What is the recommended treatment for a 10-year-old with amblyopia?

Part time patching. I part time patch amblyopia until 12 y old and have seen improvement. Starting earlier is always best though. Make sure the patient has the proper glasses correction too.
Not very much. Generally, it is believed that the bulk of ocular maturation occurs before 7-8 years of age. There may be some benefit in treating for severe amblyopia with patching or glasses even up to 18 years or so but the improvements may be modest. Best to see what the underlying cause of amblyopia is and if desired, treatment. Best discussed with your ophthalmologist.