I have the privilege of working with a small group of young (12-14) highly gifted math students for 45 minutes a week for the next 5 weeks. I have extraordinary freedom with what we cover. Mathematically, we’ve covered some game theory and Bayes’ theorem. I’ve also had a chance to discuss some non-mathy things, like Anki.
I only found out about Anki after I’d taken a bunch of courses, and I’ve had to spend a bunch of time restudying everything I’d previously learned and forgotten. It would have been really nice if someone had told me about Anki when I was 12.
So, what I want to ask Lesswrong, since I suspect most of you are like the kids I’m working with except older, is what blind spots did 12-14-year-old you have I could point out to the kids I’m working with?
Heh, if I was 12-14 these days, the main message I would send to me would be: Start making and publishing mobile games while you have a lot of free time, so when you finish university, you have enough passive income that you don’t have to take a job, because having a job destroys your most precious resources: time and energy.
(And a hyperlink or two to some PUA blogs. Yeah, I know some people object against this, but this is what I would definitely send to myself. Sending it to other kids would be more problematic.)
I would recommend Anki only for learning languages. For other things I would recommend writing notes (text documents); although this advice may be too me-optimized. One computer directory called “knowledge”, subdirectories per subject, files per topic—that’s a good starting structure; you can change it later, if you need. But making notes becomes really important at the university level.
I would stress the importance of other things than math. Gifted kids sometimes focus on their strong skills, and ignore their weak skills—they put all their attention to where they receive praise. This is a big mistake. However, saying this without providing actionable advice does not help. For example, my weak spots were exercise and social skills. For social skills a list of recommended books could help; with emphasis that I should not only read the books, but also practice what I learned. For exercise, a simple routine plus HabitRPG could do the job. Maybe to emphasise that I should not focus on how I compare with others, but how I compare with yesterday’s me.
Something about an importance of keeping contact with smart people, and insanity of the world in general. As a smart person, talking with other smart people increases your powers: both because you develop with them the ideas you understand, and because you can ask them about things you don’t understand. (A stupid person will not understand what you are saying, and will give you harmful advice about things you asked.) In school you are supposed to work alone, but in real life a lot of success is achieved by teams; but the best teams are composed of good people, not of random people.
Another advice that is risky to give to other kids: Religion is bullshit and a waste of time. People will try to manipulate you, using lies and emotional pressure. Whatever other positive traits they have, try to find other people that have the same positive traits, but without the mental poison; even if it takes more time, it’s worth it.
Some actionable advice: Keep written notes about people (don’t let them know about that). For every person, create a file that will contain their name, e-mail, web page, facebook link, etc., and the information about their hobbies, what you did together, whom they know, etc. Plus a photo.
This will come very useful if you haven’t been in contact with the person for years, and want to reconnect. (Read the whole file before you call them, and read it again before you meet them.) Bonus points if you can make the information searchable, so you can ask queries like “Who can speak Japanese?” or “Who can program in Ruby?”.
This may feel a bit creepy, but many companies and entrepreneurs do something similar, and it brings them profit. And the people on the other side like it (at least if they don’t suspect you to use a system for this). Simply think about your hard disk as your extended memory. There would be nothing wrong or creepy if you simply remembered all this stuff; and there are people with better memory who would.
Maybe make some schedule to reconnect with each person once in a few years, so they don’t forget you completely. This also gives you an opportunity to update the info.
If you start doing it while young, your high-school and university classmates will already make a decent database. Then add your colleagues. You will appreciate it ten years later, when you would naturally forget most of them.
When you have a decent database, you can provide useful social service by connecting people. -- Your friend X asks you: “Do you know something who can program in Ruby?” “Uhm, not sure, but let me make a note and I’ll think about it.” Go home, look at the database. Find Y. Ask Y whether it is okay to give their contact to someone interested in Ruby. Give X contact to Y. At this moment, your friend X owes you a favor, and if X and Y do some successful business, also Y owes you a favor. The cost of you is virtually zero; apart from costs of maintaining the database, which you would do anyway.
An important note is that of course there is a huge difference between close friends and random acquaintances, but both can be useful in some situations, so you want to keep a database for both. Don’t be selective. If your database has too much people, think about better navigation, but don’t remove items.
I’m inclined to ask: Are there ready-made software solutions for this or should I roll my own in Python or some office program? If it wasn’t for the secretive factor I’d write a simple program to put on my github and show off programming skills.
I don’t know. But if I really did it (instead of just talking that this is the wise thing to do), I would probably use some offline wiki software. Preferably open source. Or at least something I can easily extract data from if I change my mind later.
I would use something like wiki—nodes connected by hyperlinks—because I tried this in the past with hierarchical structure, and it didn’t work well. Sometimes a person is a member of multiple groups, which makes classification difficult. Or if you have a few dozen people in the database, it becomes difficult to navigate (which in turn becomes a trivial inconvenience for adding more people, which defeats the whole purpose).
But if every person (important or unimportant) has their own node, and you also create nodes for groups (e.g. former high school classmates, former colleagues from company X, rationalists,...), you can find anyone with two clicks: click on the category, click on the name. Also the hyperlinks would be useful to describe how people are connected with each other. It would be also nice to have automatic collections of nodes that have some atrribute (e.g. can program in Ruby); but you can manually add the links in both directions.
A few years ago I looked at some existing software, a lot of it was nice, but missed a feature or two I considered important. (For example, didn’t support Unicode, or required web server, or just contained too many bugs.) In hindsight, if I would just use one of them, for example the one that didn’t support Unicode, it would still be better than not having any.
Writing your own program… uhm, consider planning fallacy. Is this the best way to use your time? And by the way, if you do something like that, make it a general-purpose offline Unicode wiki-like editor, so that people can also use it for many other things.
One can read in one’s spare time or learn languages or act. If one does not come from wealth not majoring in something remunerative in college is a mistake if you will actually want money later.
He didn’t dismiss the humanities he said studying them at university was a poor decision.
He didn’t dismiss the humanities he said studying them at university was a poor decision.
Moreover, it wasn’t really presented as general advice, but advice for their own younger version. It’s not generally applicable advice (not everyone will be happy or successful in STEM fields), but I think it’s safe to assume it is sound advice for Young!nydwracu.
Or even if it was intended as generally applicable advice, it’s still directed at kids gifted at mathematics, who will have a high likelihood of enjoying STEM fields.
My parents made me study business management instead of literature. My life has been much more boring and unfulfilling as a result, because the jobs I can apply for don’t interest me, and the jobs I want demand qualifications I lack. In my personal experience, working in your passion beats working for the money.
Why haven’t you gone back to college for a Masters in English Literature or something along those lines? Robin Hanson was 35 before he got his Ph.D. in Economics and he’s doing ok. The market for humanities scholars is not as forgiving as that for Economics but that’s what you want, right?
The implicit claim that humanities jobs are uniformly non-remunerative seems difficult to support.
if you will actually want money later
How about doing a humanities major to make connections to people who are any combination of rich, creative, or interesting and teaching yourself to program in the meantime?
There’s a difference between choosing a subject as your college major (which amounts to future employment signalling) and engaging in the study of a subject.
It was a blind spot that I had until my senior year of college, when I realized that I wanted to make a lot of money, and that it was very unlikely that majoring in philosophy would let me do so. Had I realized this at 12-14, I would’ve saved myself a lot of time; but I didn’t, so I’m probably going to have to go back for another degree.
If you don’t care about money or you have the connections to succeed with a non-STEM degree, that’s another thing. But that’s not the question that was asked.
I never learned how to put forth effort, because I didn’t need to do so until after I graduated high school.
I got into recurring suboptimal ruts, sometimes due to outside forces, sometimes due to me not being agenty enough, that eroded my conscientiousness to the point that I’m quite terrified about my power (or lack there of) to get back to the level of ability I had at 12-14.
I suppose, if I had to give my younger self advice in the form of a sound-byte, it’d be something like: “If you aren’t—maybe at least monthly—frustrated, or making less progress than you’d like, you aren’t really trying; you’re winning at easy mode, and Hard Mode is likely to capture you unprepared. Of course, zero progress is bad, too, so pick your battles accordingly.”
Also, even if you’re on a reasonable difficulty setting, it pays to look ahead and make sure you aren’t missing anything important. My high school calculus teacher missed some notational standards in spite of grasping the math, and her first college-level course started off painful for it; I completely missed the cross and dot products in spite of an impressive math and physics High school transcript, and it turns out those matter a good deal (and at the time, the internet was very unsympathetic when I tried researching them).
Speaking as a somewhat gifted seventeen year old, I’d really like to have known about AoPS, HPMOR and the Sequences.
Also, I’d like to have had in my mind the notion that my formal education is not optimised for me, and that I really need to optimise it myself. Speaking more concretely, I think that most teenagers in Britain pick their A Levels (if they do them at all) based on what classes the other people around them are doing, which isn’t very useful. Speaking to a friend though, I realised that when he was picking his third A Level to study, there was no other A Level he needed to study to get into his main area of specialisation (jazz musician), and his time would be better spent not doing the A level at all; he needed to think more meta. He was just doing an A level because that’s what everyone seems to think you should do. I’m about to give up a class because it’s not going to help me get anywhere, I can use the time better and learn what I want to better alone anyway. So, really optimise.
Don’t know if that helps. And AoPS is ridiculously useful.
Instill the importance of a mastery orientation (basically, optimizing for developing skills rather than proving one’s innate ability). My 12-14 year old self had such a strong performance orientation as to consider things like mnemonics and study skills to be only for the lazy and stupid. Anyone stuck in the performance orientation won’t even be receptive to things like Anki.
I had these blind spots as a 20some year old, so I assume I had them when I was 12-14 too:
I assumed that if I was good at something, I would be good at it forever. Turns out skills atrophy over time. Surprise! (This seems similar to your Anki revelation.)
I am agenty. I had no concept of the possibility that I might be able to cause* some meaningful effect outside my immediate circle of interaction.
* I did, of course, daydream about becoming rich and famous through no fault of my own; I wouldn’t say I actually expected this to happen, but I thought it was more likely than becoming rich and famous under my own steam.
I have been in such a program when I was 12-14 (run by the William Stern foudnation in Hamburg, Germany) and the curriculum consisted mostly of very diverse ‘math’ problems prepared in a way to make them accessible to us in a func way without introducing too much up-front terminology or notation. Examples I remember of the spot:
turing machines (dresses as short-sighted busy beavers)
Drawing fractals (the iterated function ones; with printouts of some)
In general only an exposition was given and no task to solve. Or some introductory initial questions, The patterns to be detected were the primary reward.
We were not introduced to really practical applications but I’m unsure whether that had been helpful or rather whether it had been interesting. My interest at that time stemmed from the material being systematic patterns that I could approach abstractly and symbolically and ‘solve’. I’m not clear whether the Sequences would have been interesting in that way. Their patterns are clear only in hindsight.
What should work is Bayes rule—at least in the form that can be visualized (tiling of the 1⁄1 grid) or symbolcally derived easily.
Also guessing and calibration games should work. You can also take standard games and add some layer of complexity on them (but please not arbitrary but helpful ones; a minimum example is: Play Uno but cards don’t have to match color+number but some number theoretic identity e.g. +(2,5) modulo (4,10)).
Yes of course. That and we tried variations of the rule-set. We also discovered the flyer.
It is interesting what can come out of this seed. When I later had an Atari I wrote an optimized simulator in assembly which aggregated over multiple cells and I even tried to use the blitter reducing the number of clock cycles per cell as far as I could. This seed become a part of the mosaic of concepts that sits behind understanding complex processes now.
The story goes as follows (translated from German):
“Once I dreamed that there was an island called “the island of dreams”. The inhabitants of the island dreamed very vivid and lucid. Indeed the imaginations which occurred during sleep are as clear and present as perceived during waking. Even more their dreamlife follows from night to night the same continuity as their waking perception during the day. Consequently some inhabitants have difficulties to distinguish whether they are awake or asleep.
Now every inhabitant belongs to one of two groups: Day-type and night-type. The inhabitants of day-type are characterized by their thinking during the day being true and during the night being false. For the night-type it is the opposite: Their thoughts during sleep are true and those during waking are false.”
Questions:
Once an inhabitant though/believed that he belonged to the day-type. Kann be tested whether this is true? Was be awake or asleep at the time of the thought?
I think most of my blindspots before roughly the age of 18 involved not understanding that I’m personally responsible for my success and the extent of my knowledge and that “good enough” doesn’t cut it. If I were to send a message back to 14-year-old!Me, I’d tell him that he has a lot of potential, but that he can’t rely on others to fulfill that potential.
I don’t know how much of this falls under your remit, but I had quite a few educational blind-spots I inherited from my parents, who didn’t come from a higher-educated background. If any of your students are in a similar position, it’s worth checking they don’t have any ludicrous expectations out of the next several years of education which no-one close to them is in a position to correct.
I’m not sure any specific examples from my own experience would generalise very well.
If I were to translate my comment into a specific piece of generally-applicable advice, it would be to give students a realistic overview of what their forthcoming formal education involves, what it expects from them, and what options they have available.
As mentioned, this may be outside of the OP’s remit.
One example: certain scholastic activities are simply less important than others. If your model is “everything given to me by an authority figure is equally important”, you don’t manage your workload so well.
No. I know one of my former teachers outside of school, and we decided it would be a good thing if I ran an afterschool program for the mathcounts kids after it had ended.
I have the privilege of working with a small group of young (12-14) highly gifted math students for 45 minutes a week for the next 5 weeks. I have extraordinary freedom with what we cover. Mathematically, we’ve covered some game theory and Bayes’ theorem. I’ve also had a chance to discuss some non-mathy things, like Anki.
I only found out about Anki after I’d taken a bunch of courses, and I’ve had to spend a bunch of time restudying everything I’d previously learned and forgotten. It would have been really nice if someone had told me about Anki when I was 12.
So, what I want to ask Lesswrong, since I suspect most of you are like the kids I’m working with except older, is what blind spots did 12-14-year-old you have I could point out to the kids I’m working with?
Heh, if I was 12-14 these days, the main message I would send to me would be: Start making and publishing mobile games while you have a lot of free time, so when you finish university, you have enough passive income that you don’t have to take a job, because having a job destroys your most precious resources: time and energy.
(And a hyperlink or two to some PUA blogs. Yeah, I know some people object against this, but this is what I would definitely send to myself. Sending it to other kids would be more problematic.)
I would recommend Anki only for learning languages. For other things I would recommend writing notes (text documents); although this advice may be too me-optimized. One computer directory called “knowledge”, subdirectories per subject, files per topic—that’s a good starting structure; you can change it later, if you need. But making notes becomes really important at the university level.
I would stress the importance of other things than math. Gifted kids sometimes focus on their strong skills, and ignore their weak skills—they put all their attention to where they receive praise. This is a big mistake. However, saying this without providing actionable advice does not help. For example, my weak spots were exercise and social skills. For social skills a list of recommended books could help; with emphasis that I should not only read the books, but also practice what I learned. For exercise, a simple routine plus HabitRPG could do the job. Maybe to emphasise that I should not focus on how I compare with others, but how I compare with yesterday’s me.
Something about an importance of keeping contact with smart people, and insanity of the world in general. As a smart person, talking with other smart people increases your powers: both because you develop with them the ideas you understand, and because you can ask them about things you don’t understand. (A stupid person will not understand what you are saying, and will give you harmful advice about things you asked.) In school you are supposed to work alone, but in real life a lot of success is achieved by teams; but the best teams are composed of good people, not of random people.
Another advice that is risky to give to other kids: Religion is bullshit and a waste of time. People will try to manipulate you, using lies and emotional pressure. Whatever other positive traits they have, try to find other people that have the same positive traits, but without the mental poison; even if it takes more time, it’s worth it.
Social capital is important. Build it.
Peer pressure is far more common and far more powerful than you think. Find an ingroup that puts it to constructive ends.
Don’t major in a non-STEM field. College is job training and a networking opportunity. Act accordingly.
Something about time management, pattern-setting, and motivation management—none of which I’ve managed to learn yet.
Some actionable advice: Keep written notes about people (don’t let them know about that). For every person, create a file that will contain their name, e-mail, web page, facebook link, etc., and the information about their hobbies, what you did together, whom they know, etc. Plus a photo.
This will come very useful if you haven’t been in contact with the person for years, and want to reconnect. (Read the whole file before you call them, and read it again before you meet them.) Bonus points if you can make the information searchable, so you can ask queries like “Who can speak Japanese?” or “Who can program in Ruby?”.
This may feel a bit creepy, but many companies and entrepreneurs do something similar, and it brings them profit. And the people on the other side like it (at least if they don’t suspect you to use a system for this). Simply think about your hard disk as your extended memory. There would be nothing wrong or creepy if you simply remembered all this stuff; and there are people with better memory who would.
Maybe make some schedule to reconnect with each person once in a few years, so they don’t forget you completely. This also gives you an opportunity to update the info.
If you start doing it while young, your high-school and university classmates will already make a decent database. Then add your colleagues. You will appreciate it ten years later, when you would naturally forget most of them.
When you have a decent database, you can provide useful social service by connecting people. -- Your friend X asks you: “Do you know something who can program in Ruby?” “Uhm, not sure, but let me make a note and I’ll think about it.” Go home, look at the database. Find Y. Ask Y whether it is okay to give their contact to someone interested in Ruby. Give X contact to Y. At this moment, your friend X owes you a favor, and if X and Y do some successful business, also Y owes you a favor. The cost of you is virtually zero; apart from costs of maintaining the database, which you would do anyway.
An important note is that of course there is a huge difference between close friends and random acquaintances, but both can be useful in some situations, so you want to keep a database for both. Don’t be selective. If your database has too much people, think about better navigation, but don’t remove items.
I’m inclined to ask: Are there ready-made software solutions for this or should I roll my own in Python or some office program? If it wasn’t for the secretive factor I’d write a simple program to put on my github and show off programming skills.
I don’t know. But if I really did it (instead of just talking that this is the wise thing to do), I would probably use some offline wiki software. Preferably open source. Or at least something I can easily extract data from if I change my mind later.
I would use something like wiki—nodes connected by hyperlinks—because I tried this in the past with hierarchical structure, and it didn’t work well. Sometimes a person is a member of multiple groups, which makes classification difficult. Or if you have a few dozen people in the database, it becomes difficult to navigate (which in turn becomes a trivial inconvenience for adding more people, which defeats the whole purpose).
But if every person (important or unimportant) has their own node, and you also create nodes for groups (e.g. former high school classmates, former colleagues from company X, rationalists,...), you can find anyone with two clicks: click on the category, click on the name. Also the hyperlinks would be useful to describe how people are connected with each other. It would be also nice to have automatic collections of nodes that have some atrribute (e.g. can program in Ruby); but you can manually add the links in both directions.
A few years ago I looked at some existing software, a lot of it was nice, but missed a feature or two I considered important. (For example, didn’t support Unicode, or required web server, or just contained too many bugs.) In hindsight, if I would just use one of them, for example the one that didn’t support Unicode, it would still be better than not having any.
Writing your own program… uhm, consider planning fallacy. Is this the best way to use your time? And by the way, if you do something like that, make it a general-purpose offline Unicode wiki-like editor, so that people can also use it for many other things.
ISTR there’s something in the Evernote family that does this.
Downvoted for dismissing the humanities.
One can read in one’s spare time or learn languages or act. If one does not come from wealth not majoring in something remunerative in college is a mistake if you will actually want money later.
He didn’t dismiss the humanities he said studying them at university was a poor decision.
Moreover, it wasn’t really presented as general advice, but advice for their own younger version. It’s not generally applicable advice (not everyone will be happy or successful in STEM fields), but I think it’s safe to assume it is sound advice for Young!nydwracu.
Or even if it was intended as generally applicable advice, it’s still directed at kids gifted at mathematics, who will have a high likelihood of enjoying STEM fields.
My parents made me study business management instead of literature. My life has been much more boring and unfulfilling as a result, because the jobs I can apply for don’t interest me, and the jobs I want demand qualifications I lack. In my personal experience, working in your passion beats working for the money.
How sure are you what your life would have been like if you had studied literature instead?
Why haven’t you gone back to college for a Masters in English Literature or something along those lines? Robin Hanson was 35 before he got his Ph.D. in Economics and he’s doing ok. The market for humanities scholars is not as forgiving as that for Economics but that’s what you want, right?
After some years of self-analysis and odd jobs, I’m close to finishing a second degree in journalism.
The implicit claim that humanities jobs are uniformly non-remunerative seems difficult to support.
How about doing a humanities major to make connections to people who are any combination of rich, creative, or interesting and teaching yourself to program in the meantime?
There’s a difference between choosing a subject as your college major (which amounts to future employment signalling) and engaging in the study of a subject.
It was a blind spot that I had until my senior year of college, when I realized that I wanted to make a lot of money, and that it was very unlikely that majoring in philosophy would let me do so. Had I realized this at 12-14, I would’ve saved myself a lot of time; but I didn’t, so I’m probably going to have to go back for another degree.
If you don’t care about money or you have the connections to succeed with a non-STEM degree, that’s another thing. But that’s not the question that was asked.
I never learned how to put forth effort, because I didn’t need to do so until after I graduated high school.
I got into recurring suboptimal ruts, sometimes due to outside forces, sometimes due to me not being agenty enough, that eroded my conscientiousness to the point that I’m quite terrified about my power (or lack there of) to get back to the level of ability I had at 12-14.
I suppose, if I had to give my younger self advice in the form of a sound-byte, it’d be something like: “If you aren’t—maybe at least monthly—frustrated, or making less progress than you’d like, you aren’t really trying; you’re winning at easy mode, and Hard Mode is likely to capture you unprepared. Of course, zero progress is bad, too, so pick your battles accordingly.”
Also, even if you’re on a reasonable difficulty setting, it pays to look ahead and make sure you aren’t missing anything important. My high school calculus teacher missed some notational standards in spite of grasping the math, and her first college-level course started off painful for it; I completely missed the cross and dot products in spite of an impressive math and physics High school transcript, and it turns out those matter a good deal (and at the time, the internet was very unsympathetic when I tried researching them).
Speaking as a somewhat gifted seventeen year old, I’d really like to have known about AoPS, HPMOR and the Sequences.
Also, I’d like to have had in my mind the notion that my formal education is not optimised for me, and that I really need to optimise it myself. Speaking more concretely, I think that most teenagers in Britain pick their A Levels (if they do them at all) based on what classes the other people around them are doing, which isn’t very useful. Speaking to a friend though, I realised that when he was picking his third A Level to study, there was no other A Level he needed to study to get into his main area of specialisation (jazz musician), and his time would be better spent not doing the A level at all; he needed to think more meta. He was just doing an A level because that’s what everyone seems to think you should do. I’m about to give up a class because it’s not going to help me get anywhere, I can use the time better and learn what I want to better alone anyway. So, really optimise.
Don’t know if that helps. And AoPS is ridiculously useful.
Instill the importance of a mastery orientation (basically, optimizing for developing skills rather than proving one’s innate ability). My 12-14 year old self had such a strong performance orientation as to consider things like mnemonics and study skills to be only for the lazy and stupid. Anyone stuck in the performance orientation won’t even be receptive to things like Anki.
This. My upbringing screwed me up horribly in this respect.
I had these blind spots as a 20some year old, so I assume I had them when I was 12-14 too:
I assumed that if I was good at something, I would be good at it forever. Turns out skills atrophy over time. Surprise! (This seems similar to your Anki revelation.)
I am agenty. I had no concept of the possibility that I might be able to cause* some meaningful effect outside my immediate circle of interaction.
* I did, of course, daydream about becoming rich and famous through no fault of my own; I wouldn’t say I actually expected this to happen, but I thought it was more likely than becoming rich and famous under my own steam.
I have been in such a program when I was 12-14 (run by the William Stern foudnation in Hamburg, Germany) and the curriculum consisted mostly of very diverse ‘math’ problems prepared in a way to make them accessible to us in a func way without introducing too much up-front terminology or notation. Examples I remember of the spot:
turing machines (dresses as short-sighted busy beavers)
generalized Nim really with lots of matches
tilings of the plane
conveys game of life (easy on paper)
More I just looked up in an older folder:
distance metrics on a graph
multi-way balances
continuous fractions (cool for approximations; I still use this)
logical derivations about beliefs of people whose dream are indistinuishable from reality
generalized magical squares
Fibinacci sequences and http://en.wikipedia.org/wiki/Missing_square_puzzle
Drawing fractals (the iterated function ones; with printouts of some)
In general only an exposition was given and no task to solve. Or some introductory initial questions, The patterns to be detected were the primary reward.
We were not introduced to really practical applications but I’m unsure whether that had been helpful or rather whether it had been interesting. My interest at that time stemmed from the material being systematic patterns that I could approach abstractly and symbolically and ‘solve’. I’m not clear whether the Sequences would have been interesting in that way. Their patterns are clear only in hindsight.
What should work is Bayes rule—at least in the form that can be visualized (tiling of the 1⁄1 grid) or symbolcally derived easily.
Also guessing and calibration games should work. You can also take standard games and add some layer of complexity on them (but please not arbitrary but helpful ones; a minimum example is: Play Uno but cards don’t have to match color+number but some number theoretic identity e.g. +(2,5) modulo (4,10)).
I assume you mean Conway’s game of life.
Yes of course. That and we tried variations of the rule-set. We also discovered the flyer.
It is interesting what can come out of this seed. When I later had an Atari I wrote an optimized simulator in assembly which aggregated over multiple cells and I even tried to use the blitter reducing the number of clock cycles per cell as far as I could. This seed become a part of the mosaic of concepts that sits behind understanding complex processes now.
That sounds interesting. Would you care to elaborate?
The story goes as follows (translated from German):
“Once I dreamed that there was an island called “the island of dreams”. The inhabitants of the island dreamed very vivid and lucid. Indeed the imaginations which occurred during sleep are as clear and present as perceived during waking. Even more their dreamlife follows from night to night the same continuity as their waking perception during the day. Consequently some inhabitants have difficulties to distinguish whether they are awake or asleep.
Now every inhabitant belongs to one of two groups: Day-type and night-type. The inhabitants of day-type are characterized by their thinking during the day being true and during the night being false. For the night-type it is the opposite: Their thoughts during sleep are true and those during waking are false.”
Questions:
Once an inhabitant though/believed that he belonged to the day-type. Kann be tested whether this is true? Was be awake or asleep at the time of the thought?
...
I think most of my blindspots before roughly the age of 18 involved not understanding that I’m personally responsible for my success and the extent of my knowledge and that “good enough” doesn’t cut it. If I were to send a message back to 14-year-old!Me, I’d tell him that he has a lot of potential, but that he can’t rely on others to fulfill that potential.
I don’t know how much of this falls under your remit, but I had quite a few educational blind-spots I inherited from my parents, who didn’t come from a higher-educated background. If any of your students are in a similar position, it’s worth checking they don’t have any ludicrous expectations out of the next several years of education which no-one close to them is in a position to correct.
Blind spots such as?
I’m not sure any specific examples from my own experience would generalise very well.
If I were to translate my comment into a specific piece of generally-applicable advice, it would be to give students a realistic overview of what their forthcoming formal education involves, what it expects from them, and what options they have available.
As mentioned, this may be outside of the OP’s remit.
The specific examples may not be used, but would clarify what sort of thing you’re talking about.
One example: certain scholastic activities are simply less important than others. If your model is “everything given to me by an authority figure is equally important”, you don’t manage your workload so well.
Just curious—are you teaching at a math camp? Which one? (I have a lot of friends from Canada/USA Mathcamp, although I didn’t go myself.)
No. I know one of my former teachers outside of school, and we decided it would be a good thing if I ran an afterschool program for the mathcounts kids after it had ended.