Mathematicians are hoarding a type of Japanese chalk (2015)
gizmodo.com
gizmodo.com
https://www.math.columbia.edu/~bayer/LinearAlgebra/Video/Cha...
CNN is doing a short web video on this chalk, and I was interviewed last week. They particularly liked my custom attache case for carrying all my colors to teach. When I drew diagrams revealing Catalan number correspondences, they were quite worried that these pictures "weren't math" and I might be hoodwinking them.
The "eraser" is a side category that doesn't get enough attention. At MSRI one uses auto detailing "applicator sponges" which choke pretty quickly with chalk dust, but are nevertheless superior to traditional erasers. Far better is a supply of auto detailing towels; here, Korean microfiber is unrivaled. For classes late in the day, I use one wet to wash the boards, then a dry one to erase as I work. When I run out I do laundry; these towels are indestructible.
So why use the sponges in a public setting? We're learning that animals in many particular tasks exceed human intelligence; it's a matter of each creature's focus of attention. Mathematicians like to believe that we're smarter than average, but we're actually just very focused. That can make us pretty dumb away from our focus of attention. A nervous mathematician giving a public lecture is unlikely to recognize what a towel is for, but a sponge has the right form factor. It's like making your modern heating in a bed and breakfast look like fireplace logs, to not confuse the customers.
Good note about the microfiber! I'll have to try that. I've become increasingly frustrated with erasers. When it comes to washing the board, do you use a squeegee at all? I've found a sponge/squeegee combo to make cleaning quick.
A dimension of chalk usage that seems to be missing from your page - what do you think of chucks (holders)? Hagoromo chalk is quite wide (11mm) and it seems that most chalk holders are built for 9mm chalk. I use the Hagoromo branch chalk holders, they seem to have good grip. The other alternative I've found is to look for artist-oriented graphite or pastel holders.
Wrong person to ask about holders. I like gripping bare chalk; my hand is too forceful for a holder.
Serious question: does this spell doom for people with ADHD?
When I was in school, I have a hard time staying engaged in lecture, and homework was near-impossible. I got a C in physics, but set the curve on the tests. It was a fascinating topic, but I couldn't stay focused on the bookwork.
Occasionally I will find a project that fully engages hyperfocus, and it's incredibly satisfying. I once fabricated a motorcycle carrier in a day and a half, pausing only to eat and sleep.
Caveat: undergrad in math, working on a part time coursework masters (I'm hoping to talk someone into being my advisor for a part time thesis)
No more so than any other academic subject.
If anything, I've found math more friendly to my ADHD than philosophy, literature, etc.
To your credit it was quite good, and produced some really great writing. I wished my other math professors had your passion. Half the time I could barely see the writing on the board after the first erasing.
Main benefit was in the speed of presentation. Writing on a blackboard takes some time, the lecturer is slow enough in presenting that you can really follow along, while not "standing still". What a contrast to powerpoint presentations where the lecturer paused for a minute or two to let students read the equations. Either time was not enough, or you'd start to get bored.
Until I graduated at the end of my 5 year program, I tutored freshmen students. Towards the end of my time at uni, they almost exclusively had lectures with powerpoints. I sat in one of the into lectures and what had been a good introductory course to classical mechanics had turned into a mind-numbing powerpoint karaoke show.
I'm sure most people have seen professors skip numerous steps on blackboards, too, but in my experience there's at least a heightened awareness of what it looks like to actually work through the problem.
The point of going to classes versus studying alone at home is that you get to watch mathematicians doing mathematics. It's apprenticeship learning, the same as carpentry. Watching the professor reason and make mistakes and second-guess himself is invaluable. The typed class notes where everything is neat and theorems are numbered gives the impression of an immaculate birth that the student can't fathom arriving at. The best maths classes are the ones that teach you how to be a mathematician.
Everyone jokes about the frustration of copying a full blackboard worth of notes and then having the professor go "wait no, that wasn't right" (myself included) but it's a valuable experience. That moment of "hm, hold on a second" is where the math is happening, and a chalkboard helps professors and students notice that. (And of course, when something "isn't quite right" on the Powerpoint, it's a tremendous pain to fix...)
A great teacher will be a great teacher with whatever you give them. But anyone not 100% tuned to that part of their teaching greatly benefits from some of the constraints that chalk gives them.
I'm a K-12 admin and once we had a HS teacher who was brilliant but her classes were often too difficult to follow for the kids. We just told her she couldn't use the powerpoint slides anymore. Yes, there was a huge discussion of timing and pedagogy and all of that, but ultimately, placing that constraint on her naturally put her at a much more equal footing to the students she was trying to teach.
The people who don't show up would have not showed up class recorded or not. It is very useful though when you have a morning class miss or be dead tired and not pay attention to re-watch the lecture to get a better understanding.
Content aside, it was a very interestingly run course. Assignments were at your own pace, you had a large list of the kinds of projects you could turn in for credit. There were quizzes, exams, essay topics, interview topics, and an option for independent projects to get credit. Each kind of project had it's own maximum point value it would be graded out of and the final grade was totally based on how many points your actually earned, not out of how many. Even if you did a shit job on every assignment, as long as you did enough of them, you could get an A. It was a nice way to boost the GPA from just sheer effort rather than actual achievement.
While I love chalk, and miss it since my current university uses whiteboards (actually stupid @#@#* WallTalkers, despite our pleas), it's hardly the case that the two options are 'chalk' or 'Powerpoint'. Also, Powerpoint slides can be delivered at a reasonable pace—I've seen many professors fruitfully use slides with blanks, distributed to the students in advance, on which students can take notes—and chalk-and-talk lectures are scarcely universal models of pacing—one 'remedy' often pursued by lecturers who want to go faster than they can write is just not to write anything.
1. Colours are harder to distinguish, or to see at all. Chalk is easy, even a brand new pen is difficult from more than a few rows back, possibly made worse by my colour blindness;
2. You can't go over an existing pen line. You can _sort of_ make it thicker (but typically remove part of it at the same time) but you can't draw a square and then go over one edge in red, for example.
And I agree with a sibling comment on this thread. The speed of information is ideal with live ‘writing/derivation’, as you can follow along at the teacher’s own pace and write each step yourself.
I used to do his for my own section classes I taught as a TA. I’d come in with a small post-it size note of starting points, and just work brought problems without referencing anything else. Kept it down to Earth, and I think (or hope) showed the students there’s nothing insanely hard here, just lots of small bite-sized steps.
I hadn't given it thought before, but I assume transparencies weren't as present in college because the room a given college class will be is essentially random. It's not an environment controlled by the person teaching. in high school and middle school, that was the teachers' classroom. The teacher stayed in their room, and we moved around. Projectors require more maintenance (bulbs going out!), and the college teachers would need to lug around their transparencies and pens. But all college classrooms have blackboards and some chalk.
Overhead projectors require a fairly dark room, and only work well up to a certain size and distance. Much beyond that, their light gets too dim, and if it is a large lecture hall, you need a large projection with very bright light for everyone to see.
Then there's off-axis people who might find a projector difficult to read. In a small classroom, both of these issues don't really come into play.
A blackboard, however, can be seen in a brightly lit room, almost anywhere in the room, even if the room is very large. For the really massive size lecture halls, you can have multiple blackboards that span the width of the room, plus sliding and portable ones.
Each system has its benefits and detriments I guess...
And the hard limit on how bright you can make that is that the lecturer is staring into that light while writing so you can only make it so bright before it becomes painful or damaging. Anecdotally when I was in elementary/middle school we'd sometimes have to work things out writing on a projector and it was tough sometimes and looking up you couldn't really see because your eyes had adjusted to the brightness of the projector. Maybe they could improve the lenses to spill less light out but it wasn't back then.
Having the last 10 minutes of progress, or more in special lecture theatres - allowed cross-referencing and observation that is hard to replicate with pre-prepared slides or with a single window of view.
http://pagine.dm.unipi.it/gobbino/Home_Page/ArchivioDidattic...
In my eyes, a hand-out + computer notes (which can later be emailed to the pupils) is by far the superior teaching method for most students. This is of course just personal preference, but I much prefer simply sitting and listening to the teacher while occasionally asking questions - taking in as much as I can, then copying up the notes later using material provided by the lecturer so as to commit it to memory. Frantically writing out the notes during the lecture, then going home and trying to eek out some sort of understanding from them just never sat well with me.
As you get into higher math, though, the chalkboard becomes more important, because it's a lot more like working it out in front of the student. The class is far more likely to ask questions that are going to consume a couple of boards of scribbles to answer, and the professor may not be able to anticipate it all in advance. Trying to do this on a slide is very inconvenient and I'm still yet to see a computer interface in common use that can pull it off at all.
Many of those classes I took were actually hybrid; there was a core set of projected slides that could be mailed out (though they weren't always) that set the agenda and gave the basics and results, but there was a lot of chalkboard use as well, since as long as the room is even modestly large, there's no particular need to use just one or the other.
Graduate-level graph theory in particular used the chalkboard pretty heavily for what were essentially impromptu animations, between the numbers being added to a diagram as whatever algorithm we were learning about progressed, and the gestures being used by the professor.
On the other hand, the lecturers that used a blackboard at my uni all had prepared the lecture, what they wrote was meant to be written in a notebook. They wrote it at a pace that could easily be followed. This allowed me to go over proofs as I wrote them down, and I could then ask right away if there was anything unclear.
I also found several typos (usually a sign error or a missing term) this way, something which would probably have confused me a lot if I didn't catch it until I got home.
So, for me, well-prepared blackboard lectures is preferable, at least for math heavy stuff.
1.Elementary Reading 2.Inspectional Reading 3.Analytical Reading 4.Syntopical Reading
The first 2-3 are covered in the lecture. The time at home can then be spent putting it to paper, applying it in practice (usually in MatLab or some other form of programming), then summarising. That's why I like the lecturers electronic hand-outs, as it can fill the gaps of knowledge that have formed between lecture and study. My background is in EE however, so assumedly this type of learning might not apply as well to pure Math/Physics!
If you weren't stuck with following a chalkboard, typos could be fixed once and for all time at the source, instead of reappearing at random in every lecture.
Merely sitting there passively listening would not be paying full attention.
Of course, this required the lecturers to write in a suitable tempo.
I got a big porcelain board for 5 bucks on eBay because one corner was dented. Best purchase of my life.
It's not a lack of familiarity with melamine boards, it's acute familiarity with incompetent penny-pinching marker supplies. Most public whiteboard lectures involve the search for markers that aren't dry; the organizer might as well be standing there in their whitey-tighties.
Of course, Universities rarely provide Hagoromo chalk, and those of us reading this would also be bringing our own markers to any whiteboard lecture. So if faced with whiteboard conversion, we should speak up for melamine.
Still, I imagine that in five hundred years there will still be Steinway grand pianos, and some people will still prefer sex in person, and some people will prefer using actual blackboards. A whiteboard reminds me of that humiliating scene in "La La Land" where Ryan Gosling plays a solo one-handed on a toy electric piano.
In case you or others aren't aware:
Bathroom tile backer board is commonly sold at big-box home improvement centers for a very low price per 4x8 foot sheet of material. It's the exact same stuff as commonly sold whiteboards, just without the aluminum edging and large price.
I've worked at a couple of employers who had open-plan style work areas, with the walls lined with such boards. Everyone had a set of white-board markers and a rag or eraser, and maybe some windex.
It's a cheap and practical solution for brainstorming and other uses software engineers often find themselves involved in.
Seems like a decent overview
In my opinion (which seems to mostly be shared by other mathematicians), the quality is quite good -- approximately comparable to the Japanese original. Also the price is cheaper, $17.00 for a 72-piece box.
We chalk snobs have breathed a collective sigh of relief.
BTW, there are also circle drawers:
Glad to hear that he's cornered the market on quality chalk!
I have never used an original Blackwing, so I cannot comment on those, but the new ones are enjoyable to write with. It's similar to the feeling I have when using fountain pens – they're such an improvement for the act of writing that I actively seek out reasons to hand-write things.
The specifics of this chalk story versus the Blackwing story are different, but it's neat to see the passion people have for their writing implements. And that many of these, admittedly higher-quality, versions seem to be unable to survive the decrease in hand-written forms.
As for me, I do prefer chalk to whiteboards. I've always been slightly annoyed at getting chalk on my hands and so think I would have enjoyed using this chalk if I'd had the opportunity. But I see fewer and fewer chalkboards around.
[1] https://blackwingpages.com/facts-fiction-and-the-blackwing-e...
I also find disposable markers to be a bit of an environmental horror. In the grand scheme of things maybe it's not that much waste, but replacing something like chalk with a thick plastic non-recycleable marker for little if any gain is disturbing.
Do the manufacturers of this chalk (or any chalk) regularly test for asbestos contamination?
From what I understand, it is kinda the same safety hazard you'd have with cosmetic uses of talc (for makeup and the like); the risk is low for contamination, but it is possible - which is why they do testing on talc (and even then, there is still the possibility of it being present in very, very low amounts).
I'm just wondering if the same applies to chalk?
But I definitely can't imagine replacing either with PowerPoint, of all things.
A clean blackboard is not that fun either. To clean it nicely you need to sweep the whole of it down vertically with a wet sponge. This requires a water source and it's a messy deal. In high-school there was a daily designated pupil who was responsible for wiping down the boards and keeping a wet clean sponge.
Anyway, for the cleaning, he had a flat mop. The lecture hall had three separate boards, so he used them in rotation. When he was finished filling board A with text, he would wipe board B with his mop while recapping the contents of board A. Then he would rinse the mop and leave it in the sink next to the boards. At this point, board C had dried enough from the previous round of cleaning that he could start writing there again.
Overall, an incredibly efficient and fluent process. The gap in writing gave the students enough time to finish copying everything in their notes or taking a short break to drink something, and it gave him enough time to recap the last 10 minutes before moving on to the next section.
I took Calc 2 with a lecturer like this. She had been working there for a few eternities and could probably have taught the wall how to integrate. She had a reputation of being the "easy" professor but after comparing with other students it turned out she actually assigned substantially more work and covered the material faster. Her quality of teaching was just so highly refined that it made the work easier.
https://www.amazon.com/gp/product/B00GXRG64I/
In Germany they outfit classrooms with sinks and squeegees.
Over decades I've tried absolutely everything. I see colleagues in earlier stages of evolution on this (e.g. carrying a squeegee and a bucket), but mathematicians are unbelievably stubborn (think zebra) so one learns not to say anything. This is like debating programming languages: If all parties haven't written significant projects in all languages under debate, just learn to walk away.
Wet or dry, nothing beats a Korean microfiber auto detailing cloth. One or two passes damp (not wet enough to drip while walking) will clean a board better than the overnight cleaning staff. Dry will erase better than any eraser.
Keep in mind that isopropyl alcohol is available at different concentrations, and the different concentrations have different MSDS. Here are the hazard / precautionary statments from the MSDS:
H335 - May cause respiratory irritation P261 - Avoid breathing mist, vapors, spray. P271 - Use only outdoors or in a well-ventilated area.
Note that "avoid breathing mist, vapors, spray" is not an especially strong statement.
https://www.jetpens.com/Rikagaku-Dustless-Chalk-Accessories/...