As a firm believer in building figure skating skills from the ground up, I've pulled out the description of what skaters learn, class by class. I already did tots (where you'll find the answer to "teaching kids to glide on ice"). Here's an Alpha/Basic 3-4 outcome.
To be successful at Alpha/Basic 3-4, you must have a comfortable, steady one-foot glide right and left before starting class; I always make my students learn how to hold a one-foot glide on a circle as well, both inside and outside edges. (I teach in an ISI program. The Basic Skills program makes forward edges around a circle a testable skill.)
A strong one-foot glide is the key to successful beginner cross overs. Don't be fooled by speed at beginning levels. If your skater wants to be more than what I call a "pond skater," make sure they can glide on one foot before they start to work on cross overs. If your child is in an Alpha class where the teacher seems to be spending "too much time on one foot glides, why aren't they learning cross overs," it's because the beginning level teacher passed the kids without the skills necessary to even start the next level. See the post called "Cute" about the phenomenon of passing children based on their bright smiles.
Alpha/Basic 3&4 is all about strong forward skating-- stroking, crossovers, stops.
Crossovers are a power move, useful for getting around corners and covering a lot of ice with minimal effort. They travel in either direction (Right over Left (counter-clockwise) and Left over right (clockwise) and are, by definition, continuous forward stroking around a circle, pushing with the “outside” foot, then crossing it over the “inside” foot, and returning to the starting position. You'll also hear these referred to as "progressives," especially in a hockey program. Not quite the same thing, but close enough for our purposes today. There is also something called a cross-behind, which is a dance step and does not generate any power. (In skating you can never do anything actually wrong. We just give it another name.)
To pass beginning crossovers (for skating schools that divide the ISI "weSkate" classes into level 1 and level 2) you must be able to hold the first stroke, cross easily over the skating foot, glide briefly with feet crossed, and return to starting position. You must do five in a row with no extra pumps or pushes. A two-footed glide between crossovers is acceptable in Alpha 1. Toe pushes on the first stroke are not. I take the toe push on the undercut under advisement with Alpha 1, depending on the quality of the rest of the skating. (Don’t tell.)
In Alpha 2, Advanced Forward Cross-Overs, the crossed foot pushes (in a move called the “undercut”) to the outside of the circle, and then returns to the starting position. To pass, you must demonstrate proper arm position, a strong first push with no toe pick, understanding of the undercut, and be able to lift and return the crossed foot to the starting position without catching the toe pick. Five consecutive cross-overs are required to pass, with no additional pumps, pushes, or two-footed glides. In my classes, I don’t insist on an actual undercut push at Alpha 2, just that the student is not toe pushing on the undercut and has a correct weight shift. At any Alpha 2 skill I'm not looking for power, but for proper understanding of the technique.
My neglect, if you will, of the true power undercut is controversial. Technically, students should be required to do this. However, I have found that especially younger and more recreational skaters will translate power into a mongo-toe push, rather than just learning to be comfortable with the set up for the undercut. It takes a lot of patience and nerves of steel with parents who don't understand why their kid didn't pass alpha "when she's the fastest one in the class."
Necessary to proper crossovers—understanding that you’re skating on a circle, and the distinction between inside and outside edges. ISI leaves the teaching of this to the discretion of the coach; USFS Basic Skills makes it a testable skill. In the USFS Basic Skills curriculum crossovers are taught without lifting on the first stroke. Personally I don’t like introducing this here because I think it makes it harder for kids to understand the necessary weight shift, but either method of teaching is fine.
Continuous alternating pushes side to side to move straight down the ice. To pass a level 1 class you must be able to stroke from foot to foot, with free leg straight and extended behind. Toe pushes not allowed, but we usually let the kids do a brief two-foot glide between strokes (see more about toe pushes below). To pass Alpha 2, and the ISI registered test, you must be able to stroke from foot to foot, with good posture, free leg straight and extended behind, no toe pushes, no two-footed glides, and some evidence of ability to accelerate. You must sustain good flow for six pushes. A pointed toe is nice!
Forward Snowplow Stop:
A one-foot stop pushing forward with the inside edge of either foot, creating snow and gliding to a full stop. To pass, you must demonstrate the ability to stop from a slow glide. You get to choose the foot. I always tell my students that they can tell that their stopping technique is correct if they actually stop.
A word about toe pushes:
I consider an unacceptable toe push to be of what I call the “slip and grip” variety. This is when the skater slides the blade straight back until the toe pick catches, then bends his knee and blasts off. I tell the kids “slip and grip leads to trip.” They all groan, then someone trips on a toe pick and I get to say I told you so.
There is however an “acceptable” toe push. This is when the skater catches the toe after pushing with the side of the blade, and is a very common error at the Learn-to-Skate/Basic Skills level. It can almost always be attributed to not enough knee bend or not staying down in the ice as you push, and leading with the wrong part of the blade, and is an easy error for an observant coach to fix. But if the student is pushing with the whole blade, this should not be an error that holds them back. You may tell your coach I said so.