How did you learn to analyze problems? And does it generalize?
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A current push in the education world is to teach "higher-order thinking" and to not really worry about "content" (by which is meant facts and specific fact-bound algorithms and skills). The idea is that they can just google anything they need, but what they really need to be taught is how to analyze and synthesize information.
I've been struggling with this myself, and want to ask a few related questions of all of you.
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
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Math class. I was in on the tail end of "new math". So we learned naive set theory really young.
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This is not a direct answer yet, but I was toying with posting a similar question, "For those who were not CS majors, did programming help you see the world more analytically?"
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@jinpa No. In fact, I'm surprised at how un-analytical CS people are in most domains.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
How were you taught/how did you learn to break down problems into their pieces?
Asking me to remember how I was taught is asking for inaccuracy.
I have no clue how I was taught to analyse problems.
I can probably log my thought processes for a problem you give if you're that interested though...
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@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
I have no clue how I was taught to analyse problems.
This.
@jinpa said in How did you learn to analyze problems? And does it generalize?:
did programming help you see the world more analytically?
I don't know whether programming helped my see the world more analytically, or I'm good at programming because I see the world analytically, or a bit of both.
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@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
I have no clue how I was taught to analyse problems.
This.
Pretty much. Although it was essential to what I wanted to do, you don't get very far in electronics either unless you can think in a structured manner. So maybe it was simply acquired by necessity?
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
I don't think I was ever specifically taught this. Not sure how I learned either, I don't think I've had a massive shift of way of thinking at any point about this (I have changed how I think about other things).
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
I think the key method for me is identifying exactly what it is I'm trying to accomplish, what the end result should look like, and then identifying what I'm missing to accomplish it. Then recursively do the same for the missing requirements, until I reach tasks that I can complete. Then complete the tasks I can do until the initial task is done.
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
I think the method is pretty general. I often see people, even smart people, attempt to fix problems before they clearly know what the completed task would look like.
Funny anecdote: my older sister is very intelligent. She has a PhD in economics, got scholarships all along her education, best grades in her class and such. So one day she'd gotten a new cellphone, and it used a smaller SIM than her old one. Knowing that the bigger SIM can be cut down to the size of the smaller SIM, she proceeded to cut the SIM to fit. Except she didn't actually check how to cut it, she went straight for the scissors and started cutting. And ended up nicking the circuit and breaking the SIM. When facing the same issue (and not yet aware of my sister's blunder) I looked for a template from the internet that showed how to cut it, printed it, and used it to guide me in making the necessary cuts. My SIM then fit the new cellphone and worked fine.
When I learned of how she broke hers, and I asked her why did she go straight for cutting when she didn't even know how it was supposed to be cut. She was pretty embarrassed and couldn't really offer an explanation. She'd acted without thinking through the whole task. Of course we all (my siblings and I) mercilessly teased her for it, although the rest asked me to adjust their SIMs just to be safe.
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@Kian said in How did you learn to analyze problems? And does it generalize?:
I often see people, even smart people, attempt to fix problems before they clearly know what the completed task would look like.
Toby Faire, sometimes we have to fix problems before the manglement who are demanding the fix know what the solution should look like, either.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
A current push in the education world is to teach "higher-order thinking" and to not really worry about "content" (by which is meant facts and specific fact-bound algorithms and skills). The idea is that they can just google anything they need, but what they really need to be taught is how to analyze and synthesize information.
I've been struggling with this myself, and want to ask a few related questions of all of you.
Okay.
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
I pretty much taught myself. I was one of those annoying kids that took apart everything to see how it worked, and then put it back together again. I've bought toys not to play with, but because I was curious of their inner workings.
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
Eh? I look at the problem at hand, try to identify the important bits, and the broken bits and then I try to fix the problem in a way that causes as few new problems as possible. Depending on what manner of problem I am trying to fix, the way to find important and broken bits vary, but it's mostly just up to learning about that particular field to also learn the ways to identify problems and broken bits.
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
Well, yeah. The above is rather general I'd say.
Apart from needing to know enough about what you're looking at to fix it. (Unless the plan is to keep fixing it a few times, which may be a great way to learn.)
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@Carnage said in How did you learn to analyze problems? And does it generalize?:
I was one of those annoying kids that took apart everything to see how it worked, and then put it back together again.
I don't remember how old I was — maybe 10, or so — but I remember taking apart a stopwatch (mechanical — springs, gears, lots of tiny screws) and putting it back together. It worked after I put it back together, too (until I wound it too tight and snapped the shaft that wound the mainspring, but that was user error, not take-it-apart-and-put-it-back-together error).
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@HardwareGeek 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?:
I was one of those annoying kids that took apart everything to see how it worked, and then put it back together again.
I don't remember how old I was — maybe 10, or so — but I remember taking apart a stopwatch (mechanical — springs, gears, lots of tiny screws) and putting it back together. It worked after I put it back together, too (until I wound it too tight and snapped the shaft that wound the mainspring, but that was user error, not take-it-apart-and-put-it-back-together error).On of my mildly amusing anecdotes on the topic was when at the age of 7, I fixed a broken phone.
My mom complained about how the phone had broken, and then placed it on the kitchen table. I can't remember what I was doing at the time, but a broken phone! That meant I would not get yelled at for taking it apart! So, as soon as every adult went on with their adulting business in other rooms I took it apart, found the problem and fixed it. (it was something trivial, but I don't remember what), put it all together again and plugged it in to see if it was working. When satisfied, I left.
A little while later my mother almost shat herself when it rang while she was adulting in the kitchen. There wasn't supposed to be a phone in there, and the one that was there was broken and not even connected. Except that it was both working and connected.And I did get a mild scolding, for leaving it connected and not telling anyone I'd fixed it. You just can't win!
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@Benjamin-Hall There was a special class for the genius kids at my first middle school that was designed to teach higher-order thinking to people young enough to change their ways of thinking. I think it was called ACE or something. Shame I had to switch schools after a year.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
On my own. My classmates at every level of education either also learned on their own, or they haven't learned it at all.
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
As a programmer working on high-level applications - how I usually approach implementation tasks is to restate any problem at hand into the form of what inputs should give what outputs. I'd mostly qualify it as "higher-order thinking", but in a semi-structured way and the output of the process is always a specific fact-bound algorithm (of implementing the feature). And that requires decent expertise in applying specific fact-bound algorithms of all kinds to all kinds of problems.
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
Dunno about other engineering disciplines (and non-engineering ones), but I'd guess it'd be much less useful there than in programming. Although if you're asking about tips for teaching students, I think this sort of thing would work for your typical STEM exercise of "here's a set of facts, find x." But to do that effectively, you need a lot of exercises - the "content", as you called it.
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How were you taught/how did you learn to break down problems into their pieces?
I don't remember there being anything specific before university (and my story is much the same as others here -- fortunately my parents allowed me to dissassmble a ton of stuff early on. Within reason. For example, I wasn't allowed to mess with the TV's innards.).
I think in university, being able to attack and solve problems was a bit more of a thing. It started out easy (and early, like, a few weeks in): we were given a very specific task ("find a relation that describes the speed of water outflow from the following vessels") with very specific tools. We were then required to identify what the relevant variables were, how to measure those and finally how to put that together into a single workable model. The tasks became more and more hands-off over time (i.e., "here's a task, you have N days and access to this generic lab. Try to not burn down the building, please."(*))
(*) They never said anything about not flooding it, though.
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?Physics is rather reductionist, so that was the general theme to begin with: break down the problem into smaller pieces, until you can solve it. How to break down a problem into smaller parts...? I guess that would be where either experience or domain-specific knowledge comes in.
I think teaching the skill to identify the "core problem(s)" is something that generalizes (and a lot of people lack). I often get surprised by students who don't really seem to understand what they are trying to do or what they are supposed to do...
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
A current push in the education world is to teach "higher-order thinking" and to not really worry about "content" (by which is meant facts and specific fact-bound algorithms and skills). The idea is that they can just google anything they need, but what they really need to be taught is how to analyze and synthesize information.
I disagree and think both skills are important. If you don’t know basic facts and things about a subject, you very likely won’t be able to effectively figure out how to start looking for the information you currently need but don’t have, or to separate the wheat from the chaff with the information you do find.
How were you taught/how did you learn to break down problems into their pieces?
I couldn’t really tell you. I don’t think anybody ever really taught me this sort of thing, so I must have picked it up as I went along. Unfortunately, this explains the vast majority of my skills and knowledge so it’s not very helpful.
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
See above. It boils down to looking at something and just seeing the snags (not necessarily immediately, of course), or if it’s something someone else has done/made/designed, wondering why they didn’t do this or that differently. I couldn’t tell you how I do that, it just appears in my mind — and I sometimes wonder how it is that not everybody seems to have this.
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@Carnage said in How did you learn to analyze problems? And does it generalize?:
I pretty much taught myself. I was one of those annoying kids that took apart everything to see how it worked, and then put it back together again. I've bought toys not to play with, but because I was curious of their inner workings.
child after my own heart!
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@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
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@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
I've once took down electricity in our entire block of flats by plugging in broken Christmas lights. Not sure what I've learned from that, but it was scary and also kinda awesome.
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A lot of it can be learned. Some people are just naturals but this book helped me quite a bit when I was just out of college. It's fairly generic too. You're not going to find tips like using buffers for log messages when dealing with load bearing print statements in threaded code. It's more about breaking down and isolating the problem.
*edit I'm tempted to start a thread about books that helped people on this forum. Kind of a leg up for those of us tackling new issues.
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@Captain Was that before or after CS programs started lowering the bar to attract more/different people? I've worked with some people that I can't figure out how they graduated or kept from being outed as a fraud on the job. Like their answer to everything was "I don't know (and won't find out)" or "no, that's too hard."
I don't recall exactly how I was taught to solve problems. Programs were usually easy to work backwards up to Main() via cause and effect. It was 10 years into my career before I ever used a debugger. That still feels weird, having to watch a process over and over and over to figure out what's happening.
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@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
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I'd say it started by doing "word problems" in elementary school math. Doing simple proofs in high school geometry was the next step, and then probably my abstract math classes in college. Having tried to help people with stuff like that I'm not sure I know of a way to teach that sort of thing to people.
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@boomzilla 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. Formal logic/abstract math seems as close to a "analytic thinking" class as it gets...and my kids are no where near ready for such a class. Nor am I qualified to teach such a class.
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@Benjamin-Hall in my more charitable moments I believe that people aren't willing to put in the effort. Right now I'm not feeling charitable at all and I believe that most people simply aren't capable of it (see my WTF bites from this morning).
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@Benjamin-Hall Get a book on logic puzzles or geometry puzzles or "recreational math" for kids.
You're looking for stuff with solutions in the back (and logical ones at that), not "joke" puzzles, if that makes sense.
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@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
Keep in mind this was after the paperclip-in-the-socket incident. That one actually blew the breaker... After a while.
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@Tsaukpaetra 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?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
Keep in mind this was after the paperclip-in-the-socket incident. That one actually blew the breaker... After a while.
My best was taking an old lamp cord (the ones with 2 distinct conductors independently insulated), stripping it back to expose the conductors, wrapping them around iron nails, plugging it in, and carefully touching the nails together.
Sparks across the room, spot-welded nails, and a blown breaker. It was amazing.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
My best was taking an old lamp cord (the ones with 2 distinct conductors independently insulated), stripping it back to expose the conductors, wrapping them around iron nails, plugging it in, and carefully touching the nails together.
When I was in secondary school, there was a tale of the time someone I knew (sort of — I knew his name and general personality, but never really interacted with him much) inserted two Parker pen fillings into the 220 volt electrical socket underneath his desk and then dropped a third onto them.
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@Gurth 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?:
My best was taking an old lamp cord (the ones with 2 distinct conductors independently insulated), stripping it back to expose the conductors, wrapping them around iron nails, plugging it in, and carefully touching the nails together.
When I was in secondary school, there was a tale of the time someone I knew (sort of — I knew his name and general personality, but never really interacted with him much) inserted two Parker pen fillings into the 220 volt electrical socket underneath his desk and then dropped a third onto them.
Fun times.
I'd never do it at school or anywhere I didn't have access to the circuit breakers. Then again, now that I'm an adult and actually paying a mortgage...I wouldn't do it even at home (or anywhere else).
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@HardwareGeek said in How did you learn to analyze problems? And does it generalize?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
I still have burn scars from those damn HV rectifiers!
I blame being thrown across the repair room multiple times for some of my oddities.
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@M_Adams 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?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
I still have burn scars from those damn HV rectifiers!
I blame being thrown across the repair room multiple times for some of my oddities.If we're talking about taking electrical damage...
I once was cleaning up a college physics teaching lab (I worked in the back room). They were using spark timers. Ancient ones from well before I was born. The power supplies (used to kick the voltage up to 30kV or so) were old as well. Because of their age they were kept running while the lab was set up (since every power cycle ran the risk of them not coming back up).
So I was turning things off, and when I put my fingers on the switch of one of them, it bit me. No clue how much voltage or current, but it hurt. I could feel the charge go up my arm, down my side, and out my leg. It left things tingly and painful for most of a week, with the muscles feeling like they were exhausted/sore.
I also had a "friend" (kid from the neighborhood) who was playing around in a disused (but still live) train yard. He decided to mess with one of the big track switches (a big knife-style one). The insulation on the handle was gone, and so when he grabbed it, the current grounded through his body. Good thing it was AC--it blew him back a few feet and stunned him instead of frying him. 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.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@M_Adams 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?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
I still have burn scars from those damn HV rectifiers!
I blame being thrown across the repair room multiple times for some of my oddities.If we're talking about taking electrical damage...
I once was cleaning up a college physics teaching lab (I worked in the back room). They were using spark timers. Ancient ones from well before I was born. The power supplies (used to kick the voltage up to 30kV or so) were old as well. Because of their age they were kept running while the lab was set up (since every power cycle ran the risk of them not coming back up).
So I was turning things off, and when I put my fingers on the switch of one of them, it bit me. No clue how much voltage or current, but it hurt. I could feel the charge go up my arm, down my side, and out my leg. It left things tingly and painful for most of a week, with the muscles feeling like they were exhausted/sore.
I also had a "friend" (kid from the neighborhood) who was playing around in a disused (but still live) train yard. He decided to mess with one of the big track switches (a big knife-style one). The insulation on the handle was gone, and so when he grabbed it, the current grounded through his body. Good thing it was AC--it blew him back a few feet and stunned him instead of frying him. 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.
On a related note... the good times of convincing my brother that “the fence is off, really”, over and over and over…
😈
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@M_Adams 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?:
@M_Adams 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?:
@Tsaukpaetra said in How did you learn to analyze problems? And does it generalize?:
@cvi said in How did you learn to analyze problems? And does it generalize?:
For example, I wasn't allowed to mess with the TV's innards
I learned that it is a Bad Idea taking them apart while actively operating.
A few people were scared shitless, and how you forum denizens can share a bit of that feeling.
Not only that. There are some big capacitors in there that store high voltages even after they're turned off. I have an EE degree, and I won't mess with (old CRT) TVs.
I still have burn scars from those damn HV rectifiers!
I blame being thrown across the repair room multiple times for some of my oddities.If we're talking about taking electrical damage...
I once was cleaning up a college physics teaching lab (I worked in the back room). They were using spark timers. Ancient ones from well before I was born. The power supplies (used to kick the voltage up to 30kV or so) were old as well. Because of their age they were kept running while the lab was set up (since every power cycle ran the risk of them not coming back up).
So I was turning things off, and when I put my fingers on the switch of one of them, it bit me. No clue how much voltage or current, but it hurt. I could feel the charge go up my arm, down my side, and out my leg. It left things tingly and painful for most of a week, with the muscles feeling like they were exhausted/sore.
I also had a "friend" (kid from the neighborhood) who was playing around in a disused (but still live) train yard. He decided to mess with one of the big track switches (a big knife-style one). The insulation on the handle was gone, and so when he grabbed it, the current grounded through his body. Good thing it was AC--it blew him back a few feet and stunned him instead of frying him. 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.
On a related note... the good times of convincing my brother that “the fence is off, really”, over and over and over…
😈One of the best parts of my job is that teenagers are super gullible. They'll fall for the same trick over and over. Even the "Did you know they're taking gullible out of the dictionary?" one. Or the "So, ready for your test today?" trick. That's one of my favorites.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
Or the "So, ready for your test today?" trick. That's one of my favorites.
Instant bonus points if they pee themselves a little.
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@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?:
Or the "So, ready for your test today?" trick. That's one of my favorites.
Instant bonus points if they pee themselves a little.
I usually just get the wide eyes and the uncontrollable shaking. I've had some hyperventilation and near breakdowns. I've had them walk in and stop in mid stride before. Tons of fun.
They usually learn about half-way through the semester, but it encourages them to pay attention to the calendar instead of just winging it. Or so I tell myself. Mainly I do it because they react so beautifully.
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@Benjamin-Hall I think I'll condition my next group doing just that. At the beginning of every lesson, exactly this question.
And then, when they are accustomed to it being a ruse - BAM! instant pop quiz.
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@Rhywden said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall I think I'll condition my next group doing just that. At the beginning of every lesson, exactly this question.
And then, when they are accustomed to it being a ruse - BAM! instant pop quiz.
I do give pop quizzes. Usually well-telegraphed, but sometimes not so much.
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@Benjamin-Hall Isn't "not so well telegraphed" the definition of a pop quiz?
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@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?
Yeah, but...
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
A current push in the education world is to teach "higher-order thinking" and to not really worry about "content" (by which is meant facts and specific fact-bound algorithms and skills). The idea is that they can just google anything they need, but what they really need to be taught is how to analyze and synthesize information.
I've been struggling with this myself, and want to ask a few related questions of all of you.
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
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.
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@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 Isn't "not so well telegraphed" the definition of a pop quiz?
Yeah, but...
So, it's more of a *pffffffffffrblblblblbl* quiz?
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@Benjamin-Hall My math teacher recently gave us a test that was nearly impossible to finish on time. She didn't let on until the end that this was on purpose, to give us an idea of what to expect from ourselves on the midterm.
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@pie_flavor said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall My math teacher recently gave us a test that was nearly impossible to finish on time. She didn't let on until the end that this was on purpose, to give us an idea of what to expect from ourselves on the midterm.
Yeah, that's also what I tell my students if it turns out that I overestimated their capabilities.
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@pie_flavor said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall My math teacher recently gave us a test that was nearly impossible to finish on time. She didn't let on until the end that this was on purpose, to give us an idea of what to expect from ourselves on the midterm.
I had a Calc 2 test my freshman year in college (50 minute test):
12 questions, one of which was a full proof and another was a trick question (integral that couldn't be done due to a (hidden) divergence in the middle of the range). The remainder were multi-part questions.
The teacher came in the next day and said "That one went a bit long." The high was a 66%, and there were 2 of us above 60%.
Of course, I've had others where I walked out going "I know I got 30%, 50% would be him being merciful, and anything higher would involve direct divine intervention."
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@xaade 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?:
A current push in the education world is to teach "higher-order thinking" and to not really worry about "content" (by which is meant facts and specific fact-bound algorithms and skills). The idea is that they can just google anything they need, but what they really need to be taught is how to analyze and synthesize information.
I've been struggling with this myself, and want to ask a few related questions of all of you.
How were you taught/how did you learn to break down problems into their pieces? This might be troubleshooting, debugging, the first stages of planning new software, or anything. Not just formal "solving problems in class"
What methods of identifying the key pieces work for you in your jobs/vocations/etc?
Do they generalize? Can you use the same methods across many business or technical domains or are they fact/domain specific?
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.
I tend to agree, although I'm not sure about the causal relationship. At the least, word problems provide practice in analysis. I still don't know whether it can really be taught or is an innate ability, but based on how common word problems were when I was in primary and secondary school, teachers certainly seem to have thought it either could be learned or the innate ability was nearly universal. Either way, judging by the widespread lack of the ability, they appear to have been wrong.
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@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.
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@Benjamin-Hall said in How did you learn to analyze problems? And does it generalize?:
@pie_flavor said in How did you learn to analyze problems? And does it generalize?:
@Benjamin-Hall My math teacher recently gave us a test that was nearly impossible to finish on time. She didn't let on until the end that this was on purpose, to give us an idea of what to expect from ourselves on the midterm.
I had a Calc 2 test my freshman year in college (50 minute test):
12 questions, one of which was a full proof and another was a trick question (integral that couldn't be done due to a (hidden) divergence in the middle of the range). The remainder were multi-part questions.
The teacher came in the next day and said "That one went a bit long." The high was a 66%, and there were 2 of us above 60%.
Of course, I've had others where I walked out going "I know I got 30%, 50% would be him being merciful, and anything higher would involve direct divine intervention."
I've posted this before, but when I took Linear Algebra in community college, I was sure I was going to fail, because I just. Didn't. Get. It. But I not only passed, but did so with a good grade due entirely to the instructor's bizarre grading scheme.
Every exam was worth 100 points, and every question worth 10. But few if any tests had 10 questions.
So how did 10 points * less than 10 questions total 100? Basically, you started with 100 and lost 10 for each question you got wrong. I remember one test that had two questions. I got one of them completely wrong, I didn't even have the concept right to get any partial credit. In other words, I got only 50% of the test correct. I scored 90%. I'm not sure if I'd have gotten 80% for a blank piece of paper, but I think I would have for a paper that looked like I tried to solve both problems, even if I was totally faking it.
During the final, as I was struggling, in despair, hoping that I could somehow manage to do well enough to eke out a passing grade, he interrupted us to announce, "I've totalled up your grades so far. Nobody's getting less than a B, and there aren't many of those." I wound up with an A.
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So, how could you fail the class?
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@xaade Probably by not even trying. But I felt like I was failing, because I knew I didn't understand the material, and in my mind getting 1/2 or 1/3 of questions wrong felt like (and should have been) a failing score.
https://www.amazon.co.uk/Debugging-Indispensable-Software-Hardware-Problems/dp/0814474578
