It is tempting to be in a hurry to get children to read music. There is no way to speed up the process except by dumbing it down to a tabulature system in which this symbol stands for that specific key on the piano or fingering on whatever instrument.
But the auditory sense of music cannot be written down because tones that are visually close together are often farthest apart in terms of resonance or sound quality, while those that are acoustically so close as to be almost indistinguishable from one another appear on paper to be considerable distances apart.
It is a matter of subtle coordination but it can be taught. It just takes time.