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> Why do we make kids learn how to do math if they can pull out their phone and open the calculator app? Because learning how to learn is important and there is

> Why do we make kids learn how to do math if they can pull out their phone and open the calculator app? Because learning how to learn is important and there is value in understanding how the answer is produced, even if you have a machine that can produce it for you. I actually appreciate this question very much because this question is extremely pertinent to our discussion. Before I continue my response, I want to turn around and ask you: 1. What's your definition of "learn how to do math"? i. Would it be sufficient if they proved they understood what addition, subtraction, multiplication and division was? Or do they need to be able to correctly calculate what 4592 * 314 is? What if they could show you using diagrams of squares and rectangles *why* (a + b)** 2 expands to the equation it does but refused to chart out results for various values of a and b? ii. Would you fail a student who could reliably chart out results for (a + b)** 2 given various values of a and b, but failed to explain that using diagrams of squares and rectangles? iii. Would you fail a student who could reliably add 1 + 3 or 7 - 5 or 7 * 5 but fail to compute 4592 * 314? iv. Is a student who could reliably add 1 + 3 or 7 - 5 or 7 * 5 but fail to compute 4592 * 314 at the age of 5 superior or inferior to a student who is capable of doing the same at age 7? 2. If an exam is composed of tables of long division and your score on the test boils down to your ability to how many of those long divisions you can complete in 45 minutes, does the person who scores the highest have a superior understanding of division than the slowest student who suffers from mental fatigue due to an underlying, undiagnoised health condition? 3. When you say "understand how the answer is produced", what level of abstraction is acceptable to be not considered as cheating? Do they need to understand how the calculator physically computes the floating-point math, or is pushing the button enough? If pushing the button is cheating, why isn't using a base-10 shortcut algorithm also cheating? What if the button pusher explained to you precisely how IEEE 754 worked, how a digital calculator works and then refused to do long division citing it was a complete waste of their time and yours? Would you refuse to let them pass the class or fail them unless they yielded to your demands and complied with your specific definition of learning? Is the math class also doubling as ability to pass compliance and behavioral standards or is it purely a test of mathematical ability? 4. If a student uses an LLM to generate the boilerplate code for a script, but can perfectly explain the architecture, debug the logic, and scale the deployment, have they failed to 'learn how to learn' just because they didn't manually type the syntax? Educational resources and classroom time is a zero sum game. We cannot afford to educate everyone if they all require 1:1 coaching from a qualified human in a room that has limited space. Time in a day is zero sum as well. Every minute someone spends on doing the 135th long division is a minute they're not spending thinking if solving long division problems is a meaningful differentor in their long term success - whether it's the long division that will make them wealthy, happy and successful or something else entirely?

Aurornis 1mo ago
> i. Would it be sufficient if they proved they understood what addition, subtraction, multiplication and division was? Or do they need to be able to correctly calculate what 4592 * 314 is? What if they could show you using diagrams of squares and rectangles why (a + b)* 2 expands to the equation it does but refused to chart out results for various values of a and b? I’m not an educator by profession but I’ve done a lot of training and mentoring. There is no replacement for actually doing the work. People who study something but don’t go through the exercises feel they understand topics better than they do. It’s only when they are put in a position where they have to apply it that the cracks in their understanding are revealed. This would 100% result in students who thought they could explain multiplication but only had a surface level idea. The knowledge would also be fleeting because actually doing the thing makes the knowledge stick more than just observing and understanding the thing. So yes, you still need to have the students do the thing. Replace math with writing and it will be more obvious. It’s easy to look at someone’s writing and critique it. It’s much harder to write well without practicing.
- subhobroto 1mo ago
  > It’s much harder to write well without practicing Is the point of writing, to communicate information from one person to another group or something else? Which of these fail to communicate the need: i. "Need to go poo poo! NOW!" ii. "Excuse me Sir. I sincerely apologize for the inconvenience, I didn't mean to intrude but could you, please, point me to the direction of the nearest latrines, or the head as some might say, so I can relieve myself. The burrito didn't sit well with me unfortunately and it's causing me much distress! I must stress, time is of the utmost essence!" > So yes, you still need to have the students do the thing. I don't disagree with "There is no replacement for actually doing the work". What I do disagree with is the exact nature of the work done: when you have access to a gas/electric driven auger, trying to dig a hole by hand with a teaspoon is neither smart nor productive, like learning how to do long division. > The knowledge would also be fleeting because actually doing the thing makes the knowledge stick more than just observing and understanding the thing Define "stick". 1. I recall, in school, sitting in classes for days where the teacher went over multiplication tables 5x5 through 99x99. It was painful. I don't recall the top off my head what 93x95 is but I know how to calculate it now and I knew how to calculate it then. Hearing and doing 93x95 on a balckboard was not specially valuable nor additionally insightful nor marginally instructive over 13x19 and we could easily have stopped there and done something else with the remaining time. 2. I also recall, sitting in classes where we did long division by hand. You had to show your work and it was incredibly exhausting. I taught myself special tricks just to finish the long division exercises quickly and just be done with it so I could actually do the things that interested me more like reading manuals about vacuum tubes and how triodes worked. 3. Then there was this phase of "unitary method" which was just batshit crazy. They would ask questions like "if it takes 1 person to cut 1 block of wood 10 hours, how long would it take 10 men to cut the same wood?", and you would have to follow this insane mechanical process of decomposing the problem into its constituents and do all this crazy, laborious steps to arrive at the answer. It made absolutely no sense to me then and it still doesn't. It felt like digging a trench with a teaspoon. I had taught myself symbolic manipulation by then and used the "X, Y, Z" method to rapidly solve the problem. I recall annoying the teacher with "if it takes 1 person 10 days to cross a river, how long would it take 10 people to cross the same river?" So back to my question - define "stick". What's the window of "stickiness"? Who defines that window and why? Next: 4. Has long division been sticky for me (I don't recall it at all but I do remember I scored very well on those exercises then because the alternatives would leave me with even less time to do the things I actually liked doing like building mechanical robots)? 5. Exactly how many exercises were necessary and sufficient to prove that I understood long division? 1 page of long division? 5 pages? 100? 6. Do you recall how to do long division? I don't. I can bet you that I can look it up and do it correctly but I won't out of principle: There's absolutely 0 value in knowing how to do long division. It was as useful to me back then as it is now. We should have done something more productive with our time. "But doing long division laid the very foundation of logic and mathematical ability!" - Nonsense. There were students in my class who excelled at long division but couldn't grok calculus no matter how hard they tried. The only thing that being able to do long division proves is that you can pay attention long enough and maintain state. There are far more exciting, interesting ways of proving that ability. If I need to learn long division, I always had the ability to look it up, do some exercises, verify I understand it correctly and complete the task I was relying on long division for. Before the age of LLMs, one might argue that I needed to have some idea that long division was the tool I needed for solving my problem, and thus, having learned long division was valuable. In 2026, I can tell my desired state to a frontier model and it will propose various ways to solve it, then solve it for me if I so desire and walk me through the solution step-by-step if I want it to. So no, long division, "unitary method" and all such matters were and are nonsense, a waste of time and we should replace them with something more meaningful. If we can't come up with that, we should atleast let the kids go outside and play games they like. So again - what's this worry about knowledge being fleeting? Do either you, I or my teacher who taught me long division care whether I posses the knowledge of long division in 2026? Even though I knew long division in 1997, mastered it, excelled at it back then, do I still know it now? Does my inability to explain long division at a moment's notice in 2026 imply long division hasn't been "sticky"? If I never, ever knew long division at all, can I correctly learn it now? Who defines what knowledge is worth fleeting and which one is not? My history teacher and chemistry teacher certainly disagreed on that matter in 1997 and still do! The only truce they were willing to sign is that history and chemistry are both equally important but given that I am a software engineer by trade and deploying high quality systems to production is how I support my lifestyle, I provably disagree with both of them.

Aurornis 1mo ago

> i. Would it be sufficient if they proved they understood what addition, subtraction, multiplication and division was? Or do they need to be able to correctly calculate what 4592 * 314 is? What if they could show you using diagrams of squares and rectangles why (a + b)* 2 expands to the equation it does but refused to chart out results for various values of a and b? I’m not an educator by profession but I’ve done a lot of training and mentoring. There is no replacement for actually doing the work. People who study something but don’t go through the exercises feel they understand topics better than they do. It’s only when they are put in a position where they have to apply it that the cracks in their understanding are revealed. This would 100% result in students who thought they could explain multiplication but only had a surface level idea. The knowledge would also be fleeting because actually doing the thing makes the knowledge stick more than just observing and understanding the thing. So yes, you still need to have the students do the thing. Replace math with writing and it will be more obvious. It’s easy to look at someone’s writing and critique it. It’s much harder to write well without practicing.

subhobroto 1mo ago
> It’s much harder to write well without practicing Is the point of writing, to communicate information from one person to another group or something else? Which of these fail to communicate the need: i. "Need to go poo poo! NOW!" ii. "Excuse me Sir. I sincerely apologize for the inconvenience, I didn't mean to intrude but could you, please, point me to the direction of the nearest latrines, or the head as some might say, so I can relieve myself. The burrito didn't sit well with me unfortunately and it's causing me much distress! I must stress, time is of the utmost essence!" > So yes, you still need to have the students do the thing. I don't disagree with "There is no replacement for actually doing the work". What I do disagree with is the exact nature of the work done: when you have access to a gas/electric driven auger, trying to dig a hole by hand with a teaspoon is neither smart nor productive, like learning how to do long division. > The knowledge would also be fleeting because actually doing the thing makes the knowledge stick more than just observing and understanding the thing Define "stick". 1. I recall, in school, sitting in classes for days where the teacher went over multiplication tables 5x5 through 99x99. It was painful. I don't recall the top off my head what 93x95 is but I know how to calculate it now and I knew how to calculate it then. Hearing and doing 93x95 on a balckboard was not specially valuable nor additionally insightful nor marginally instructive over 13x19 and we could easily have stopped there and done something else with the remaining time. 2. I also recall, sitting in classes where we did long division by hand. You had to show your work and it was incredibly exhausting. I taught myself special tricks just to finish the long division exercises quickly and just be done with it so I could actually do the things that interested me more like reading manuals about vacuum tubes and how triodes worked. 3. Then there was this phase of "unitary method" which was just batshit crazy. They would ask questions like "if it takes 1 person to cut 1 block of wood 10 hours, how long would it take 10 men to cut the same wood?", and you would have to follow this insane mechanical process of decomposing the problem into its constituents and do all this crazy, laborious steps to arrive at the answer. It made absolutely no sense to me then and it still doesn't. It felt like digging a trench with a teaspoon. I had taught myself symbolic manipulation by then and used the "X, Y, Z" method to rapidly solve the problem. I recall annoying the teacher with "if it takes 1 person 10 days to cross a river, how long would it take 10 people to cross the same river?" So back to my question - define "stick". What's the window of "stickiness"? Who defines that window and why? Next: 4. Has long division been sticky for me (I don't recall it at all but I do remember I scored very well on those exercises then because the alternatives would leave me with even less time to do the things I actually liked doing like building mechanical robots)? 5. Exactly how many exercises were necessary and sufficient to prove that I understood long division? 1 page of long division? 5 pages? 100? 6. Do you recall how to do long division? I don't. I can bet you that I can look it up and do it correctly but I won't out of principle: There's absolutely 0 value in knowing how to do long division. It was as useful to me back then as it is now. We should have done something more productive with our time. "But doing long division laid the very foundation of logic and mathematical ability!" - Nonsense. There were students in my class who excelled at long division but couldn't grok calculus no matter how hard they tried. The only thing that being able to do long division proves is that you can pay attention long enough and maintain state. There are far more exciting, interesting ways of proving that ability. If I need to learn long division, I always had the ability to look it up, do some exercises, verify I understand it correctly and complete the task I was relying on long division for. Before the age of LLMs, one might argue that I needed to have some idea that long division was the tool I needed for solving my problem, and thus, having learned long division was valuable. In 2026, I can tell my desired state to a frontier model and it will propose various ways to solve it, then solve it for me if I so desire and walk me through the solution step-by-step if I want it to. So no, long division, "unitary method" and all such matters were and are nonsense, a waste of time and we should replace them with something more meaningful. If we can't come up with that, we should atleast let the kids go outside and play games they like. So again - what's this worry about knowledge being fleeting? Do either you, I or my teacher who taught me long division care whether I posses the knowledge of long division in 2026? Even though I knew long division in 1997, mastered it, excelled at it back then, do I still know it now? Does my inability to explain long division at a moment's notice in 2026 imply long division hasn't been "sticky"? If I never, ever knew long division at all, can I correctly learn it now? Who defines what knowledge is worth fleeting and which one is not? My history teacher and chemistry teacher certainly disagreed on that matter in 1997 and still do! The only truce they were willing to sign is that history and chemistry are both equally important but given that I am a software engineer by trade and deploying high quality systems to production is how I support my lifestyle, I provably disagree with both of them.