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What educator David Page said many years ago about math is true across the disciplines: When kids give the wrong answer, they're often just answering a different question. And our challenge is to figure out what that question is.
Related: A nice essay on the value of encouraging students to ask "I wonder what if...?" rather than "Did I do this correctly?": https://www.kqed.org/mindshift/40537/seeing-struggling-math-learners-as-sense-makers-not-mistake-makers. (Again, this essay focuses on math, but the shift in question is just as valuable in other fields.)
@alfiekohn definitely see variations of this with beginners learning to program where you see them be confused about what the rules for evaluation or whatever are, but they are applying the incorrect rules consistently.
@alfiekohn In my experience a lot of these ideas work well in higher education, too!
@alfiekohn When a student gives a "wrong" answer in class - for any topic - I try to see what question they are actually asking. Half the time, I have phrased the question ambiguously, and the other half, it is a legitimate confusion of similar ideas. I think (hope) it helps them to venture answers even when unsure.
@alfiekohn The switch from punishing to nurturing doesn't seem to come naturally to modern teachers.
@alfiekohn Nice to see this spelled out:
"Many math teachers will say a community of learners like Wees describes is a fairytale classroom with no time constraints and no standards to cover. They say their jobs depend on covering all the topics on the test and helping students correct their errors, not taking days to uncover the thinking behind that error. Wees acknowledges the limitations that many math teachers struggle with, but points out the way most people teach math now doesn’t work, so it could be considered a waste of time anyway."
@albertcardona @alfiekohn
Indeed, skill learning has same try->observe->try-again-correcting loop in walking and math. And in walk learning we have more humility and encourage a small person. Not with math. Class already has some dynamic, etc.
@albertcardona @alfiekohn Yes. The point of standardization is to eliminate thinking. This is news?
@alfiekohn
There was a story about young grad student Stephen Hawking. He was once late to his class. When he arrived, class was empty, and a blackboard had 4 problems on it. Stephen worked on them. Some solutions, some just started, one was unclear.
It turned out that lecture was a show of "open problems" kind of relaxed lecture.
Don't quote me, but one or two he actually pushed to solution, and they generally were forming his futire carrier.
@alfiekohn
Quoting quote in the article:
By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.