Particularly I was trying to make games with Pascal and Assembly on an 80386. Asphyxia tutorials. No Stack Overflow, no Khan Academy, Wikipedia, in fact no Internet or even BBS at all. I feel nostalgic towards this time, but I guess that those feelings are more attached to the curiosity of an analog child being introduced to the digital magic.
I was introduced to it slightly after I was in school, but unlike school, gamedev is what made me actually understand it. Then the whole trigonometry, and basics of vector arithmetic and matrices. School for me was boring repetition of arbitrary tasks forced top-down by unpleasant people. Wanting to make my own game, that gave me huge motivation.
(Then I went to university, and on the first year's physics lab, I was asked to solve something on a whiteboard. It was a simple thing involving a vector cross product, so I proceeded to write out the formula and calculate the result. TA looked bewildered and asked me what the hell am I doing? Turns out, I was supposed to first do a whole dance around base vectors and 3x3 matrices to derive the appropriate formula, which I simply memorized when I was 14, having implemented it in C++ half a dozen times. Turns out, gamedev-driven education can leave you with holes in theory.)
So like, the TA asked you to compute
and you jumped straight to
<2x6-3x5, -(1x6-3x4), 1x5-2x4>,
without the intermediate step of
| i j k |
| 1 2 3 |
| 4 5 6 |?
Or did you begin by computing the angle between the two vectors, so as to use the sine formula for cross product? Either way, I can certainly understand how your classmates (and TA) would be bewildered (especially if the two vectors were such that it wasn't immediately obvious what the angle between them was).
I understand why TA didn't like it, though back then I wasn't happy that my short and "obvious" solution wasn't received well.
In high school, my electricity teacher made us draw the sine waves of monophasic and tri-phasic (if that's what it's called in English?) voltages manually by drawing into a Cartesian arrangement and projecting onto a line diagram, much like the animation about halfway through the article. It was tedious and it seemed very repetitive to draw the various variations, but in later years I started to understand its relevance (also with regards to the relation between current, voltage and power). Just in general it gave me such a good example of the relationship between the geometry, trigonometry and calculus involved, much better than the canonical speed/distance example ever did (for me). There are only a few core concepts I learned in high school that I still use often, and this is definitely one of them.
I don't know if children in today's generation can at all be called as 'analog children'? And that plausibly is not good, overall.
But it's certainly not avoidable.
The best that parents can do is to try and teach and encourage children to focus on healthier stuff. To not be slaves to their mobile phones. To have empathy. Easier said than done though.
It certainly is avoidable. The difference between my friends who are very conscious of the exposure they give their children to TV, phones, tablets, etc vs those who don’t is striking.
Case study A: a friend who lives with her 6 year old son in a tiny Paris apartment. She has a laptop for work and an old phone she uses for WhatsApp/basic tasks, and that’s it. When I spent a few days at her place last winter, the kid helped us cook, we played board games after dinner, and he was really excited to go to the park the next day.
Case study B: San Francisco friends who let their kid use an iPad pretty much any time there is any chance the kid might be bored, moody, etc. She is pretty much addicted, and it’s quite hard to get her excited about anything else.
It's hard to say if at some point the disadvantages of limiting screen use is outweighing the benefits. Worse, if children already use social media heavily, stripping them of access during the school hours (or longer) will actually increase their anxiety levels. Children's social dynamics are tricky, especially for adults, and a lot can go wrong.
In my youth I wasn't spending so much time with a computer because it was my free choice. I lacked the social skills to make friends and was bullied heavily through my entire school life.
Next problem: To entertain a child without iPads requires a lot of time and conscious effort, which not all parents can spare, despite their best efforts. Instead of iPads, especially with preschool children, you'll see parents give them some food item when they need to be still for a time (bus, train etc). That's not necessarily a better solution.
Nor is letting them cry all the time because children at such ages can't control their focus and impulses for a meaningful amount of time.
I didn't remember what it was by read those back in the early 90s as well, learning to program on a 486 with an early SVGA card. I think I downloaded them on a trial of AOL, my parents wouldn't/couldn't pay for AOL but I sucked all those tutorials down when I had a chance.
I was taking Pascal in school but learned a ton more from those tutorials. I wrote an asteroids type game and got tons of eye rolls from the teacher as the other students were playing my game after I shared the source. I had done the whole years curriculum in a month or two and then sat there and wrote games in class. The teacher didn't really care as I'd just about matched his knowledge by the middle of the year. He was a great teacher, had a PhD in math which was pretty darn rare for high school.
Those tutorials had a significant effect on my chosen career path.
Quite a surprise when I was finally introduced to trig at school and found out it had a name!
And then one day someone explained the high-level point to me: "Of the six quantities of a triangle (three angles and three sides), given any three of them, at least one of which is a side, the other three are automatically nailed down." Suddenly a switch was flipped. After that, the rest is just details that write themselves.
I was kind of surprised that the article used circular motion as its main motivating point, since I feel like just moving at some angle is so much more common.
And it really doesn't take much to learn programming in class 5 or 6...
I believe my teachers were pretty good, overall. At least as good as can be expected.
And I suspect it's also dangerous to teach coding to teachers: It's a skill that can land them much more lucrative and less stressful jobs.
I've never taught, but I remember transitioning from school to a job and it was a huge thing for me that I could keep work at work and I could start focusing on things outside without distraction. For friends that teach there's a lot of work that's expected that's not scheduled work hours (grading, lesson planning, etc). Dealing with parents is one of the largest stressors and that's almost exclusively outside of classroom time.
Also, many teachers don't think "no parent engagement" is more desirable than high parent engagement. Differences in the parents ability to engage the school (available time, money, language skills etc) contributes to social and ethnic disadvantages in many nations' school systems.
> Also, many teachers don't think "no parent engagement" is more desirable than high parent engagement.
I've never heard a teacher argue for no engagement. My point was that parent engagement is inevitable and always outside of scheduled class time. It's also one of the top complaints (along with administration and mandatory testing), so it's doubly unfortunate its unbounded.
And I highly doubt that they got above a 40 hour work week including their lesson preparation.
But I guess expectations and regulations vary and it takes a personal strength that shouldn't be required of teachers. It's doubly sad that school systems are increasingly relying on teachers giving in and carrying more than their contractual burden.
I'm not totally familiar with US coding/teaching jobs, and it also depends on how you deal with "stress" and the managing styles etc.
But teachers are on the front lines dealing with teenagers who are (at times) unruly, mean, sometimes outright violent, and parents will blame you for all those problems. Maybe 99% of your students are nice or well behaving, but it doesn't take a lot. I've heard quite a few stories of classes driving teachers mad. A lot of fresh teachers even drop out...
Why do you believe this? Speaking for myself, I learned to program in three programming languages by 11 and I think it was very helpful.
Programming does not teach those, indeed it allows the production of scrappy stuff that seems to work and is great fun. I found it hugely distracting myself in the way that social media is addictive to current kids.
I'm not explaining myself well and perhaps I'm extrapolating too much from my own case, but I hope that gives you an idea of what I'm trying to say - the very thing in programming - the bringing of something to a kind of life - is the very thing that makes it valuable to hang mathematics off, is also the thing that makes it a shiny bauble that kids/younger adults love to dabble with and be distracted by.
But your experience suggests a different POV. I may well be wrong.
Interacting with people is also often part of it. Perhaps you make something with your friends (eg we made a class website for our school class where we uploaded photo galleries of our events and had forums and chat - all pre-facebook, around 2002-03).
By contrast math is very individual and often taught quite bad without any interaction. You learn each type of calculation task you may get on the test, memorize definitions and proofs...
And it's pretty much impossible to work on a "math project" with your friends in your free time to hone those interaction skills. Perhaps if you went to a special math focused school you could talk about math with them in your free time, in most schools that's not the case, outside perhaps discussing how to solve the test questions.
I used to do very well at my maths, but lost interest in large part because the maths I learned was largely disconnected from everything else I was doing despite an interest in programming.
It was first when I picked up a book on Prolog that I got symbolic derivation. The reason being that the Prolog book contained it as an example, and it was sufficiently compelling that it made me write an expression parser so that I could implement that symbolic derivation in Pascal, and the process of implementing the parser and implementing the rules applied to the syntax tree to carry out symbolic derivation brought it home in a way my teacher never did.
[Incidentally that expression parser also became the starting point for my first compiler.]
Of course programming can be distracting, because it can also allow you to explore almost any subject in more depth. E.g. what I know of complex numbers, I know because I was experimenting with fractals. What I know of graph theory is almost entirely down to playing around with parsing and compilation. And most of my understanding of trigonometry is down to toying with 3D rendering; certainly not from my maths classes in school that mostly made me loathe the subject.
There are plenty of languages that allows you to bridge a formal approach to maths with programming. But there are also plenty of ways to explore and demonstrate the concepts that will make them easier to grasp that require just very simple visualization. E.g. visualizing fractals as a means to explore topography; visualizing derivation, integration, limits, trig. For many of these presenting it as programs rather than visualization and letting students play with and see the consequences of changes has a lot of potential to make people grasp the concepts more deeply.
Different ages have different priorities. The best way to attract kids to any activity, including programming, is to give them something fun to do. Let them make crappy stuff that's flashy and fun. If they choose to stick with it, teach them to do it well and help them unlearn the bad habits.
Incidentally, I consider bad habits to be incredibly important. Yeah, sure, you can read about how to program well, but it's not the same as having your own bad habit bite you in the ass and learning from it. It's even better if you learn bad habits and then unlearn them while you're still young and not when it might impact customers.
I can get that. In 1985 when I was programming my own BBS from scratch I would skip going out with friends to work on it. All that time spent on a computer as a child provided a very lucrative and rewarding career however so I don’t think I’d change any of it.
Ironically though based on your other comments in this thread I do wish I learned maths more!
I agree. Maths is more important than programming IMO. But wider skills (job-related, planning, and social skills) are just as important, probably more so. But programming is an almost magical process of animating a thing. It can be too attractive, addicting, distracting...
Just my POV. I should not have posted originally without some evidence to support my claim.
Not everyone is cut out for programming, and schools will inevitably teach it in a lowest common denominator style, where the bright kids will be bored to tears doing and redoing for loops in scratch.
If someone wants a single number for representing a rotation, consider using the stereographic projection (instead of angle measure), which takes only 1 division to go back and forth to cartesian coordinates.
Floating point is fine for modern hardware though.
Here's the trigonometry playlist: https://www.youtube.com/watch?v=yAHl_kpqr-k&list=PL7wAPgl1JV...
My french is bad... Which is made even worst as I'm a French national...
I learnt programming about the time we started on algebra. I credit my game programming efforts with teaching me the intuition to put "text problems" into formulas and how to look at the physical or natural world.
And no, I was no genius, and even in school I was less successful than many of my peers who didn't do any programming (though quite a few did).
- Not really sure who the original author is.
Use one value to drive the forward/backwards motion of the leg. Use the other to drive the up/ down motion of the leg, although you want to clamp the range from 0.0 to 1.0 so the foot doesn't clip under the floor (although you could use realtime inverse kinematics to prevent that as well, in a game engine with reasonable IK support such as UE4).
You'll also need to negate the values for the leg on the opposing side of the body, and keep flipping those values for each pair from front to back (ie. the third pair matches the first pair, the fourth pair matches the second pair).
See https://www.youtube.com/watch?v=GtHzpX0FCFY for an example of a (hand) animated spider gait.
This summary was a nice refresher for me but if I were just learning it (i.e. looking for a tutorial) I would probably want more in-depth explanation along the way.
If the author is reading this: Try removing the controls attribute on the videos and see if you like it better that way, I think I would (since they are so short and looping they are just distracting from the great animations)
I've always thought Trigonometry is taught poorly in our high schools. I've frequently seen people see the animation showing the dot going around the circle while graphing the X and Y values and suddenly having everything "click" for them, and question why that animation wasn't shown to them in high school.
I'd recommend searching for more of them :)