How did you learn to analyze problems? And does it generalize?
-
@xaade said in How did you learn to analyze problems? And does it generalize?:
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
Either way, judging by the widespread lack of the ability, they appear to have been wrong.
I highly suspect that education has been unintentionally geared towards avoiding presenting the need for critical thinking, and thus it's not learned.
Even back in my day (
), when they were supposedly teaching it, word problems were widely hated. I liked them, because it seemed pretty obvious to me what needed to be solved for, and the actual calculations were generally fairly easy. Other people disliked them, because they couldn't figure out what to solve for. Even when critical thinking was taught, it doesn't seem to have been learned very well. (And this is just in the area of Math. Critical thinking, or the lack thereof, in social and political arenas is the foundation of most of the 
.)
-
@HardwareGeek Word problems suck, and I say that as someone who enjoys a challenge. The thing about word problems these days is that it's mostly just the equation but with 'x' substituted for 'apples' or whatever. I welcome a complex problem that you have to use several different concepts to solve without any direct clue where to start, but to give me a problem where I can start setting up the equation after skimming for the same sentence structure as the last six is just wasting both my time and the teacher's.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
That was the same idiot who decided that lighting a butane lighter under his (down) jacket during the winter was a good way to keep warm.
If he had done it even more "properly" he would have stayed warm for the rest of his life.
He must have been the luckiest guy around to survive all that...
-
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@xaade said in How did you learn to analyze problems? And does it generalize?:
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
Either way, judging by the widespread lack of the ability, they appear to have been wrong.
I highly suspect that education has been unintentionally geared towards avoiding presenting the need for critical thinking, and thus it's not learned.
Even back in my day (
), when they were supposedly teaching it, word problems were widely hated. I liked them, because it seemed pretty obvious to me what needed to be solved for, and the actual calculations were generally fairly easy. Other people disliked them, because they couldn't figure out what to solve for. Even when critical thinking was taught, it doesn't seem to have been learned very well. (And this is just in the area of Math. Critical thinking, or the lack thereof, in social and political arenas is the foundation of most of the .)Word problems are a good example of a lot of the issues with this topic.
Word problems are most often hated because people can't read well. I'm firmly convinced that it's the reading, not the actual algorithms, that give people issues. Because they can't parse for meaning.
Word problems are also usually very narrow--I'm testing you on solving this particular type of force problem. So they're not really high-level analysis--once you see what's being asked for the procedure is obvious. But you have to do that style to be able to do the more involved ones.
Word problems are also presented as it's obvious, without actually intentionally teaching how to solve these word problems. Not all word problems need the same methods, although they generalize pretty well. For example, numerical sciences and math can follow a "look for numbers with units, assign them to variables. Look for question words, assign that as an unknown" flow, but history and even biology can't use that pattern. So word problems are more like practice for small parts of analytic thinking, rather than a full teaching tool.
My current thoughts are as follows.
There are several "levels" of thinking.
- concrete facts and skills. These are the vocabulary and concrete pieces you have to do (knowing what variables are what concept). Thinking at this level is about memorizing facts and assimilating skills (practical or theoretical).
- Concrete algorithms and relationships. These take facts and skills and apply them to concrete problems. You might need multiple facts and skills here, and there's the concept of sequencing of tasks, but it's a relatively straight-forward flow. If written as a flowchart, you at most need simple loops and conditionals built on the skills as the base units. Learning these is about direct practice. This is the level most high school word problems get to.
- Abstract algorithms and meta-algorithms. Here, you have algorithms whose outputs are algorithms (often chained together). Use these algorithms, combine the output and apply that algorithm. This is true analytic and synthetic thinking. Here you have to have mastered the algorithms to be successful and are doing lots of multi-step transformations. Still doing toy problems, but they're well beyond most high-school courses.
- Pathfinding thinking. Here you're the one creating the meta-algorithms for others to use. Here you need lots of intuition and judgement built from lots of experience to decide when to prune a branch of investigation and to know what's been done before. This is really really hard.
One last thought--how do you know you're "thinking outside the box" if you're not sure what the box even is? It's like writing--they say "you have to know the rules before you can successfully break them." Unless you understand the "current" methods and patterns you can't really go beyond just by stabbing in the dark.
If you all can't tell...I'm much more a traditionalist than lots of my colleagues. I think that content matters a whole lot, to the point that they can't really do the higher-order thinking (step 3) without having lots of mastered content and basic skills (steps 1 & 2 above). And so many kids have so weak foundations in basic skills (both lived and learned). Most don't/can't cook, have never really tinkered with things, have no real-world concept of what life is really like. Which is sad.
-
@HardwareGeek That's too bad, linear algebra has a lot of important ideas in it.
-
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall Isn't "not so well telegraphed" the definition of a pop quiz?
It's a very slow pop.
-
@xaade said in How did you learn to analyze problems? And does it generalize?:
After thinking a bit, I think the earliest examples of being taught formally were word-math problems.
You have to break down a story into mathematical information and then determine the process used to solve the problem.
You mean the ones that go kind of like, “Anne has three apples, if she eats one how many does she have left?” That, apparently, has been the preferred way of teaching pretty much all maths in this country for the last decade or so. And then I read a newspaper article the other week that says that research has now shown this doesn’t make any difference in the end compared to teaching that 3 − 1 = 2.
(Edit: bloody Ctrl+M =
submit!)
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Based on a lot of responses here and on Facebook (where I posted the same question), I'm coming around to the idea that it can't be effectively taught as a "thing", but it can be learned mainly by experience.
One of the key aspects with tackling a larger problem, and something that a great many people fail on, is the ability to stop going down an unproductive sub-rabbit-hole and to step back and reevaluate whether the approach you're using is right. It's the key to being able to tackle almost anything truly complicated, and it is where ever so many folks just fail. If you can somehow think of a way of getting the kids in your class to remember that sometimes in life you need to try a completely different approach, you'll be giving them one of the best life skills ever, almost a mental superpower.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd never do it at school or anywhere I didn't have access to the circuit breakers.
You don't have access to breakers at school!?
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Mainly I do it because they react so beautifully.
You are a magnificent evil bastard!
Yet that's still nicer to them than the universe has any need to be…
-
@dkf said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Based on a lot of responses here and on Facebook (where I posted the same question), I'm coming around to the idea that it can't be effectively taught as a "thing", but it can be learned mainly by experience.
One of the key aspects with tackling a larger problem, and something that a great many people fail on, is the ability to stop going down an unproductive sub-rabbit-hole and to step back and reevaluate whether the approach you're using is right. It's the key to being able to tackle almost anything truly complicated, and it is where ever so many folks just fail. If you can somehow think of a way of getting the kids in your class to remember that sometimes in life you need to try a completely different approach, you'll be giving them one of the best life skills ever, almost a mental superpower.
Appeal to laziness. "This is too much effort, there HAS to be a better way." is usually a good sign you need to rethink. :)
Also, "This seems like a common enough task, someone else must have a workable solution already" is also solving the problem, taking the lazy route. You can even spend some extra energy on trying to improve the found solution.
-
@Carnage said in How did you learn to analyze problems? And does it generalize?:
Appeal to laziness. "This is too much effort, there HAS to be a better way." is usually a good sign you need to rethink. :)
Yes. Lots of people won't. I don't know if it is inflexibility or stupidity, but it dooms them to struggling with the first idea they think of.
-
@dkf said in How did you learn to analyze problems? And does it generalize?:
@Carnage said in How did you learn to analyze problems? And does it generalize?:
Appeal to laziness. "This is too much effort, there HAS to be a better way." is usually a good sign you need to rethink. :)
Yes. Lots of people won't. I don't know if it is inflexibility or stupidity, but it dooms them to struggling with the first idea they think of.
Like an old colleague used to say: "Weeks of hard work can save you HOURS of planning!".
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Word problems are most often hated because people can't read well. I'm firmly convinced that it's the reading, not the actual algorithms, that give people issues. Because they can't parse for meaning.
Word problems are also usually very narrow--I'm testing you on solving this particular type of force problem. So they're not really high-level analysis--once you see what's being asked for the procedure is obvious. But you have to do that style to be able to do the more involved ones.
I'd say another area where I applied this was less math related. It was talking about business case studies in college classes where the "answers" weren't nearly so well defined. I suppose a lot of literature classes were like this, too, TBH.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
There are several "levels" of thinking.
Hmm....now this reminds me of a book I recently re-read:
Highly recommended, but it's pretty dense. I'm pretty sure this was actually the first time I read it all the way through. This is more about your step 4.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Word problems are most often hated because people can't read well. I'm firmly convinced that it's the reading, not the actual algorithms, that give people issues. Because they can't parse for meaning.
If you all can't tell...I'm much more a traditionalist than lots of my colleagues. I think that content matters a whole lot, to the point that they can't really do the higher-order thinking (step 3) without having lots of mastered content and basic skills (steps 1 & 2 above). And so many kids have so weak foundations in basic skills (both lived and learned). Most don't/can't cook, have never really tinkered with things, have no real-world concept of what life is really like. Which is sad.
One class I remember when trying (and failing) to get a teaching credential was specifically for teaching reading, the idea being that every teacher, even subject-matter high school teachers, should be teaching reading and watching for problems. I don't know how widespread this is at other credential programs (this was at San Diego State University), but there are programs that focus on basics at all levels. The title for the textbook for that class was "But I'm Not A Reading Teacher!"
As for how I learned problem solving, I don't remember being taught as such. Most of what I've figured out about problem solving came from tutoring and teaching others. It was while helping students who didn't just "get it" like I did that I came up with explicit strategies for solving almost all physics problems.
- Draw a picture of the situation.
- Lay down a coordinate system.
- Identify the known and sought after quantities.
- Use equations to connect the known quantities to the unknown quantities.
- Math.
- Check that the answer make sense.
More abstractly, this could be rendered as
- Sketch an abstract overview of the problem (outline, flowchart, actual sketch, etc.)
- Identify relevant concrete details (e.g., measurements and data) to validate the overview
- Increase the amount of detail in the problem/solution specification as needed
- Use relevant subject-area knowledge to plan the work to be done.
- Work.
- Iterate the solution/work plan as more details come to light.
So, the main problem solving tool is abstraction: can one figure out the important data that guides a high-level, non-detailed plan that can be refined with less important details? Make sure you know where home is before thinking about street lights along the way. Students get lost when one bit of information seems just as important as any other. Like you said, reading for meaning is crucial. Unfortunately, the way to learn how to recognize important data is to see a lot of it through drills. I imagine that every subject has its own unique way of determining what's important.
-
@pie_flavor said in How did you learn to analyze problems? And does it generalize?:
@HardwareGeek Word problems suck, and I say that as someone who enjoys a challenge. The thing about word problems these days is that it's mostly just the equation but with 'x' substituted for 'apples' or whatever. I welcome a complex problem that you have to use several different concepts to solve without any direct clue where to start, but to give me a problem where I can start setting up the equation after skimming for the same sentence structure as the last six is just wasting both my time and the teacher's.
I'm not saying it's a very complex problem.
I'm saying it's probably the first introduce to breaking down problems that I was formally taught with.
-
@MZH said in How did you learn to analyze problems? And does it generalize?:
It was while helping students who didn't just "get it" like I did
I struggled with this when tutoring in college. I didn't know how to explain something that was so obvious to me.
-
@Gąska said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd never do it at school or anywhere I didn't have access to the circuit breakers.
You don't have access to breakers at school!?
Not without asking permission. All my equipment has individual fuses.
-
@MZH said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Word problems are most often hated because people can't read well. I'm firmly convinced that it's the reading, not the actual algorithms, that give people issues. Because they can't parse for meaning.
If you all can't tell...I'm much more a traditionalist than lots of my colleagues. I think that content matters a whole lot, to the point that they can't really do the higher-order thinking (step 3) without having lots of mastered content and basic skills (steps 1 & 2 above). And so many kids have so weak foundations in basic skills (both lived and learned). Most don't/can't cook, have never really tinkered with things, have no real-world concept of what life is really like. Which is sad.
One class I remember when trying (and failing) to get a teaching credential was specifically for teaching reading, the idea being that every teacher, even subject-matter high school teachers, should be teaching reading and watching for problems. I don't know how widespread this is at other credential programs (this was at San Diego State University), but there are programs that focus on basics at all levels. The title for the textbook for that class was "But I'm Not A Reading Teacher!"
As for how I learned problem solving, I don't remember being taught as such. Most of what I've figured out about problem solving came from tutoring and teaching others. It was while helping students who didn't just "get it" like I did that I came up with explicit strategies for solving almost all physics problems.
- Draw a picture of the situation.
- Lay down a coordinate system.
- Identify the known and sought after quantities.
- Use equations to connect the known quantities to the unknown quantities.
- Math.
- Check that the answer make sense.
More abstractly, this could be rendered as
- Sketch an abstract overview of the problem (outline, flowchart, actual sketch, etc.)
- Identify relevant concrete details (e.g., measurements and data) to validate the overview
- Increase the amount of detail in the problem/solution specification as needed
- Use relevant subject-area knowledge to plan the work to be done.
- Work.
- Iterate the solution/work plan as more details come to light.
So, the main problem solving tool is abstraction: can one figure out the important data that guides a high-level, non-detailed plan that can be refined with less important details? Make sure you know where home is before thinking about street lights along the way. Students get lost when one bit of information seems just as important as any other. Like you said, reading for meaning is crucial. Unfortunately, the way to learn how to recognize important data is to see a lot of it through drills. I imagine that every subject has its own unique way of determining what's important.
This is a great point. Sadly, abstraction is something people (and teenagers even more-so) struggle with. I found that if I broke algorithms (my level 2 thinking) down into a flow-chart, they remembered it and were able to use it much better. But they'd never be able to do so themselves.
And it's totally a case of "easier said than done". Because each of those steps (in the abstract view) hides whole worlds of complexity and often requires you to circle back and realize that your first concept was totally inadequate or just plain wrong.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@Gąska said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd never do it at school or anywhere I didn't have access to the circuit breakers.
You don't have access to breakers at school!?
Not without asking permission.
Really? What about fire safety laws!? You don't have those either?
-
@Gąska said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@Gąska said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd never do it at school or anywhere I didn't have access to the circuit breakers.
You don't have access to breakers at school!?
Not without asking permission.
Really? What about fire safety laws!? You don't have those either?
My key may open the door to the electrical cabinet. Haven't tested it yet.
All my outlets (in the chem lab) are GCFI-protected. The circuit breakers are down the hall quite a ways. And we have rated fire extinguishers and overhead sprinklers. Having access to the circuit breakers wouldn't do much extra if something goes catastrophically wrong.
We really don't do anything significantly dangerous (electrically, anyway) here at a high school. I'd wager that the art teacher with a kiln is a much bigger danger that way.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd wager that the art teacher with a kiln is a much bigger danger that way.
More a fire hazard than an electrical hazard — as in the heat from the kiln igniting something, not an electrical fire.
-
@Benjamin-Hall ...I might've misunderstood what "circuit breaker" means, and thought you have no way of cutting off power in case of emergency at all.
Yes, I agree that electricity is the least of your worries in nearly any situation. But still, it just sounded weird.
-
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I'd wager that the art teacher with a kiln is a much bigger danger that way.
More a fire hazard than an electrical hazard — as in the heat from the kiln igniting something, not an electrical fire.
I was only worried about the power draw. The biggest my power supplies go is like 2A @ 12 V (AC or DC), and they're fused for that. I do have a handheld tesla coil, but that's super low energy (despite really high voltage). Enough to sting and ignite paper, but only if you hold it real close and spend some time.
-
@Benjamin-Hall Well, I sometimes demonstrate the Jacob's Ladder or try to melt an iron nail when talking about transformers. Those can flip the circuit breaker pretty quick if you choose the wrong coil ratio
-
@dkf said in How did you learn to analyze problems? And does it generalize?:
One of the key aspects with tackling a larger problem, and something that a great many people fail on, is the ability to stop going down an unproductive sub-rabbit-hole and to step back and reevaluate whether the approach you're using is right.
Heh … I actually have a useful personality trait, it seems :)
-
@Gurth Hell, most people even fail at the "Does this result make sense?" part.
Well, the calculator said so, thus I'm taking it as gospel!
-
@Rhywden said in How did you learn to analyze problems? And does it generalize?:
@Gurth Hell, most people even fail at the "Does this result make sense?" part.
Well, the calculator said so, thus I'm taking it as gospel!
I once asked a question (in college) about calculating the drift speed of electrons in a current-carrying wire. The correct answer was something like 1e-4 m/s. As a red herring I included Avogadro's number (6.02e23).
I got answers ranging from
1e-40 m/sto1e+20 m/s. Yes, one trillion times the speed of light.
-
@Benjamin-Hall Yeah. I got similar results from students of medicine while I was still at university and I was overlooking their physics labs. One of the experiments (all moulded along actual medical problems ("problem" in the scientific sense, of course!)) tasked them with calculating the flow rate of a liquid through a rubber hose.
One group's results would have been a flow rate of 1 picoliter per time since the Big Bang.
One of the reasons why this year I spent two whole lessons on "Working with the Scientific Notation".
-
@Rhywden said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall Yeah. I got similar results from students of medicine while I was still at university and I was overlooking their physics labs. One of the experiments (all moulded along actual medical problems ("problem" in the scientific sense, of course!)) tasked them with calculating the flow rate of a liquid through a rubber hose.
One group's results would have been a flow rate of 1 picoliter per time since the Big Bang.
These also were pre-meds (undergraduates who would go into medical school). They also told me things like
1/(1/2 + 1/2) = 4when dealing with the lens/mirror equations. I think I made a comment about how if you give someone half a dose, then half another dose, you haven't given them 1/4 of a dose.They just have no number sense at all.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I was only worried about the power draw.
A big kiln might draw as much as 100A@240V. (When my mom bought a new kiln, they had to get the house's service upgraded from 100A (total), which had been standard when it was built, to 200A. I don't think the kiln took all of the additional 100A, but I was grown and living elsewhere at the time.) The kiln is (I hope!!!) connected to a suitably rated circuit, so the current draw shouldn't be an issue (except for the utility bill
).
-
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I was only worried about the power draw.
A big kiln might draw as much as 100A@240V. (When my mom bought a new kiln, they had to get the house's service upgraded from 100A (total), which had been standard when it was built, to 200A. I don't think the kiln took all of the additional 100A, but I was grown and living elsewhere at the time.) The kiln is (I hope!!!) connected to a suitably rated circuit, so the current draw shouldn't be an issue (except for the utility bill).
I looked it up--some I saw were ~50A at 240V. So about 12 KW. That's way more than anything we use, probably near as much as one of the big HVAC units for the school.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I was only worried about the power draw.
A big kiln might draw as much as 100A@240V. (When my mom bought a new kiln, they had to get the house's service upgraded from 100A (total), which had been standard when it was built, to 200A. I don't think the kiln took all of the additional 100A, but I was grown and living elsewhere at the time.) The kiln is (I hope!!!) connected to a suitably rated circuit, so the current draw shouldn't be an issue (except for the utility bill).
I looked it up--some I saw were ~50A at 240V. So about 12 KW. That's way more than anything we use, probably near as much as one of the big HVAC units for the school.
You've got HVAC? Nice. We're glad if the ventilation system at least tries to do its job.
Though our new facility manager seems to know his job and may have fixed it - after all, he discovered all on his own why the entrance doors were so damn hard to open: Someone had misconfigured the ventilators and thus created a massive underpressure in the whole building.
-
@Rhywden said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I was only worried about the power draw.
A big kiln might draw as much as 100A@240V. (When my mom bought a new kiln, they had to get the house's service upgraded from 100A (total), which had been standard when it was built, to 200A. I don't think the kiln took all of the additional 100A, but I was grown and living elsewhere at the time.) The kiln is (I hope!!!) connected to a suitably rated circuit, so the current draw shouldn't be an issue (except for the utility bill).
I looked it up--some I saw were ~50A at 240V. So about 12 KW. That's way more than anything we use, probably near as much as one of the big HVAC units for the school.
You've got HVAC? Nice. We're glad if the ventilation system at least tries to do its job.
Though our new facility manager seems to know his job and may have fixed it - after all, he discovered all on his own why the entrance doors were so damn hard to open: Someone had misconfigured the ventilators and thus created a massive underpressure in the whole building.
Ouch. I'm in Florida. No HVAC = no school. I once came in on a break where they turned it to minimal (ie around 85 F, just low enough to pull the humidity out so the walls don't rot) and it was painfully hot and stuffy.
-
@Benjamin-Hall Yeah, we have an additional building where the old caretakers seem to have had problems understanding how the heating works - because the radiators in all the rooms were binary: Either full power or ice cold. And they also didn't have much of a clue on how or when to turn the damn thing off.
Which lead to me coming into my Physics room on a Monday morning at 7:30am to the subtropical temperatures of 90° F. We didn't get much done that day.
-
@Rhywden said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall Yeah, we have an additional building where the old caretakers seem to have had problems understanding how the heating works - because the radiators in all the rooms were binary: Either full power or ice cold. And they also didn't have much of a clue on how or when to turn the damn thing off.
Which lead to me coming into my Physics room on a Monday morning at 7:30am to the subtropical temperatures of 90° F. We didn't get much done that day.
Ugh. I remember my college buildings were like that, except reversed for seasons. So you'd bundle up for the cold and get to class...except it was a billion degrees in there. And during the summer, it'd be freezing.
-
@Benjamin-Hall That reminds me of an old lecture hall at my former university - it was the largest one on campus (for about 500 students) and called the Audimax. It sported massive glass windows to either side from the floor to the ceiling (about 10 meters in height)
And, due to its age, they were all single pane windows.
Which meant that in the winter there'd be a huge amount of cold air flowing down from those windows. Which then, due to its momentum, would flow into the middle of the auditorium from either side. So you'd get a steady draft of cold air around your ankles with a really cold zone right in the middle of the lecture hall.
-
@Rhywden Incentive to keep lectures short and to keep moving around, I guess.
Where I taught at the college level it was the opposite. Florida, so if someone left a door open it was a bajillion degrees and 100% humidity instantly.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@Rhywden Incentive to keep lectures short and to keep moving around, I guess.
Where I taught at the college level it was the opposite. Florida, so if someone left a door open it was a bajillion degrees and
100% humidityneck deep in alligators instantly.FTFY
-
@boomzilla If you enjoyed that, check out Thomas Kuhn on science.
-
@Rhywden said in How did you learn to analyze problems? And does it generalize?:
Which lead to me coming into my Physics room on a Monday morning at 7:30am to the subtropical temperatures of 90° F. We didn't get much done that day.
I believe we must be sharing heating engineers.
-
Thinking back to grade school, I also used to do these puzzles that were sortof a cross between crossword puzzles and sudoku. My memory's a little foggy on the details but I had to reason through the clues until only one answer was logically possible. It reminds me of sudoku because after you got through the obvious stuff, you had to think a few steps ahead outside of the immediate question. Anybody else remember something like that?
-
@Zenith said in How did you learn to analyze problems? And does it generalize?:
Anybody else remember something like that?
Yes, but it's not the same thing.
-
@Zenith I just know them as "Logic puzzles". Wikipedia has it under a section called "Logic grid puzzles".
-
@Zenith @kazitor I did those in school too, it was the primary classwork we had in my elementary school's REACH program, which was 3rd to 6th grade for me. I remember really enjoying those logic puzzles.
-
...
-
@sockpuppet7 I probably had slightly lower expectations than you but reality's matched mine. But getting higher analytical thinking from autism is a bit of a monkey's paw type thing.
-
@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
I think I made a comment about how if you give someone half a dose, then half another dose, you haven't given them 1/4 of a dose.
I'm really disappointed you used 1/2 as your fractions, 'cuz I can't really make a joke about cross multiplication or anything far-removed from addition....
-
@Zenith said in How did you learn to analyze problems? And does it generalize?:
Anybody else remember something like that?
Yes, and I greatly dislike them due to the shear amount of random guessing needed just to start and the revisit roundtrips involved.
Proofs and Refutations - Wikipedia
