I put this opener on the board three times today and each time the weakest student in each class figured it out first. In two classes, the weakest student was the only student to land it.

In one class it was the soft-spoken student whose father committed suicide earlier this year, who’s been in and out of class all year, whose eyes were bright like a torch after I told him, “Nice! Now hide that, hide that.”

The Oakland presentation is behind me but the value of this digital projector becomes more apparent every day. This digital projector is decreasingly an affectation and is increasingly essential to my math practice.

Here is a Vimeo clip [1:14] I edited to illustrate what is no doubt some well-known cognitive theory which I’ve been too lazy to study, but which I arrived at through two years of error and trial and error just the same.

So Happy Together #6 from Dan Meyer on Vimeo.

In summary: as you’re scaffolding a complicated task, it’s essential to highlight the small differences, the subtle ways an easy problem – one which we’ve mastered – now becomes difficult. The brain senses differences and a digital projector makes those differences more apparent than does a) a pencil and paper, b) your voice, or c) a whiteboard and dry-erase marker.