveal math relationships between two real quantities and ask learners to craft mathematics that predicts future values.
Summary
I gave myself a one hour time constraint to write this post. This just scratches the surface of the idea of wholegazing and its implications. I will continue to explore this idea and its potential to transform my teaching. I’d love to hear your thoughts on this idea. Please comment.