The first thing is not to panic. Reasons for failing a school screening range from just being nervous to mixing up letters to needing glasses to more severe reasons like strabismus (misaligned eye) or amblyopia (lazy eye). The best thing is to get it checked as soon as possible.
If it's nearsightedness or farsightedness: Glasses may make a huge difference in your child's academic performance.
If it's an eye misalignment: Your child may be seeing double. Believe it or not, kids sometimes go for a long time seeing double without complaining, thinking that's just the way people see. Visit an optometrist first and figure out the best course of action. Sometimes its glasses with prism lenses. Sometimes its Vision Therapy.
If it's amblyopia/lazy eye: Don't delay. If one eye sees significantly better than the other this can have detrimental long term effects. Lazy eye can be fixed but only if action is taken in a timely way. The hardest part is, many times since the child has one good eye, he or she functions very well and is resistant to glasses, therapy, patching, or whatever the course of action may be. But do be persistent- don't ignore this problem even when the child says everything is fine.
If it's an ocular disease: Ocular diseases such as glaucoma are very rare in children but do occur. If this is the case, the first step is a visit to the optometrist who will direct you to the appropriate ophthalmologist as needed.
If my child passed the screening... We're good right?
Kids are clever and crafty (I'm a parent too, I know). Imagine your kid standing in a line with other kids. The first kid in line reads the bottom row: EVOTZ with the right eye. EVOTZ with the left. The second kid says the same. Next its your child's turn. Uh-oh. Blurry. But heck, he knows the answer already- he was listening carefully and just heard his classmates say it: EVOTZ. School nurse checks off his name and he moves on happily with his day. Same thing can happen if your child can see it perfectly with one eye and then realizes upon switching the occluder over that the second eye is blurry. Good thing he remembers what the letters were.
Part of getting an accurate eye test on a kid is making sure he or she can't outsmart the system. That's where we come in.
Remember there are some limitations to what a school screening can actually detect. Read more about it here: https://www.aoa.org/patients-and-public/caring-for-your-vision/comprehensive-eye-and-vision-examination/limitations-of-vision-screening-programs#1