Add X,
Add Y,
Do Z till Z is in Q state.
Accomplishing tasks with recursion? That's utterly counter-intuitive imo. A given person can learn it but feels like a trick. Maybe a cool trick they're cool for having learned and maybe a weird trick someone is pushing on them.
Recursive solutions to programming problems can be great once you get the whole idea but recursion is not an easy way to start people programming. It might not be a bad way - if you're a highly committed 17 teen year old hot learn new things and willing to put in serious effort. learning LISP at MIT back when they taught is something would have like to have done. IE, Hard isn't necessarily bad. But don't expect people who want to put in minimal effort, who are terrified by just showing up to learning programming, to learn this hard way. And especially don't expect them to appreciate that you decided to teach this way.
A lot of programming geeks are in denial about the inherent conceptual difficulty of functional programming (which isn't even to say fp is bad, it has many virtues but easy for novices will never be one).
Edit: To put it in the author's terms, there's hierarchy of modalities and procedural processes are on the bottom and thus everyone can get them. Maybe 1-1 tutoring can different.
Stack of papers, flight of stairs, layers of onions, circle of life, etc. they all just harken back to what it actually is without having to define it directly.
If we're using an 80x86 processor, the function concept is more or less implemented by several facilities - you have a sequence of instructions somewhere in memory, you have a stack area (shared by everything in a given address-space, using a stack pointer in the cpu), you a call instruction that pushes the current instruction pointer to the stack as well as pushing flags and similar stuff to the stack and you have the return instruction, which does the opposite, restore instruction pointer and whatever else was pushed in the call.
Which is to say that on a raw, low level, functions don't "exist" in the fashion a programmer imagine at a higher level. That's not saying the concept is wrong but is saying that the people don't easily see functions as the natural building blocks of everything might be wrong either.
There are recursive structures in nature. Some people might respond to the neatness of recursively generated graphics. Pointing out recursion in language could be useful. Introduce a program for recursively generating random sentences and such.
Similarly when we look at a picture on a wall, we interpret the scene within using the same machinery as we interpret the real world, while also being aware that the scene is "on the stack" relative to real things like the wall. There is nothing about a picture within a picture that breaks our comprehension of what we are looking at.
I think {you know {what I'm talking about}}.
It is strange that recursion seems hard and loops seem easy to most brains.
Start with a basket of tomatoes and a bowl. If there are no tomatoes in the basket, you’re done. Otherwise: Take one tomato. Dice it. Put the output in the bowl. Recur.
How about this example as an example of recursion: Looking up a word in a dictionary (a real-life binary search).
Every shampoo bottle has recursive instructions:
Wash, rinse, repeat.
Also: Eat, work, sleep, then do it all again tomorrow.
Who are your ancestors? Your parents and all their ancestors.
Oof, shade thrown.
Personally I think it should not be used for implementation, I consider it to be a security risk. It's ok for high-level pseudocode.
> I consider it to be a security risk.
Again, non-issue if your language handles recursion properly (and in some languages like Haskell, "blowing the stack" is not a thing that happens).
[0] https://en.wikipedia.org/wiki/Tail_call#Implementation_metho...
For some, it’s practically the only way to loop.
It’s not about how to explain recursion or programming, it’s about explaining abstract and complex concepts via adopting to the listener’s worldview and letting them experiment to evolve that view.
Singling out details and sidetracking the comment thread about this one detail is just a thing that HN tends to do frequently. Usually the first few comments determine the tone/topic of the thread instead of the article itself. Which is not always bad.
to square
forward 100
right 90
forward 100
right 90
forward 100
right 90
forward 100
end
Then you can do:
forward 100
square
forward 100
square
Any child can get this. I did when I was 10 years old, with a bunch of other pre-teens.
Got it right away and absolutely loved drawing various geometrical patterns.
Of course, Logo is based on Lisp, so you can go pretty deep with it.
[1] - Draw it for them as you explain it, or just show it directly on the computer using Logo and turtle graphics.
[2] - Pardon if my program has any bugs.. I'm doing this from memory.. haven't touched Logo in decades...
△ n = [ ↻ 30, ↑ n, ↻ 120, ↑ n, ↻ 120, ↑ n, right ]
square :: Float -> Turtle ()
square n = do
penDown
moveForward n
rotateTurtle 90
moveForward n
rotateTurtle 90
moveForward n
rotateTurtle 90
moveForward n
rotateTurtle 90
penUp
[0] https://github.com/siraben/vpl/blob/4b5d39cbf8d16a988218e62f...
Precise explanations are fantastic for people who already understand the concept: they let them go a level deeper and explore the underlying truth. However, they're intimidating and unhelpful for people who have yet to grasp the concept.
For concepts, analogy works best - 'code is like a...' along with minimal examples of ideas in accessible situations for your audience. Alice and Bob, etc.
Teaching code is about finding the right metaphor for your students - whether that's recipes or language or robots or something else - not bashing at them with "All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor."
It’s your first job as a teacher to (1) listen and understand where your students mindset is, and then (2) teach from that mindset.
Using their vocabulary, their analogies, their interests, etc is super key.
I was a Graduate Student Instructor in college and I LOVED this because to me it was like a puzzle: (1) try to figure out where a student took a wrong turn when learning a complex topic, (2) take them back to the wrong turn and walk with them down the “right turn” until they finally have that lightbulb moment. The key to all of that was speaking/explaining in their language, not mine.
> Formally, we define a behavior to be a sequence of states, where a state is an assignment of values to variables. We specify a system by specifying a set of possible behaviors—the ones representing a correct execution of the system.
Programming is creating an executable description of a set of possible sequences of states. Nothing more.
There are emergent properties of programming, the craft, that you need to master if you want to navigate the next levels of complexity. Just reasoning about sequences of state transition is going to be I'll suited for many occasions, even if technically that's all you need to model everything.
The Lamport quote does the same thing, but to software. The thing died in the process.
When editing (mostly C-like languages) I can "see" the execution thread pass through the code like a step-through debugger. At a function call I can mentally "step into" the function and the function is visualized to the right of the current function with its first line on the same height as the call site. Doing this for recursing functions means a visualization that progresses downwards and to the right.
I guess my mental model evolved this way after years of step-through debugging.
Mental models for code and other things are a fascinating topic. I also have a very specific calendar/timeline model that is not a straight line at all. A full year "view" arranges months in a 2D layout where some months progress "up", others "down" and they are connected in weird ways. For example 31/01 and 01/02 are adjacent, but 30/11 and 01/12 are not. 31/12 is the last box of the year and is adjacent to 01/01 repeating the pattern for the new year.
Circular, "Penrose Stairs" (https://en.wikipedia.org/wiki/Penrose_stairs) might be a better extension to the student's staircase model.
* What do they know now (or think they understand)? You can only build knowledge on existing knowledge, so first find out what foundations exist (this connects to the author's "listener's worldview" idea).
* Tutoring (1-on-1) will almost always be better than teaching (1-to-many) because you can (if you try) better understand what's being understood and what's not.
* Learning is construction of desired knowledge, so learners have to "do" something and be provided quick feedback to build the desired concept (which is why learning on your own with little feedback is subject to learning the "undesirable" thing, even though it might have "worked" for you).
I did a talk on this topic (Human Learning) that you can find on YouTube (JitterTed.TV).
Oh, that's nice!
That's pretty much what happens when we are 4 or 5 years old and learning. You don't teach a child 1+1=2, oh no. You take one rock, then a second rock, and ask them how many. The rock is one. "1" is not 1, and "1" + "1" is not "2", because the young children don't understand it that way. Then you put the number 1 next to each rock and add them, and eventually they understand. But it is very concrete. As adults, we don't need the actual rocks, but we do need a known structure to compare things and assign the "rock" we know to the number "1".
This applies to rote memory as well as understanding concepts. As an example how concreteness helps rote memory, let's take the following list of 11 words: dog, cantaloupe, priest, hill, tornado, ocean, yellow, urn, fox, moon, mushroom.
Most people (not all) will not be able to memorize these abstract words/ideas, even if familiar with them all. But if you match them with something more concrete, they will.
So instead of looking at the abstract words, just match each word with something more concrete in your imagination. So see in your mind's eye this story, and the words you hve to memorize are in italics: A huge 20 foot German Shepard (dog), has a cantaloupe in his mouth and spits it out super hard and fast and it goes through the air like a cannonball and hits a priest who is standing on a big hill, and the priest rolls down to the bottom of a hill where a big tornado comes by at that instant and scoops him up and travels a little while to a big ocean that is bright yellow. Floating on the water is a huge 10 foot tall black and white striped urn and all of a sudden, a very sexy cartoon fox (https://cdn4.vectorstock.com/i/1000x1000/03/28/fox-sexy-posi...) comes out of the top and then shoots straight up out of the atmosphere at supersonic speed and goes up and lands on the moon, where the fox creates a big mushroom cloud when she lands.
If you imagine this story in great detail, you will have little problems memorizing those words and be able to say them all in order with ease. Even backwards order is easy. And this is almost always with 100% accuracy.
So it is the same thing when trying to teach someone an abstract idea for the first time, the exact same. Use concrete examples. Like the stairs in this guy's example, that was great that he finally understands about using analogies.
