So, I was looking for a method that a very bright beginner can pick up, and i didnt want it to involve the idea of commutators because they are too hard to explain.
Completely agree, 100%. Teaching commutators and how they work is extremely difficult, and every time I have tried I succeed in only frustrating the learner to the point of not wanting to cube.
I do, however, still teach commutators. I have only drastically changed my approach to how I teach them.
For cycling corners I teach the same commutator method that Joël van Noort teaches on his site. The actual 3 cycle, in full notation, is:
R' D2 R U R' D2 R U R' D2 R U2 R' D2 R
As a commutator this is: [R' D2 R U : R' D2 R, U]
or
S = Setup Move = R' D2 R U
A = R' D2 R
B = U
and the algorithm is: S A B A' B' S'
Although this is a commutator, and a complicated one at that, I teach it as follows:
R' D2 R I call the "baseball move". In a visual sense it is like someone is throwing a low sidearm throw. The R' is the dropping of the arm, the D2 turn "throws" the corner at DRF to DLB. Then the R is the motion of the arm coming back up. The U turns I call "pinwheel" turns. I tell students that it is like one of those pinwheels on a plastic stick. You blow into the pinwheel and it spins, like a windmill. The U layer turns are like that.
So a student remembers the algorithm
(R' D2 R U) (R' D2 R) (U) (R' D2 R) (U') (U' R' D2 R)
like this:
(baseball move) (pinwheel the next corner around) (baseball move) (pinwheel the next corner around) (baseball move) (pinwheel the original corner around) (baseball move).
They are doing commutators, and complicated ones at that, but don't even realize it!
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I also teach twisting corners as commutators.
R' D2 R F D2 F' U F D2 F' R' D2 R U' is a commutator I teach. In notation it is written:
[R' D2 R F D2 F', U]
I also teach this as baseball moves and pinwheels. The R' D2 R I call "the right baseball glove move" and F D2 F' I call "the front baseball glove move"
Students remember:
(R' D2 R F D2 F') (U) (F D2 F' R' D2 R) (U')
as
(right baseball glove move) (front baseball glove move) (pinwheel the next twisted corner over) (front baseball glove move) (right baseball glove move) (pinwheel the corner back to its original spot)
Easy as pie. Trust me, if 6 and 7 year old kids can learn this, then any adult can. The failing is not in the learner but in the teacher. I don't mean this as an insult to you, but rather to get your attention. I have learned so much in terms of how to teach cubing through my
many failures in teaching kids how to cube. I have tried teaching commutators as commutators, and just like you said it was a
miserable failure. Just find a way to present the topic to the student that makes more sense to the student. You'd be surprised how complicated of a thing they can learn by doing this. Don't ever teach them the term "commutator" or talk about As and Bs and (A')s and (B')s, just phrase it in a very visual sense.
Again, I'm not trying to come across as insulting, I am just relaying things I have learned by teaching cubing to young kids. The failure of the student to learn is really in not teaching it a good way to learn
for that particular student. If you can find a good method
for that student then they will comprehend it just as well as you do, they might only think of the concept in
completely different terms than you do.
Hope this helps, and yes I am an ally to what you are doing, even though it might not sound like it!
Chris
--*******EDIT*******--
To preempt the question of how to twist 3 corners, here is how I teach kids to do this:
(R' D2 R F D2 F') (R' D2 R F D2 F') U (F D2 F' R' D2 R) U (F D2 F' R' D2 R) U2
As a commutator, this is the best I can come up with as to how to represent how that algorithm works:
Let
A = R' D2 R F D2 F'
B = U
The commutator is actually not a single commutator, but rather a cyclic shift of the concatentation of a commutator with a conjugated commutator. Here is what I mean by that.
Using the above definitions of A and B we will call the "conjugated commutator": (A'A') A B A' B' (AA)
The "commutator" we will call: (A'A') B' (AA) B
The concatenation of the two will do the commutator first, followed by the conjugated commutator. This concatenation is:
(A'A') B' . (AA) B (A'A') A B A' B' (AA)
The cyclic shift starts at the period and wraps around after reaching the end. This makes the algorithm become:
(AA) B (A'A') A B A' B' (AA) (A'A') B'
Including the cancellations this becomes: A A B A' B A' B' B' which is the structure of the above alg that twists 3 corners.
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Anyway, the way I teach kids to do this is to cycle the first corner "the wrong way" the very first time. This means they do R' D2 R F D2 F' to twist the corner in the opposite direction that they should. After this, they will cycle all corners the "correct" way. They finish the first corner with R' D2 R F D2 F', which is now the correct way to twist the corner. Then they "pinwheel" the next corner over, and continue similar to above.
In the student's mind they are doing:
(Read the first corner incorrectly the first time around) (Read the first corner correctly the second time around) (pinwheel the next twisted corner over) (twist the next corner correctly) (pinwheel the next corner over) (twist the final corner correctly) (bring the U layer back into the original start position)
In actuality I have them skip the last U turn, as the corners all show the correct sticker on top, which makes this step already completed by that point.
[/ridiculously long post]
D)
