3 ms·

> Watching someone reason with a writing implement in hand is an incredibly valuable learning exercise, since effective technical problem solving is largely do

by lisper 3y ago

> Watching someone reason with a writing implement in hand is an incredibly valuable learning exercise, since effective technical problem solving is largely done that way in practice. I vehemently disagree. Classroom lectures almost always present results that are already in the bag. I can't remember a single class where a professor actually walked us through the process of figuring something out. The closest I've ever seen is 3blue1brown, and he obviously doesn't use a chalk board. Nowadays technical problems are often solved by writing code, which is almost never done on a chalk board outside of job interviews.

jacobolus 3y ago
Even when chalkboard lectures present material that was prepared in advance, there's a significant difference vs. prepared material presented in slides or a typeset document or a video. Writing imposes a speed limit on the lecturer, and forces them to verbalize the whole reasoning process. In slides it is much easier to skip past the meat of the work, and much harder to be responsive in writing/pictures to questions and discussion. > can't remember a single class where a professor actually walked us through the process of figuring something out This can't really be blamed on the tool of the chalkboard. I promise you this does happen in some classrooms. It certainly happens all the time in informal discussion between professionals. In my opinion schools should strive much harder to induct students into a problem-solving culture than teach specific content trivia. A blackboard is an invaluable tool for the former. > often solved by writing code Writing code is a narrow and constrained tool with much less freedom than writing on paper, and thoughts made first in code are substantially blinkered in my experience compared to thoughts worked through on paper. Many of the best programmers I know do their most important work on paper (sketching, planning, doodling, drawing diagrams, ...) before ever touching the keyboard. And that is far more true still for mathematicians, physicists, etc. What is true is that many programmers are not very effectively taught to use paper to its full advantage as a tool for thought, and either never learn or largely figure it out on their own. Our typical computer science pedagogy is frankly terrible at this, and professionals' on-the-job training isn't much better.
- lisper 3y ago
  >> can't remember a single class where a professor actually walked us through the process of figuring something out > This can't really be blamed on the tool of the chalkboard. That is true, of course, but that was not the point. The point is that blackboards do not necessarily produce, or even encourage, good pedagogy. The two things are largely orthogonal. > Writing code is a narrow and constrained tool with much less freedom than writing on paper Yes, I think this is a feature, not a bug. It enforces a certain amount of rigor that blackboards don't. Of course, the language in which the code is written matters a lot.
  - deleted 3y ago
    [deleted]
WalterBright 3y ago
> I can't remember a single class where a professor actually walked us through the process of figuring something out. I'm sad for you. All my professors did that in every lecture. I'd copy it down in a spiral notebook as he'd describe it step by step. Later, when reviewing the notes, it would bring back the lecture in my head. This was before the days of videotape, but I still regret not taping the lectures with a cassette recorder.
- lisper 3y ago
  Just to be clear, they did walk us through the process of solving the kinds of problems that would be on the final exam. But the starting point was always a set of equations that were simply given as gospel with no motivation nor justification nor hint as to how they were arrived at. It drove me nuts. You can see this happening today. My favorite contemporary example is elliptic curves, which are a hot topic. Most introductory materials on elliptic curves will tell you that an elliptic curve is defined by an equation of the form: y^2 = x^3 + ax + b. Where did that come from? Why is there no x^2 term? How did anyone ever figure out that this particular equation would be good for cryptography? What other polynomial equations might be good for cryptography? And then one day you learn about Montgomery curves, which do have an x^2 term but no x^0 term. So was the whole x^3 + ax + b thing a lie from the beginning? What about a complete cubic equation with all terms included? Is that an elliptic curve? Is it useful for cryptography? Maybe my brain is just wired differently from most people, but those kinds of questions just pop up naturally for me, but I hardly ever see them either asked or answered. And this is true in every technical field I have ever studied, and I've had a very long and diverse career.
  - abdullahkhalids 3y ago
    Those are very valid questions, and as a (former) professor, I know that most smart (and many 'not smart') students do ask those questions. Lecturers should do their best to set up the motivation for each topic. This can fail because - There is not enough time. Unfortunately, formal courses have a fixed time, and the lecturer has to cover a certain amount of content in that time [1]. - Sometimes, its not actually possible to answer the 'why' questions with the amount of background that students have (or the lecturer has). The above is also true for books/written down notes as well. For instance, in your example of elliptic curves, the answer to your questions about "why the form y^2 = x^3 + ax + b" requires students to understand algebraic geometry first, where such curves are defined in general (over arbitrary fields etc), rather than over the real field as you have. If you read such a book, you will see why in the general setting, its completely natural to define such curves. I don't know exactly why elliptic curves are good for cryptography, but I would hazard that the reason is perhaps only apparent when you study them in the abstract - hence why you don't see this explanation in your resources. The writer might not even know themselves. [1] Yes yes, this is broken as well. In my ideal university there would be no semesters. Courses will be as short or as long as necessary to naturally end at an appropriate location.
bayindirh 3y ago
> Nowadays technical problems are often solved by writing code, which is almost never done on a chalk board outside of job interviews. Nope. They are solved by either formulating a solution in maths or drawings or verbally, then it’s transformed to code step by step. Code is just your intention or solution distilled for a much more constrained machine, and is the very last step.
- lisper 3y ago
  Maybe in your field, but in over 40 years of work in a pretty wide variety of technical fields I have never seen a single person write an equation on a board as part of doing actual work.
  - bayindirh 3y ago
    Interesting, because I find myself writing formulae to my notebook all the time. It's not differential equations all the time, but I'm generally making sure that something is scaling correctly, or the things I'm doing are the ones I really want. I would love to have a board at office, but instead I have tons of notebooks which I finish, scan, shred and recycle.

by lisper 3y ago

jacobolus 3y ago

Even when chalkboard lectures present material that was prepared in advance, there's a significant difference vs. prepared material presented in slides or a typeset document or a video. Writing imposes a speed limit on the lecturer, and forces them to verbalize the whole reasoning process. In slides it is much easier to skip past the meat of the work, and much harder to be responsive in writing/pictures to questions and discussion. > can't remember a single class where a professor actually walked us through the process of figuring something out This can't really be blamed on the tool of the chalkboard. I promise you this does happen in some classrooms. It certainly happens all the time in informal discussion between professionals. In my opinion schools should strive much harder to induct students into a problem-solving culture than teach specific content trivia. A blackboard is an invaluable tool for the former. > often solved by writing code Writing code is a narrow and constrained tool with much less freedom than writing on paper, and thoughts made first in code are substantially blinkered in my experience compared to thoughts worked through on paper. Many of the best programmers I know do their most important work on paper (sketching, planning, doodling, drawing diagrams, ...) before ever touching the keyboard. And that is far more true still for mathematicians, physicists, etc. What is true is that many programmers are not very effectively taught to use paper to its full advantage as a tool for thought, and either never learn or largely figure it out on their own. Our typical computer science pedagogy is frankly terrible at this, and professionals' on-the-job training isn't much better.

lisper 3y ago
>> can't remember a single class where a professor actually walked us through the process of figuring something out > This can't really be blamed on the tool of the chalkboard. That is true, of course, but that was not the point. The point is that blackboards do not necessarily produce, or even encourage, good pedagogy. The two things are largely orthogonal. > Writing code is a narrow and constrained tool with much less freedom than writing on paper Yes, I think this is a feature, not a bug. It enforces a certain amount of rigor that blackboards don't. Of course, the language in which the code is written matters a lot.
- deleted 3y ago
  [deleted]

WalterBright 3y ago

> I can't remember a single class where a professor actually walked us through the process of figuring something out. I'm sad for you. All my professors did that in every lecture. I'd copy it down in a spiral notebook as he'd describe it step by step. Later, when reviewing the notes, it would bring back the lecture in my head. This was before the days of videotape, but I still regret not taping the lectures with a cassette recorder.

lisper 3y ago
Just to be clear, they did walk us through the process of solving the kinds of problems that would be on the final exam. But the starting point was always a set of equations that were simply given as gospel with no motivation nor justification nor hint as to how they were arrived at. It drove me nuts. You can see this happening today. My favorite contemporary example is elliptic curves, which are a hot topic. Most introductory materials on elliptic curves will tell you that an elliptic curve is defined by an equation of the form: y^2 = x^3 + ax + b. Where did that come from? Why is there no x^2 term? How did anyone ever figure out that this particular equation would be good for cryptography? What other polynomial equations might be good for cryptography? And then one day you learn about Montgomery curves, which do have an x^2 term but no x^0 term. So was the whole x^3 + ax + b thing a lie from the beginning? What about a complete cubic equation with all terms included? Is that an elliptic curve? Is it useful for cryptography? Maybe my brain is just wired differently from most people, but those kinds of questions just pop up naturally for me, but I hardly ever see them either asked or answered. And this is true in every technical field I have ever studied, and I've had a very long and diverse career.
- abdullahkhalids 3y ago
  Those are very valid questions, and as a (former) professor, I know that most smart (and many 'not smart') students do ask those questions. Lecturers should do their best to set up the motivation for each topic. This can fail because - There is not enough time. Unfortunately, formal courses have a fixed time, and the lecturer has to cover a certain amount of content in that time [1]. - Sometimes, its not actually possible to answer the 'why' questions with the amount of background that students have (or the lecturer has). The above is also true for books/written down notes as well. For instance, in your example of elliptic curves, the answer to your questions about "why the form y^2 = x^3 + ax + b" requires students to understand algebraic geometry first, where such curves are defined in general (over arbitrary fields etc), rather than over the real field as you have. If you read such a book, you will see why in the general setting, its completely natural to define such curves. I don't know exactly why elliptic curves are good for cryptography, but I would hazard that the reason is perhaps only apparent when you study them in the abstract - hence why you don't see this explanation in your resources. The writer might not even know themselves. [1] Yes yes, this is broken as well. In my ideal university there would be no semesters. Courses will be as short or as long as necessary to naturally end at an appropriate location.

bayindirh 3y ago

> Nowadays technical problems are often solved by writing code, which is almost never done on a chalk board outside of job interviews. Nope. They are solved by either formulating a solution in maths or drawings or verbally, then it’s transformed to code step by step. Code is just your intention or solution distilled for a much more constrained machine, and is the very last step.

lisper 3y ago
Maybe in your field, but in over 40 years of work in a pretty wide variety of technical fields I have never seen a single person write an equation on a board as part of doing actual work.
- bayindirh 3y ago
  Interesting, because I find myself writing formulae to my notebook all the time. It's not differential equations all the time, but I'm generally making sure that something is scaling correctly, or the things I'm doing are the ones I really want. I would love to have a board at office, but instead I have tons of notebooks which I finish, scan, shred and recycle.