I've just come across this post by Gary Rubenstein: You-reeka-math.
Here's a question.
For 8th grade students, Rubenstein prefers a visual proof of the Pythagorean Theorem to the algebra-based proof in Eureka Math/engageny math.
I follow the engageny math proof, but I can't make head or tails of the visual proof Rubenstein argues is more appropriate.
Am I missing something?
Is the visual proof easier for the teacher to explain, but harder for me to explain to myself?
Related: I've been meaning to read Rubinstein's Reluctant Disciplinarian forever.
I remember a fabulous passage (which I don't have time to fact-check at the moment, so if I'm remembering some other book, I'll have to come back and revise): something to do with novice teachers (Rubinstein) asking the old hands how they dealt with things like spitballs and talking out of turn and the like.
The old hands' advice: "I don't put up with that."
"I don't put up with that" is a classic example of experts having no idea how they do what they do.
Filed under: cognitive unconscious.
The cognitive unconscious is a sadly neglected concept in K-12.
K-12 education: way too much thinking, way too little knowing.