Barry Garelick’s Out on Good Behavior: Teaching math while looking over your shoulder has just come out, and it’s a fantastic read.
It is, among other things, a fascinating insider account of the struggles and insights of a novice grade school teacher who is also a seasoned mathematician and a proponent of traditional, evidence-based math instruction. We watch Garelick in action as he teaches struggling, under-motivated students how to subtract negative numbers and factor polynomials. We eavesdrop on the often awkward feedback sessions he has with mentors and other supervisors who are sometimes taken aback by Garelick’s commitment to traditional teaching methods—and by the compelling case he makes for them.
One of my favorite sections recounts a conversation between Garelick and his mentor Diane, whom he playfully calls his “parole officer.” After Garelick describes how he walked students through a problem that asked them to produce an algebraic representation of a flat fee plus hourly payment, Diane asserts that this didn’t involve “critical thinking” on the students’ part. “True critical thinking”, she observes, “would involve them struggling to come up with a solution” on their own.
Garelick’s response is to present Diane with a different word problem: one about the distance between two vehicles traveling at different speeds. “How far apart are they 1 hour before they meet?” She gives him “the same look I see on my student’s faces when they ask ‘How do you do this?’”, and Garelick starts walking her through to the solution. Once they get close enough for her to grasp the answer, she admits that solving the problem involved critical thinking on her part.
But then she attempts to reformulate her definition: “applying an algorithm repeatedly does not involve critical thinking.”
Garelick replies that since the way he teaches math is through worked examples and the kind of scaffolding he just illustrated, “you will probably never see critical thinking in my classes.”
All the better for Garelick’s students—and for the students of the many teachers who do well to read Out on Good Behavior. Garelick’s ideas about how to teach critical thinking may be renegade in the education world, but they are fully grounded in the world of cognitive science. And, as we see in his interactions with students, highly effective to boot.