Music students often learn their scales by reading them off of a piece of sheet music. To memorize the scales, they practice repeatedly until the movements required to perform the scale are committed to muscle memory. This method of memorization can be unreliable since it does not employ a cognitive understanding of the pitches in the sequence. This lack of cognition also robs the student of the true benefit of practicing scales, which is familiarizing ourselves with each key signature. Once we can mentally distinguish the pitches of a particular key signature, we can free ourselves to play a musical passage without accidentally hitting pitches outside of the key.
If we visualize the 21 pitches of music, we can practice picking out and naming the 7 consecutive pitches of a scale. We start by naming the 7 letters of that scale, beginning with the tonic letter (name of the key or scale) and looping around the 7 letters. This is something that can easily be memorized since it is the first 7 letters of the English alphabet. Then we simply apply the key signature (derived from the circle of fifths) of that scale while naming the letters. We practice naming and then playing each pitch of the scale while keeping a steady beat. Gradually, we increase the tempo and decrease the delay between naming and playing the pitches (eventually this requires naming the pitches in our head instead of out loud). Finally we reach a point where we can name and play the pitches almost simultaneously, and at a decent tempo. This method provides the confidence of cognitive pitch recognition as opposed to mere muscle memory reliance.
This Learning Music With Ray video discusses the method I use to help my students memorize their scales. The primary reason for the study of scales is to develop an understanding of key signatures. Truly knowing a scale frees musicians to mentally contain themselves within the confines of a given key. In this video, I use the circle of fifths and a display of the 21 chromatic pitches to practice visualizing the seven pitches of a particular scale. I demonstrate a process of naming and playing each pitch that ensures cognitive recognition of each pitch in the scale.