Sure. If you do enough basic math, you start to see things like how 2/8 can be simplified to 1/4 or you recognize that 10 is not a perfect square root or how you could reorder some operations to make things easier (sorry, examples from my kids). Little things like that where you don’t even think about it… it becomes second nature to you and that makes you a lot faster because you are not worrying about those basic ideas or mechanics. Instead, you can think about more complicated things such as which formulas to apply or the process to compute something.
As another example, since I teach computer science, a lot of novice students struggle with basic programming language syntax… How exactly do you declare a variable? What order do things go? How does a for loop work? Do you need a semicolon or parentheses, etc. If you do enough programming, however, these things become second nature and you stop thinking about it. You just seemily, intuitively, know these things and do them naturally without thinking, even though when you first started, it was really complicated and daunting and you probably spent a lot of time constructing a single line of code.
Once you develop a foundation however, you don’t need to worry about these low-level things. Instead you worry about high-level issues such as how to organize larger pieces of code into functions or how to I utilize different paradigums, etc.
This is why a basketball player, for instance, will shoot thousands of shots in practice or why a piano player will play a piece over and over for many hours. It’s so they don’t have to think about the low-level mechanics. It becomes muscle memory and it’s just natural to them.
Okay I understand what you are saying now, but I believe that you are conflating two ideas here.
The first idea is about learning the concepts, and not just the specifics. There’s a difference between memorizing a specific chemical reaction and understanding types of chemical reactions and using that to deduce what a specific chemical reaction would be given two substances. I would not call that intuition, however, as it’s a matter of learning larger patterns, rules, or processes.
The second idea is about making things happen faster and less consciously. In essence, this is pattern recognition, but in practice it’s a bit more complicated. Playing a piece over and over or shooting a basketball over and over is a rather unique process in that it involves muscle memory (or more accurately it involves specific areas of the brain devoted to motor cortex activation patterns working in sync with sensory systems such as proprioception). Knowing how to declare a variable or the order of operations, on the other hand, is pattern recognition within the context of a specific language or programming languages in general (as a reflection of currently circulating/used programming languages). I would consider both of these (muscle memory and pattern recognition) as aligned with the idea of intuition as you’ve defined it.
Rote learning is not necessary to understand concepts, but the amount of repetition needed to remember an idea after x period of time is going vary from person to person and how long after you expect someone to remember something. Pattern recognition and muscle memory, however, typically require a higher amount of repetition to sink in, but will also vary depending on person and time between learning and recall.
I get where you’re coming from on most points and agree overall. However, you’re not taking into consideration what secondary schooling looks like before students arrive.
I was told by multiple English teachers (including the head of the department) that I was a math student and should never attempt to write because I saw through the regurgitation assignments, didn’t agree with teacher assessments of what Dickens “was trying to do” and had zero interest in confirming their biases.
I also didn’t pursue page design and getting onto my high school paper because the only F I got there was from the advisor who was exceptionally clear that I was not welcome to attempt committing journalism after mocking up yearbook pages and being very unhappy with the results in Aldus PageMaker; there was no support system in place. (Also, our yearbook was shit on every level.)
That said, I can still write a ternary line of code where it makes sense sted an if-else block.
College coursework on the whole is a waste of time reinventing wheels. I don’t need to spend a couple of weeks working up to “Hello, world!” in C and as such left CS as a major my first quarter at uni.
For the most part, I’ve been very lucky with teachers and professors. When I started taking college classes in high school and escaped the absurdity of recitation being “thinking for myself,” I learned to love writing because my prof, a Catholic deacon, wanted thesis defense, not what he’d said in lecture. If I was 180 off of his viewpoint but could cite sources, that was an A.
But teachers do this shit every day, year after year, and we blindly say they’re doing important work even as they discourage people from finding their path and voice, because god forbid a 16-year-old challenges someone in their 50s.
Right, what I was trying to say is that 10 itself is not a perfect square. You cannot take the square root of 10 and get an integer (ie. 1, 4, 9, 16, 25, etc.).
I was told by multiple English teachers (including the head of the department) that I was a math student and should never attempt to write because I saw through the regurgitation assignments, didn’t agree with teacher assessments of what Dickens “was trying to do” and had zero interest in confirming their biases.
I think that is unfortunate and probably inappropriate. I try to avoid classifying students as particular types and generally try to encourage them whenever possible to pursue whatever their interests are (even if I disagree or don’t have the same interest myself).
College coursework on the whole is a waste of time reinventing wheels. I don’t need to spend a couple of weeks working up to “Hello, world!” in C and as such left CS as a major my first quarter at uni.
There is a reason for reinventing wheels; it is to understand why they are round and why they are so effective. To build the future, it helps to understand the past.
That said, perhaps the course was too slow for you, which is understandable… I frequently hear that about various classes (including ones I’ve taught).
But teachers do this shit every day, year after year, and we blindly say they’re doing important work even as they discourage people from finding their path and voice, because god forbid a 16-year-old challenges someone in their 50s.
Again, I think you’ve had an unfortunate experience and I think it’s a good thing to challenge your teachers. I certainly did when I was a student and I appreciate it now when students do that with me. I recognize that I am not perfect nor do I know everything. I make mistakes and can be wrong.
I wish you had a more supportive environment in secondary school and I have a better understanding of your perspective. Thanks for the dialogue.
If you had a supportive set of teachers, telling you that you can do anything, where’s the challenge? I went back to my high school and dutifully waited for the department chair with a rehearsed, belittling speech. When Columbia says you’re the best editorial writer in the country at the college level from literally the first one I wrote, teachers tend to not only back the fuck off but also to do this weird thing where they revise history and talk about the promise they saw in me.
I succeeded despite what I was told. It’s possible that I was more inclined to fucking do it right. When I was doing the Aaron Sorkin thing and moving through the newsroom and telling my reporters that their girlfriends are irrelevant on election night, and indeed told one to get the fuck out, I saw the power of my role. This was 24 years ago, and we didn’t have the phones we have today.
There are a lot of people who care deeply about others. Many of us go into journalism. We don’t want anyone else to go through what we have. It’s difficult, but one win is all one needs to feel like maybe we saved the next generation.
Could you expand upon this? I’m not sure I understand what you mean by an ‘intuition’.
Sure. If you do enough basic math, you start to see things like how 2/8 can be simplified to 1/4 or you recognize that 10 is not a perfect square root or how you could reorder some operations to make things easier (sorry, examples from my kids). Little things like that where you don’t even think about it… it becomes second nature to you and that makes you a lot faster because you are not worrying about those basic ideas or mechanics. Instead, you can think about more complicated things such as which formulas to apply or the process to compute something.
As another example, since I teach computer science, a lot of novice students struggle with basic programming language syntax… How exactly do you declare a variable? What order do things go? How does a for loop work? Do you need a semicolon or parentheses, etc. If you do enough programming, however, these things become second nature and you stop thinking about it. You just seemily, intuitively, know these things and do them naturally without thinking, even though when you first started, it was really complicated and daunting and you probably spent a lot of time constructing a single line of code.
Once you develop a foundation however, you don’t need to worry about these low-level things. Instead you worry about high-level issues such as how to organize larger pieces of code into functions or how to I utilize different paradigums, etc.
This is why a basketball player, for instance, will shoot thousands of shots in practice or why a piano player will play a piece over and over for many hours. It’s so they don’t have to think about the low-level mechanics. It becomes muscle memory and it’s just natural to them.
I hope that makes sense.
Okay I understand what you are saying now, but I believe that you are conflating two ideas here.
The first idea is about learning the concepts, and not just the specifics. There’s a difference between memorizing a specific chemical reaction and understanding types of chemical reactions and using that to deduce what a specific chemical reaction would be given two substances. I would not call that intuition, however, as it’s a matter of learning larger patterns, rules, or processes.
The second idea is about making things happen faster and less consciously. In essence, this is pattern recognition, but in practice it’s a bit more complicated. Playing a piece over and over or shooting a basketball over and over is a rather unique process in that it involves muscle memory (or more accurately it involves specific areas of the brain devoted to motor cortex activation patterns working in sync with sensory systems such as proprioception). Knowing how to declare a variable or the order of operations, on the other hand, is pattern recognition within the context of a specific language or programming languages in general (as a reflection of currently circulating/used programming languages). I would consider both of these (muscle memory and pattern recognition) as aligned with the idea of intuition as you’ve defined it.
Rote learning is not necessary to understand concepts, but the amount of repetition needed to remember an idea after x period of time is going vary from person to person and how long after you expect someone to remember something. Pattern recognition and muscle memory, however, typically require a higher amount of repetition to sink in, but will also vary depending on person and time between learning and recall.
First off, 10 is an integer square root. Of 100.
I get where you’re coming from on most points and agree overall. However, you’re not taking into consideration what secondary schooling looks like before students arrive.
I was told by multiple English teachers (including the head of the department) that I was a math student and should never attempt to write because I saw through the regurgitation assignments, didn’t agree with teacher assessments of what Dickens “was trying to do” and had zero interest in confirming their biases.
I also didn’t pursue page design and getting onto my high school paper because the only F I got there was from the advisor who was exceptionally clear that I was not welcome to attempt committing journalism after mocking up yearbook pages and being very unhappy with the results in Aldus PageMaker; there was no support system in place. (Also, our yearbook was shit on every level.)
That said, I can still write a ternary line of code where it makes sense sted an if-else block.
College coursework on the whole is a waste of time reinventing wheels. I don’t need to spend a couple of weeks working up to “Hello, world!” in C and as such left CS as a major my first quarter at uni.
For the most part, I’ve been very lucky with teachers and professors. When I started taking college classes in high school and escaped the absurdity of recitation being “thinking for myself,” I learned to love writing because my prof, a Catholic deacon, wanted thesis defense, not what he’d said in lecture. If I was 180 off of his viewpoint but could cite sources, that was an A.
But teachers do this shit every day, year after year, and we blindly say they’re doing important work even as they discourage people from finding their path and voice, because god forbid a 16-year-old challenges someone in their 50s.
Right, what I was trying to say is that 10 itself is not a perfect square. You cannot take the square root of 10 and get an integer (ie. 1, 4, 9, 16, 25, etc.).
I think that is unfortunate and probably inappropriate. I try to avoid classifying students as particular types and generally try to encourage them whenever possible to pursue whatever their interests are (even if I disagree or don’t have the same interest myself).
There is a reason for reinventing wheels; it is to understand why they are round and why they are so effective. To build the future, it helps to understand the past.
That said, perhaps the course was too slow for you, which is understandable… I frequently hear that about various classes (including ones I’ve taught).
Again, I think you’ve had an unfortunate experience and I think it’s a good thing to challenge your teachers. I certainly did when I was a student and I appreciate it now when students do that with me. I recognize that I am not perfect nor do I know everything. I make mistakes and can be wrong.
I wish you had a more supportive environment in secondary school and I have a better understanding of your perspective. Thanks for the dialogue.
I had to find my own way. That’s of value.
If you had a supportive set of teachers, telling you that you can do anything, where’s the challenge? I went back to my high school and dutifully waited for the department chair with a rehearsed, belittling speech. When Columbia says you’re the best editorial writer in the country at the college level from literally the first one I wrote, teachers tend to not only back the fuck off but also to do this weird thing where they revise history and talk about the promise they saw in me.
I succeeded despite what I was told. It’s possible that I was more inclined to fucking do it right. When I was doing the Aaron Sorkin thing and moving through the newsroom and telling my reporters that their girlfriends are irrelevant on election night, and indeed told one to get the fuck out, I saw the power of my role. This was 24 years ago, and we didn’t have the phones we have today.
There are a lot of people who care deeply about others. Many of us go into journalism. We don’t want anyone else to go through what we have. It’s difficult, but one win is all one needs to feel like maybe we saved the next generation.