I think that this is definitely not true. There are lots of things where an "aha!" moment makes things appear conceptually much simpler after you've internalized the framework, but there are plenty of things in what I consider my area of expertise that are still hard even though I know very well how.
No. I'm talking about modern LaTeX. You can easily write é outside of math mode, but not inside. By default, you cannot write α either inside nor outside of math. By using the right packages, you can do both, but other things break.
Yes, that is the problem, precisely. Lualatex and xelatex do not support all the features of plain latex (mostly "hacky" things, like pdf controls, js animations in beamer, etc). So, you have to chose between using these features and being able to type unicode letters directly.
Probably there is a magic combination of engines and packages that allows to do everything at the same time, but I haven't found it.
If this works natively in typst, it's a great selling point for me (although I dislike the markdown-like syntax).
Uh, pdftex, xetex and luatex should support everything of the original tex engine, but each has extended tex, so some things will work on pdftex (which I think is what you're thinking of as plain latex), others on xetex and then others on luatex (or pairs of engines, I know microtype works on pdftex and luatex, but not xetex). I don't think this is an tex specific problem, more a natural result when there's multiple implementations.
I suspect as typst only has a single implementation (I believe), it won't have the problem of different engines ;)
"Here the results were better than previous models, but still slightly disappointing: the new model could work its way to a correct (and well-written) solution if provided a lot of hints and prodding, but did not generate the key conceptual ideas on its own, and did make some non-trivial mistakes. The experience seemed roughly on par with trying to advise a mediocre, but not completely incompetent, (static simulation of a) graduate student. "
I'm not sure who is the audience for this, but if it is students then it is not going to be very helpful, IMHO. For students to get it the authors must give concrete examples.
Let me pick on B, on spaced learning and interleaving. In those two paragraphs there are no concrete examples. If a student asks, "OK, I'm at the library and I have my book open. What do I do?" then the answer is not there.
I'll talk about college math because that's what I teach.
If you want students to learn what to do, you have to tell them. Maybe, "Set your timer to a half hour, pick out five problems, three from the current section and two from sections you did last week, and do them. If you get stuck take a peek at the answer, but don't peek until you are stuck. If you get really stuck, mark the question in your notebook and ask about it at the start of the next class. But under no circumstances just read the book." Then you have told them how to practice recall and to interleave in a way that they can actually do it.
Four half hours remembering how to do both current problems and also some from before for every hour spent in class is a good whack at learning the class's material, at least in the first two years.
Just using the two words recall and interleave is not enough.
In its impact on teaching, I'll say that based on teaching since 1979, students take feeling stupid as convincing evidence that their instructor is doing a bad job. No amount of assuring them that it is the gateway to enlightenment or however you put it will save you.
I've become convinced that, in the end, no one really teaches you anything, you end up teaching yourself. That phrasing is a bit hyperbolic. It's more accurate to say a good teacher only gets you 50%, 60%, maybe 70% of the way there, and it's up to you to get you to 100%.
To be able to truly learn any given concept means being capable of answering a practically infinite number of different questions about that topic. The process of teaching is essentially trying to uncover which questions the student can't answer. The challenge, of course, is that the student doesn't know what questions they can't answer, because the questions haven't occurred to them. That is, until they start testing themselves, to see if they really do understand the concept.
Problem sets in textbooks are the canonical way of addressing this teaching challenge, but there are only so many pages in a textbook, and there are other concepts that need to be taught, so the scope of the problem sets are necessarily finite.
How many times have you nailed all the problems in a book, only to discover that there was some aspect of the topic you didn't understand, despite getting all the right answers?
The following two quotes from Martial Arts have been quite helpful to me in motivating my study efforts;
The Master shows the Gate, but it is the Student who has to walk through it.
To show one the Right Direction and Right Path, Oral Instructions from a Master are necessary but Mastery of the Subject only comes from one's own Incessant Self-Cultivation.
There is also a great inspirational story in the Mahabharata of "Ekalavya" (https://en.wikipedia.org/wiki/Ekalavya) who became an exceptional archer through self-training.
Eklavya inspires a life-long learning philosophy and his presence seems to be a celebration for the masses. In this EklavyaParv, the motto is 'You Create Yourself" and the legend of Eklavya is a testimony that is forwarded by many thinkers as well. The discipleship that Eklavya represents is the best for a student and enables one to be the creator of one's own destiny.
Adapting to current times, "The Master" can be a "Good Book" and you can have "Many Masters" but the effort and learning has to happen within the Student.
Source: I self-taught myself Martial Arts (JKD, Karate, Taijiquan) from books when i was young. Decades later when i did join a dojo to study under a Master, i was one of the top students with good skill and power.
> [...] my Rebbe was the geologist of the soul. You see, there are so many treasures in the earth. There is gold, there is silver, and there are diamonds. But if you don’t know where to dig, you’ll find only dirt and rocks and mud. The Rebbe can tell you where to dig, and what to dig for, but the digging you must do yourself.
"I self-taught myself Martial Arts (JKD, Karate, Taijiquan) from books when i was young."
This is very interesting and impressive. How common would you think a complete self-study of martial arts actually is? I've always thought this cannot be done alone -- or, it would be extremely easy to get lost or head to some wrong direction, eventually harming yourself mentally or physically. Akin to how a common suggestion about yoga or meditation (I used to exercise vipassana daily for quite a while) is that the first, basic principles should be taught by a good master. Possibly due to personality type, I've always wanted to challenge this assumption, though.
While learning martial arts on your own, what did you do to overcome more serious mental blocks or standstills (provided you had any)? Did you ever feel that "books are not enough"?
Looking back, that self-study of Martial Arts has been the single most defining time period (I did this in the late 80s to early 90s in India) of my Life and has directly led to my Physical Health, Self-Confidence, Self-Reliance, Mental Fortitude and Persistence in the face of hardships today, all of which are fundamental to Life. I did the above along with a study of Yoga and to this day maintain a large collection of books (of Yoga/Martial Arts/Ayurveda/Siddha/TCM/Qigong/Acupuncture) dealing with both Physical Techniques and Mental Aspects/Theory behind them.
The key aspects in learning were Overwhelming Drive (the motivation was to learn to fight like Bruce Lee :-), daily practice of basic blocks/punches/kicks, slowly progressing through the movements of the shadow-boxing/Kata routines given in the books and no self-questioning/self-doubt/no-comparing with anybody else. I also had a good friend who was also very interested in Martial Arts (he eventually joined a Shotokan Karate school) and so we would practice/encourage each other. One defining lucky moment was coming across E.J.Harrison's "The Manual of Karate" (which was a translation of a Japanese text) where the author explicitly states Karate is useless without makiwara style training/conditioning. I took that to heart and made a canvas pillow with coconut-matting, tied that to a tree (a small one which could vibrate and absorb your hits) and would train with full power on it. This worked so well that my basic punches/kicks became more powerful than my Shotokan-training friend who only did non-contact practice. To this day i can generate very good power relative to my size. Reading Gichin Funakoshi's "Karate-Do : My way of Life" was also instrumental where he mentions his two teachers and their instructions; Master Azato would tell him to think of his limbs as swords so that he went through his opponents and Master Itosu would tell him to harden/condition his body so that he could absorb any blow. Next it was Miyamoto Musashi's "The Book of Five Rings" which led me to studying Martial Arts mindset/strategy/theory and validated my approach since he was also largely self-taught in many disciplines (the concept of "Hyoho/Heiho" acquired in the study of one discipline is internalized and then used to study other disciplines effectively/effortlessly).
Today you have far more resources and avenues open to study Martial Arts but the main points i mentioned above must be kept in mind even though many teachers may not teach you those. As mentioned in the quote above, Mastery is always dependent on "one's own incessant self-cultivation".
In my previous comment i pointed to the essence that you need to focus on whether you are studying under a Master or by Yourself (harder). For actual techniques you can choose books by noted masters (eg. Mas Oyama, Masatoshi Nakayama) in the style you are interested in on Amazon. For insight/details into Martial Arts mental training and theories see the works translated by William Scott Wilson (https://en.wikipedia.org/wiki/William_Scott_Wilson).
Ever since early adolescence, I've had interest in mind-body relations/balance -- as in, how physical actions are "mental" (=thinking), and how mental actions are "physical" (=doing). So these references are really great. I'll most probably look into the William Scott Wilson works first. Many thanks again for sharing your knowledge and experiences!
This 100%. I taught myself *everything* in college. I relied on textbooks and online resources to teach myself the material outside of class. It worked pretty well. I wasn't the top of my class, nor have I retained all the things I've learned (but who does?).
Fortunately, what I have retained is the ability to pick up almost any subject and learn about it on my own. That's more important than anything they can teach you in a classroom.
I would claim there is no 100%. At least in engineering my professors were saying (paraphrasing) that it's all about trade-offs and most of the times there is not "one answer". I think many education systems (up to graduate at least) instill the idea that there is always "one answer" which has many bad repercussions later (people seeing things in black and white).
I don't think a student needs to always answer a question "on the spot". Being able to find an answer in a reasonable amount of time and explain an answer would be in my opinion more valuable. So then it's more about "how efficient can the student give the answer to the question" (answer on the spot, spend one hour, spend one week, etc.).
Tangentially, modern educational paradigms also characterize learning as a process of construction happening within the student's mind, rather than a transfer of knowledge.
Idk, one good prof made me a fifty percent better mathematician in a single course. I would have to slam my head in the wall for a year or two to do it without him.
I'm a recent graduate, but also worked in colleges for a couple of decades. Students I've interacted with almost universally blame themselves first when they don't get something. Only when they see many fellow students in the same boat do they tend to blame the teacher. From my vantage point it seems you're either assuming their frustration with the subject is frustration with the instructor, or overgeneralizing based on non-representative students, a non-representative subject, or... a non-representative instructor. I'm not trying to be a jerk, but career longevity wasn't a great indicator of pedagogical insight or its prerequisite EQ.
A good teacher can offer some tools and methods (as in methods of "learning to learn") to bridge the gap between stupidity and (for lack of a better meaning) "enlightenment" Something especially my math teachers in general lacked..
I disagree. I think good students judge their teachers based on how motivated and passionate the teachers themselves are about a topic.
Though I've had classes where I only realized their importance multiple semesters after having them. (Mostly the non technical, business classes)
I had a junior helpdesk employee that I was training/mentoring years back. He was 20 years old, fresh out of tech school. He was good at what he did, but he only did things he knew how to do. When he didn't know something, he'd ask me. Which is great. I'd say "Well, this sounds like DNS, it's like a phone book..." or "That's an APIPA address, it must not be getting DHCP. The computer shouts out to the network asking for an address..." and so forth. However, he kept asking the same questions.
After a few months in one of our monthly meetings he kind of broke "I don't understand what I'm doing out there, you need to train me! I need to be trained!" Completely perplexed I asked him what he was talking about. "You just answer my questions, but you're not training me!" I realized he was expecting me to learn him the answers to everything. I had to explain to him that the responsibility of learning was actually on him. "This isn't school, there's no study guide. We have documentation and Google. It's your responsibility to read it and make sense of it."
I told him that I can give him all the puzzle pieces but I can't put them together for him. To be fair, helpdesk is kind of about making things work and remembering the quick fixes and tricks for things to close out your tickets.
So I said, "Ok, I think you need a project. What do you do at home for fun?"
"Well I play a lot of video games."
"Perfect, we're setting up a Minecraft server". He laughed.
I said "No, I'm serious. We're using like 5% of this massively overblown server that was sold to us. Maybe this will help you put the pieces together."
I gave him a restricted vSphere account for his DMZ'd VM, sent him a guide and unleashed him.
"Well, I've never done this before..."
"Exactly. That's how you learn my dude."
"But..."
"RTFM"
"This VM doesn't do anything."
"Right, it needs an OS."
"We'll how do I install one?"
"Here's a guide."
"I installed the OS, how do I get into it?"
"SSH"
"No I mean the desktop."
"There isn't one."
And so he learned that a computer isn't the Windows desktop.
"I can't SSH in, it says connection refused."
"Right, that's the firewall."
"Well what do I do?"
"Google UFW"
"I can't SSH in anymore, it says connection timed out."
"Can you ping it?"
"No."
"Check the IP address in vSphere"
"It changed..."
"Why?" I asked.
"DHCP...! That's what a static IP is for!"
From then on he finally understood that learning actually takes a little effort and curiosity AND yes, it's OK to Google things. He had this idea that he had to know everything, memorize everything, and looking things up was "cheating". Not knowing something and feeling dumb is actually where learning happens rather than pure repetition.
About a year later he thanked me and said that he completely misunderstood my motivations initially and that he thought I was brushing him off and being lazy, when in reality I was giving him the opportunity to learn by not feeding him every detail. He felt like he was failing because he didn't know all the answers and said that he looked back at himself a year ago and couldn't believe what he was doing now and how far he'd come. "I had no idea what an IP address was but now I understand how the packets move through the switches, request an address..." etc.
We both ended up quitting and going our separate ways as the IT department there was an absolute shitshow. He's now a sysadmin and we chat now and then and he's mentioned that he's actually glad he learned in such a fucked up environment because you were absolutely forced to understand due to all the ridiculous hacks and workarounds that had been piled on over the years. Nothing could be taken for granted.
I learned in a similar way and I think trial by fire may be one of the best teachers. "Smooth seas never made a skilled sailor."
Learning only happens through a mish-mash of Trial-and-Error, Trial-by-Fire, Questioning, Curiosity, Reading/Copying/Mimicking, Thinking, Reflecting and finally Doing. All of the above are needed in some measure.
The trick is to do the above without losing our self-confidence in ourselves (we are guaranteed to feel "stupid" during the learning process) that "we can grok it" at some level and over a period of time. The problem today is that there is so many aspects and so much to learn about any one thing that students are trying to move very fast to learn everything which is an impossibility; they need to ruthlessly cut down on all inessentials and learn to focus on only one or two core things i.e. "sift the wheat from the chaff".
Predicting exponential functions is a fool’s errand. The tiniest error in your initial observation compounds real fast and we can’t even tell if we’re still in the exponential phase of the sigmoid.
