Did you pause your Tama? If so, that's the problem. When you first activate your Tama, it is in the egg. The egg will hatch in a minute or so. The next stage is the baby. If it is a girl, it will be white. If it is a boy, black. In an hour it will become a child (or toddler). Your Tama must be on (meaning OFF pause) for that entire hour in order for it to grow into a child.
I have made a little evolution chart for you (it will only work if you do NOT pause). *I am not too familiar with the "adult to oldie" evolution, so I have not included it. This chart mainly applies to Tamagotchi Connection V4 and V4.5.*
Egg to Baby-About one minute
Baby to Child-One hour
Child to Teenager-One day
Teenager to Adult-About two days