If instead of generic problem solving skills we called then common problem solving ideas such as - clarify the problem, breakdown the problem, brainstorm, sleep on it we can be sure they do exist but are all pretty well known.
As you have pointed out explicitly teaching these doesn’t appear to help much and that is likely because there is not much to teach that is not covered implicitly.
If you want to take on something more serious you can frame all of mathematics as generic problem solving. The whole point it arithmetic, algebra, logic, geometry and so on can be learned without concern for a specific physical context.
So you could change the debate and say you are exactly teaching generic problem solving and it looks like it takes about 16 years to go from nothing to novice.
Nice post, Greg. Nary a day goes by when someone doesn't mention 'skills' - "We need to teach them the skills". Knowledge barely gets a look in, perhaps because it carries pejorative associations with rote memorization, traditional teaching methods, and "mere facts" ("Now, what I want is Facts... Facts alone are wanted in life!", says Gradgrind). That to me is implicit evidence that my colleagues see them as dichotomous and possibly irreconcilable. It doesn't help that the critical thinking skills are at the apex of Bloom's Taxonomy - they are of a 'higher order' - while knowledge lingers near the bottom. Take this entrenched notion and add a dose of expertise-induced blindness and is it any wonder that many educators prioritize skills over knowledge acquisition? Never the twain shall meet.
I think arithmetic is a perfect example of a generic problem solving skill. It takes quite some time to learn and then is widely applicable.
So are the examples you link to. Such as breaking a problem into smaller pieces. But in its generic form it is trivial by comparison to mathematics. Practicing breaking down particular types of problem doesn’t transfer to other types because it is not the idea of breaking things down that takes time to learn it is how to do it for a particular context.
Good one, Greg. Side point: I remember discussions with S. Engelmann about declarative and procedural knowledge (his terms were "concepts" and "operations"). As your post shows, he contended that procedural knowledge is an example of conceptual knowledge. One can.have a concept about executing a procedure.
If instead of generic problem solving skills we called then common problem solving ideas such as - clarify the problem, breakdown the problem, brainstorm, sleep on it we can be sure they do exist but are all pretty well known.
As you have pointed out explicitly teaching these doesn’t appear to help much and that is likely because there is not much to teach that is not covered implicitly.
If you want to take on something more serious you can frame all of mathematics as generic problem solving. The whole point it arithmetic, algebra, logic, geometry and so on can be learned without concern for a specific physical context.
So you could change the debate and say you are exactly teaching generic problem solving and it looks like it takes about 16 years to go from nothing to novice.
Can we on the one hand say "there's no such thing as generic problem solving skills" and on the other hand say "they are all pretty well known"?
Nice post, Greg. Nary a day goes by when someone doesn't mention 'skills' - "We need to teach them the skills". Knowledge barely gets a look in, perhaps because it carries pejorative associations with rote memorization, traditional teaching methods, and "mere facts" ("Now, what I want is Facts... Facts alone are wanted in life!", says Gradgrind). That to me is implicit evidence that my colleagues see them as dichotomous and possibly irreconcilable. It doesn't help that the critical thinking skills are at the apex of Bloom's Taxonomy - they are of a 'higher order' - while knowledge lingers near the bottom. Take this entrenched notion and add a dose of expertise-induced blindness and is it any wonder that many educators prioritize skills over knowledge acquisition? Never the twain shall meet.
Generic problem solving strategies:
https://www.betterup.com/blog/problem-solving-strategies
Generic critical thinking strategies:
https://asana.com/resources/critical-thinking-skills
https://www.criticalthinking.org/pages/critical-thinking-in-everyday-life-9-strategies/512
https://www.forbes.com/sites/bernardmarr/2022/08/05/13-easy-steps-to-improve-your-critical-thinking-skills/ (paywall)
Generic creative thinking strategies:
https://mariopeshev.com/creative-thinking-skills-strategies/
De Bono's thinking skills course: https://www.youtube.com/playlist?list=PL_N6UbeInhwfj0RTWhlfAmGQzVk6XeWVc
De Bono... let's source some coloured hats!
I think arithmetic is a perfect example of a generic problem solving skill. It takes quite some time to learn and then is widely applicable.
So are the examples you link to. Such as breaking a problem into smaller pieces. But in its generic form it is trivial by comparison to mathematics. Practicing breaking down particular types of problem doesn’t transfer to other types because it is not the idea of breaking things down that takes time to learn it is how to do it for a particular context.
This was in reply to Ben’s earlier reply.
Can you please share your success criteria again please? I thought I bookmarked it but I can't find it and wanted to borrow.
I don't think I use success criteria so I'm not quite sure what you mean. Sorry. Can you add a bit of flesh to that?
You might have called it learning intentions?
Good one, Greg. Side point: I remember discussions with S. Engelmann about declarative and procedural knowledge (his terms were "concepts" and "operations"). As your post shows, he contended that procedural knowledge is an example of conceptual knowledge. One can.have a concept about executing a procedure.
Thanks, John. It's so cool you got to talk to Engelmann about this stuff.