Technology has not improved on the blackboard at all.
The best presentation I've ever done was when the scheduled presenter never showed up. I volunteered. Having no slides, no preparation, I was faced with a white board and a dry-erase pen. Somehow, magic ensued.
I've never felt that way with prepared slides and a video screen.
A handout or slides or video is an opaque one-way tool, a prepared polished document that students can see but typically have no easy way to imitate. It affords the lecturer more chance to put effort in up front into making a clearer document, but robs students of the chance to witness their teacher doing some of the work in real time, and ultimately leads to a relative loss of basic problem solving skills involving writing/drawing, trading them away in favor of immediate gratification. Sometimes this trade-off is worth it (e.g. Grant Sanderson's work largely couldn't be replaced by blackboard lectures https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw ), but when the school's entire pedagogy moves that way, the loss is tremendous in my opinion, an erosion of some core tools of a centuries-old mathematical/scientific culture.
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.
> 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.
> 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.
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.
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.
- 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.
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.
I would love to have a board at office, but instead I have tons of notebooks which I finish, scan, shred and recycle.
My rule of thumb is: screen for exposition, blackboard for problem-solving.
Once you have a solution in hand, you can use computer drawing tools to make a polished version for publication. But that's a different problem than the original reasoning.
Slides/notes are fixed content. It's also finite content that you have to learn. If you learn all that content, you have mastered the course. So, it's quite easy to assess how much you have learned. But slides/notes don't teach skills well, and teach even more poorly on how to think in the course domain. Books also do poorly at this. The only way to learn skills and ways of thought is, as you say, by imitation. The imitation happens on the blackboard, where a good lecturer thinks out loud, gets the students to think out loud with him, and hopefully transfers the rhyme and rhythm of the discipline to them.
The 'problem' is that you can't really nail down concretely from a blackboard lecture what you are supposed to learn. Moreover, no matter how much you read the book, and master the content, you will always feel like you aren't thinking as well as the lecturer was. So you feel bad. Of course, if you let the pain drive you, you continue on your path of learning. If you don't, then blackboard courses feel horrible [1].
[1] A huge percentage, I would hazard, majority of lecturers are not of sufficiently good quality. Teaching is incredibly difficult. So, many blackboard courses, as do many notes/slides courses fail because the lecturer was just bad.
I still get my pens and paper when I design a software or study something that I want to learn, and it works trillions times better than watching a video or going through some slides.
I still produce my notes & documentation from books or existing material, and retain that knowledge almost indefinitely.
There’s mounting evidence about both people have learning differences, and using pen and paper exercises the brain in a completely unique way.
Ignoring this is pretty counterintuitive from my perspective.
PDFs Are a nice tool for the big books where you need lots of texts, images and diagrams. The scribbles are more for helping to remember past lectures.
But when everything is a PDF, knowledge becomes too fleeting to even remember past the exams.
I learn best from lectures by paying careful attention with my eyes and ears, and keeping the narrative flow structured in my brain; trying to write a substantial amount disrupts my focus and leads to dramatically worse understanding/retention.
Other people learn best from lectures by writing everything down (but never looking at it again); just the act of writing helps them focus. Still others learn best from writing without worrying about understanding the first time, and then afterward repeatedly reading their written notes.
(If I wanted to be e.g. an ethnographer or journalist, I would have to be the type to write notes after the conversation, rather than during.)
It might sound crazy but it has none of the downsides of no-notes or ready-made-notes.
* you have to pay attention and turn up otherwise you end up with useless notes, so it still has the motivation factor of no-notes
* you don't spend all your time copying so it doesn't suffer from the "I wrote it all down but I didn't listen to a word" factor of no-notes
https://www.studocu.com/en-gb/document/university-of-cambrid...
Bit difficult to find because they aren't publicly available.
On top of me not being able to listen, my notes were basically useless
For collaborations, things are entirely different of course
He told me he started off with slides and stuff and thought it was going to be all slick and cool for everyone. Then he eventually realized it just goes through material too fast.
I think whiteboards are an improvement on blackboards.
Blackboards in universities are often painted over with new paint after a few years. Of course, this is relatively simple maintenance.
For me to write stuff down in real time I basically have to turn off the understanding part of my brain and become a dumb pipe of sounds goes in ear to words on page.
I can hear and write, or I can listen and learn, not both.
Also, you can't get students to come up to the board when using these fancy ipads and such. In my opinion, just video recording a blackboard lecture is the correct way to go.
[1] You often don't see confused students from one vantage point. Walking around, that you do naturally while using a black/whiteboard or even when using slides lets you do that.