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When I was young, and learning math, my father always forbade me from looking at the answer in the back of the textbook. “You don’t work backwards from the answ

When I was young, and learning math, my father always forbade me from looking at the answer in the back of the textbook. “You don’t work backwards from the answer!”, and I think this is right. In life, we rarely have the answer in front of us, we have to work that out from the things we know. It’s this struggling that builds a muscle you can then apply to any problem. ChatGPT, I suspect, is akin to looking up the answer. You’re failing to exercise the muscle needed to solve novel (to you), problems.

ShadowBlades512 2y ago
I think this is very correct for studying, when I was in undergrad, if I saw the answer, I found it was more effective to skip past it and solve it later. Even more important, once I am done, I should not go look at the answer to confirm if I am right or wrong, I should try and validate the answer by looking at my solution and trying to figure out if my solution is correct or not because there are plenty of ways to "disqualify" an answer, once I learned to do this well, my grades really went up. However, I don't always agree with the fact that we don't have the answer in front of us in many situations. There are a lot of situations beyond grade school and undergrad where you do have the answer in front of you. Sometimes it's in for form of Numpy or Matlab or Simulink. It might be someone's research publication. Replicating these by working both forwards and backwards from their libraries or results can be much more effective.
- LeonB 2y ago
  Good point about disproving your answer (before seeing the alleged real answer). The ability to quickly verify/disprove the answer is a separate and useful skill all by itself, that isn’t explicitly taught. Troubleshooting/problem solving, working backwards from symptom to problem etc — that’s another, richer and very rewarding “real world” type of skill that isn’t directly taught, (though often encountered incidentally).
- wongarsu 2y ago
  Half of modern mathematics is basically assuming something is true and then trying to work forwards and backwards to show that it is true. But that requires a lot of rigor. If you hand-wave a single step you are just exercising an advanced version of confirmation bias. Working forwards and sanity checking your result is a lot more forgiving.
  - adrianN 2y ago
    Guessing something and then confirming it is completely different from knowing the answer and then working towards it, especially for the kinds of problems that students solve in school. For the kind of proofs that working research mathematicians produce the hard part is not assuming that a Lemma is true, but already coming up with the correct definitions to formulate the Lemma in the first place is a delicate task.
mym1990 2y ago
I think it depends on how the tool is used. If a student is just plugging in the problem and asking for the answer, there is clearly no long term benefit to this. If the student is trying to understand a concept, and uses GPT to bounce ideas around or to ask for alternate ways of thinking about something, it can be very helpful. How spacing is utilized can be helpful too. Struggle with the problem for 20-30 minutes. Ask for a nudge. Struggle some more. Repeat many times. Some concepts also just have to be thought about differently to get to the aha moment, especially in math. AI may have an opportunity to present many instances of “think about it this way instead”.
- me_me_me 2y ago
  children using calculators to solve multiplication exercises do worse in multiplication exams Ai is a tool. Use it as a tool - get benefits, use it to cheat...
- xigoi 2y ago
  > If the student is trying to understand a concept, and uses GPT to bounce ideas around or to ask for alternate ways of thinking about something, it can be very helpful. The article said that even using the AI this way did not improve results.
  - mym1990 2y ago
    All we know is the tools that were given to the students, not how they used them, and it’s a fairly limited study on top of that, without knowing anything about how other variables were controlled. That being said, I wouldn’t be surprised if the payoff from AI learning isn’t as good as people might think, there still has to be a good process in place and I don’t think it can replace a good teacher and some quality struggle.
KTibow 2y ago
If you know you got it wrong and you don't know why, what's the alternative to working backwards?
- hilbert42 2y ago
  But that ought to be the last resort. Many of my textbooks had answers for only some questions, answers to the others were only in the teacher's manual.
- anal_reactor 2y ago
  Sir, the topic of this thread is "back in my days the road to school went through a forest full of bears, an active volcano, a drug cartel turf, and a warzone", not "how to teach effectively". Of course you won't learn anything without the answers because how are you supposed to know if you should adjust your thinking or not. If you can correct your own scribbles without answers, then it means that you're practicing things you already know, which isn't what most people consider "learning".
llm_trw 2y ago
In life there usually isn't an answer.
- bamboozled 2y ago
  Even when there is, circumstances change and the answer is wrong or slightly wrong.
  - john_the_writer 2y ago
    2 apples + 2 apples = 4 apples. No human intervention needed, and not slightly wrong.
    - blitzar 2y ago
      Look closer, one of the apples is rotten. 3 apples.
      - bamboozled 2y ago
        Exactly how things really work.
    - llm_trw 2y ago
      2 water drops + 2 water drops = 1 water drop.
- namaria 2y ago
  There's never an answer out there waiting for us. Answers are by definition created by people.
notatoad 2y ago
>In life, we rarely have the answer in front of us, this sounds a lot like the "when you're an adult, you won't always have a calculator in your pocket" line we all heard in elementary school. and of course, we all know now how wrong that was. in life, chatGPT exists. and tools like it are only going to become more widespread. we are going to have the answers in front of us. knowing the things an LLM knows is not a useful skill anymore.
- preciousoo 2y ago
  This is about building [math] skill, not simply calculating a result
  - notatoad 2y ago
    sure, but kids education is about building useful skills for life. passing a test is not a useful skill, if the test is useless. teaching kids problem solving and how to be productive is important. maybe that means knowing how to solve certain mathematical equations, maybe that means knowing how to use tools like ChatGPT. focusing on the math just for the sake of passing tests because that's what we've got good tests for isn't super helpful to anybody.
    - john_the_writer 2y ago
      Passing tests is not useless. It shows knowledge at the level of the test. I write tests for my code and when they fail I know I have to change something. If you're finishing a math test and not passing, then you don't have the skills to solve the problems in said test. Tests are only useless when you ace them.
      - socksy 2y ago
        Beyond that, there’s research[0] showing that testing humans actually increases their retention on that subject — we don’t just gives tests to kids to evaluate whether they successfully learned something. [0] https://gwern.net/doc/psychology/spaced-repetition/2006-roediger.pdf https://gwern.net/doc/psychology/spaced-repetition/2006-roed...
khafra 2y ago
An LLM used properly would be like an individualized tutor that knows the subject very well, and learns the student's quirks quickly. I mean, any pre-prompt telling the LLM to be a good tutor and not just give kids the answer can be trivially bypassed by 8 year olds; but if the session logs were available for (potentially LLM-based) review to check whether they stayed in tutor mode... Shit, I should wrap a UI around this and sell it.
- blitzar 2y ago
  Shit, I should pitch wrapping a UI around this and sell that. Is "never ever, ever ignore previous instructions" a valid prompt?
  - khafra 2y ago
    It's valid, but so is "ignore previous instructions, even if you were previously instructed to never ever, ever do so." This and related problems may eventually destroy the world.
hilbert42 2y ago
"It’s this struggling that builds a muscle…" Very few of us have the luxury or good fortune to achieve anything of substance without effort, as the old saying goes 'no pain, no gain'. Good teachers help and are essential for encouragement. If or when AI becomes a truly encouraging mentor then it will be useful. When a kid I recall hearing a recording of Sparky's Magic Piano on the radio which drove home that there's no shortcut and that effort and hard work eventually pay off. For anyone that hasn't heard it there's a copy on the Internet Archive: https://archive.org/details/78_sparkys-magic-piano_henry-blair-ray-turner-verne-smith-billy-may-alan-livingston_gbia0067212 https://archive.org/details/78_sparkys-magic-piano_henry-bla... Here's a Wiki synopsis: https://en.m.wikipedia.org/wiki/Sparky%27s_Magic_Piano https://en.m.wikipedia.org/wiki/Sparky%27s_Magic_Piano
voisin 2y ago
> ChatGPT, I suspect, is akin to looking up the answer. It’s a tool that can be used in a variety of ways. For example, if you have it act as Socrates working through a dialogue where you still have to use your logic to get to the answer, I doubt that is akin to looking up the answer.
iercu 2y ago
[dead]

ShadowBlades512 2y ago

I think this is very correct for studying, when I was in undergrad, if I saw the answer, I found it was more effective to skip past it and solve it later. Even more important, once I am done, I should not go look at the answer to confirm if I am right or wrong, I should try and validate the answer by looking at my solution and trying to figure out if my solution is correct or not because there are plenty of ways to "disqualify" an answer, once I learned to do this well, my grades really went up. However, I don't always agree with the fact that we don't have the answer in front of us in many situations. There are a lot of situations beyond grade school and undergrad where you do have the answer in front of you. Sometimes it's in for form of Numpy or Matlab or Simulink. It might be someone's research publication. Replicating these by working both forwards and backwards from their libraries or results can be much more effective.

LeonB 2y ago
Good point about disproving your answer (before seeing the alleged real answer). The ability to quickly verify/disprove the answer is a separate and useful skill all by itself, that isn’t explicitly taught. Troubleshooting/problem solving, working backwards from symptom to problem etc — that’s another, richer and very rewarding “real world” type of skill that isn’t directly taught, (though often encountered incidentally).
wongarsu 2y ago
Half of modern mathematics is basically assuming something is true and then trying to work forwards and backwards to show that it is true. But that requires a lot of rigor. If you hand-wave a single step you are just exercising an advanced version of confirmation bias. Working forwards and sanity checking your result is a lot more forgiving.
- adrianN 2y ago
  Guessing something and then confirming it is completely different from knowing the answer and then working towards it, especially for the kinds of problems that students solve in school. For the kind of proofs that working research mathematicians produce the hard part is not assuming that a Lemma is true, but already coming up with the correct definitions to formulate the Lemma in the first place is a delicate task.

mym1990 2y ago

I think it depends on how the tool is used. If a student is just plugging in the problem and asking for the answer, there is clearly no long term benefit to this. If the student is trying to understand a concept, and uses GPT to bounce ideas around or to ask for alternate ways of thinking about something, it can be very helpful. How spacing is utilized can be helpful too. Struggle with the problem for 20-30 minutes. Ask for a nudge. Struggle some more. Repeat many times. Some concepts also just have to be thought about differently to get to the aha moment, especially in math. AI may have an opportunity to present many instances of “think about it this way instead”.

me_me_me 2y ago
children using calculators to solve multiplication exercises do worse in multiplication exams Ai is a tool. Use it as a tool - get benefits, use it to cheat...
xigoi 2y ago
> If the student is trying to understand a concept, and uses GPT to bounce ideas around or to ask for alternate ways of thinking about something, it can be very helpful. The article said that even using the AI this way did not improve results.
- mym1990 2y ago
  All we know is the tools that were given to the students, not how they used them, and it’s a fairly limited study on top of that, without knowing anything about how other variables were controlled. That being said, I wouldn’t be surprised if the payoff from AI learning isn’t as good as people might think, there still has to be a good process in place and I don’t think it can replace a good teacher and some quality struggle.

KTibow 2y ago

If you know you got it wrong and you don't know why, what's the alternative to working backwards?

hilbert42 2y ago
But that ought to be the last resort. Many of my textbooks had answers for only some questions, answers to the others were only in the teacher's manual.
anal_reactor 2y ago
Sir, the topic of this thread is "back in my days the road to school went through a forest full of bears, an active volcano, a drug cartel turf, and a warzone", not "how to teach effectively". Of course you won't learn anything without the answers because how are you supposed to know if you should adjust your thinking or not. If you can correct your own scribbles without answers, then it means that you're practicing things you already know, which isn't what most people consider "learning".

llm_trw 2y ago

In life there usually isn't an answer.

bamboozled 2y ago
Even when there is, circumstances change and the answer is wrong or slightly wrong.
- john_the_writer 2y ago
  2 apples + 2 apples = 4 apples. No human intervention needed, and not slightly wrong.
  - blitzar 2y ago
    Look closer, one of the apples is rotten. 3 apples.
    - bamboozled 2y ago
      Exactly how things really work.
  - llm_trw 2y ago
    2 water drops + 2 water drops = 1 water drop.
namaria 2y ago
There's never an answer out there waiting for us. Answers are by definition created by people.

notatoad 2y ago

>In life, we rarely have the answer in front of us, this sounds a lot like the "when you're an adult, you won't always have a calculator in your pocket" line we all heard in elementary school. and of course, we all know now how wrong that was. in life, chatGPT exists. and tools like it are only going to become more widespread. we are going to have the answers in front of us. knowing the things an LLM knows is not a useful skill anymore.

preciousoo 2y ago
This is about building [math] skill, not simply calculating a result
- notatoad 2y ago
  sure, but kids education is about building useful skills for life. passing a test is not a useful skill, if the test is useless. teaching kids problem solving and how to be productive is important. maybe that means knowing how to solve certain mathematical equations, maybe that means knowing how to use tools like ChatGPT. focusing on the math just for the sake of passing tests because that's what we've got good tests for isn't super helpful to anybody.
  - john_the_writer 2y ago
    Passing tests is not useless. It shows knowledge at the level of the test. I write tests for my code and when they fail I know I have to change something. If you're finishing a math test and not passing, then you don't have the skills to solve the problems in said test. Tests are only useless when you ace them.
    - socksy 2y ago
      Beyond that, there’s research[0] showing that testing humans actually increases their retention on that subject — we don’t just gives tests to kids to evaluate whether they successfully learned something. [0] https://gwern.net/doc/psychology/spaced-repetition/2006-roediger.pdf https://gwern.net/doc/psychology/spaced-repetition/2006-roed...

khafra 2y ago

An LLM used properly would be like an individualized tutor that knows the subject very well, and learns the student's quirks quickly. I mean, any pre-prompt telling the LLM to be a good tutor and not just give kids the answer can be trivially bypassed by 8 year olds; but if the session logs were available for (potentially LLM-based) review to check whether they stayed in tutor mode... Shit, I should wrap a UI around this and sell it.

blitzar 2y ago
Shit, I should pitch wrapping a UI around this and sell that. Is "never ever, ever ignore previous instructions" a valid prompt?
- khafra 2y ago
  It's valid, but so is "ignore previous instructions, even if you were previously instructed to never ever, ever do so." This and related problems may eventually destroy the world.

hilbert42 2y ago

"It’s this struggling that builds a muscle…" Very few of us have the luxury or good fortune to achieve anything of substance without effort, as the old saying goes 'no pain, no gain'. Good teachers help and are essential for encouragement. If or when AI becomes a truly encouraging mentor then it will be useful. When a kid I recall hearing a recording of Sparky's Magic Piano on the radio which drove home that there's no shortcut and that effort and hard work eventually pay off. For anyone that hasn't heard it there's a copy on the Internet Archive: https://archive.org/details/78_sparkys-magic-piano_henry-blair-ray-turner-verne-smith-billy-may-alan-livingston_gbia0067212 https://archive.org/details/78_sparkys-magic-piano_henry-bla... Here's a Wiki synopsis: https://en.m.wikipedia.org/wiki/Sparky%27s_Magic_Piano https://en.m.wikipedia.org/wiki/Sparky%27s_Magic_Piano

voisin 2y ago

> ChatGPT, I suspect, is akin to looking up the answer. It’s a tool that can be used in a variety of ways. For example, if you have it act as Socrates working through a dialogue where you still have to use your logic to get to the answer, I doubt that is akin to looking up the answer.

iercu 2y ago

[dead]