I've started a few discussions in the past on curriculums and how they progress, including advancement of patterns, what a white belt should know, and varying teaching styles. I guess the concept of learning itself is fascinating to me. Now, I'm curious about the progression of kata.
My understanding is that the purpose of kata, regardless of what art or style you practice, is to contain a progressive understanding of the material. That a student who has learned all the katas in your art should have a pretty firm understanding of the art.
Now, katas themselves can vary widely. In Taekwondo, for example, I think that training in hand techniques is generally left up to forms, but kicking techniques are taught separately as drills. There are some kicks in the forms, but usually not nearly as many as Taekwondo uses in competitions and demonstrations. However, my school has punch and kick combinations that are rote memorized drills, so you could consider those to be part of the kata, and then most of those techniques start to sound covered under kata.
However, I'm curious about kata themselves. What is it that a kata teaches, and what is it that each kata in a curriculum teaches?
At my school, Basic Form #1 teaches the basic pattern. Basic Forms #2 & 3 each take Form #1 and add new concepts to it. These are taught at the same belt and you could almost reverse the order. Basic Form #4 combines 2 & 3 together, and I kind of think of it as the first real form. Like Forms #1-3 break down most of the concepts in Form #4.
After that form, meaning Basic Form #5 and Advanced Forms #1-8, each form adds a couple of new techniques, some new footwork, new concepts, and some increased level of complexity or intricacy. For example, the basic forms all follow an A-B-A-B-A pattern, while Advanced Form #1 is more like A-B-A(2)-B(2)-A, Advanced Form #3 is A-B-C-D-E (but uses the same basic shape as the basic forms) and Advanced Form #7 has a completely different pattern and none of the parts repeat.
As to techniques, Basic Form #5 uses spinning footwork, Advanced Form #3 has backwards motion and different styles of direction change, and Advanced Form #5 has forward-backward wave-like motions. The forms include new techniques, like Scissor Block, spear-hand thrust, supported 2-hand blocks, and more intricate striking combinations.
So, to summarize, I'd say that the way my school does katas, each kata builds on what the student already knows, by reinforcing old concepts and techniques, but also adding new ones. Sort of like how in algebra class you still practice your basic addition, subtraction, multiplication, and division when you are trying to find X.
However, I'm curious about other arts, or even Taekwondo schools that have different forms. Do your forms teach isolated concepts, such as one form focused on footwork, another focused on defense, another focused on hand strikes, another on throws? Does each form have its own theme, such as defense against certain types of attacks, or techniques of a particular variety? Or do your forms build on each other and reinforce previous concepts while adding new ones?