Various algorithms are developed by the student as needed and are not an end in themselves. NM does not use drills for the sake of drills. Conceptual understanding is far more important than the fast reaction. All the necessary exercise can be done as the student explores new ideas. If repetition is necessary, it is presented in the form of a game.
Students learn exceptionally well when they have to teach.
Math is one of the most natural and intuitive of many sciences. It should go very easy if taught right. Learning math does not have to resemble climbing a pole, when one has to follow a single path from start to finish. Most people in favorable conditions find pleasure in solving math problems. It is important to appreciate learning for the sake of the learning.