Some thoughts about body position
The theory behind swimming is important to understand, both for adult and child beginners and improvers. One of the core fundamentals of swimming is body positioning - correct streamlining and body position is a building block of a good stroke.
Particularly for children (whose heads are that bit heavier), a flat body position will accelerate your swim. To get our bodies flat on the front, we need to have our faces in the water. If the head is correctly aligned, the hips and in turn the legs will be in a better position. Think of the body as a see-saw; when the head is up, then legs are down - the legs follow the head.
In order to maintain that flat position on the front, we need to also learn to breathe correctly (to the side). Breathing to the side is often difficult for younger children to coordinate - they tend to raise their heads out of the water to grab a breath, which sinks the legs, which is hard to resolve for the remainder of the stroke.
Push and glides are excellent way to improve streamlining a breath control in a flat body position. Extend the arms until straight, put the hands together and the face in the water. Push ideally from the wall or from the pool bottom, and the hips and legs should extend at the surface of the water. Kicking your legs across with the body in this position is a great way to improve your breath control.
Luckily, there is also a benefit to swimming with the head up. "Doggy paddle" (head up and facing forward, arms performing a pulling action beneath the water) and legs only swimming with a float and the head up sinks the legs. This isn't what we want for an efficient swim, but it's an ideal way to practice and strengthen the legs. You have to work harder to bring the legs to the surface when your head is up, and that will build your stamina quickly and effectively.
To strengthen the legs using a head up practice, make sure your chin is near the water (children benefit from a ball or toy to focus on in order to keep their chins low). If you're using a float or kickboard, grip the front to give your arms some support, or if a child is doing a doggy paddle pull, encourage them to stretch out their arms and pull back to the tummy.
Just adjusting your head position can help you practise different elements of your stroke and learn more about how your body works efficiently in the water - give it a try!