The first female to win math's top prize described her two brain storming strategies.
"Iranian-born Maryam Mirzakhani of Stanford University has become the first woman to win the top award in mathematics, the Field’s Medal. The award, often described as the Nobel Prize of mathematics, is given every four years to up to four scholars and has been around since 1936. Mirzakhani was awarded the prize for her work in complex geometry and navigation within spaces."One strategy is to let discoveries sneak up on her. The other is to doodle. Both take advantage of the non-linear progression of thought. And neither are what we have children do in schools. The idea of most educational institutions is based on a brain-body oppositional model in which the teacher is the head of the class and the students the body (student body, get it?) And the body is thought to be the inferior appendage, that needs to sit still and fall under the control of mind.
But what if you brain and your gut are actually one system, each dependent on the other, and what would that tell us about the appropriate design of education? The brain gut axis is a thing coming more and more into the news as doctors learn that we are what we eat. An NPR news report Gut Bacteria Might Guide The Workings Of Our Minds describes it. You can also experiment on your own using pro-biotics and see how they make you think.
On two points... one the use of the unconscious mind to bring an indirect approach to problem solving, and the use of doodling to activate the unconscious mind, so much of problem solving involves the non-linear progression of thought. I live in Eureka Springs, Arkansas, and we are an arts colony run rampant with what we call "Eureka" moments, in which coincidences occur, and unexpected connections are made.
You can't plan those unexpected connections, but they are essential to effective learning. A state of surprise generates a dose of neuro-hormones in the body that increase the level of attention, and thus stimulate more effective learning. And those connections are most authentic and effective when they are unscripted, like when Archimedes discovered how to measure his own body volume by sitting in the bath and measuring the overflow. We know that he was so excited by his discovery that he ran naked through the streets to proclaim his discovery.
We will know that we've got schools functioning as they need to when kids are so excited about what they've discovered (not what they've been taught) that they will run naked (figuratively) through the streets. The act of discovery seem to be left out of the equation when it comes to American education.
Make, fix and create...