Was Shakespeare good in school?
We don't know; his school records have unfortunately been destroyed. However, he seems to have remembered a good deal of what he was taught in school, which is more than you can say about even some of the best students nowadays.
It is believed that he attended the King's Grammar School in Stratford. This is based on the fact that this was the only grammar school in Stratford and that Shakespeare seems to have had a good grasp of the standard grammar school curriculum. The school's records have been destroyed and so cannot be used to confirm this hypothesis.
Au contraire, just about everyone thinks he did attend it. Including the school itself which proudly lists him as one of their pupils. And indeed it is clear that Shakespeare had a pretty good grasp of the grammar school curriculum. Some people think that he didn't finish grammar school due to his father's financial trouble, but that is far from certain.
Shakespeare probably began his education at the age of six or seven at the Stratford grammar school, which is still standing only a short distance from his house on Henley Street and is in the care of the Shakespeare Birthplace Trust. Although we have no record of Shakespeare attending the school, thanks to the official position (alderman) held by his father John Shakespeare, it seems likely that he would have decided to educate young William…
The grammar school in Stratford, then called the King's New School had been founded by King Edward VI (Queen Elizabeth I's brother). Shakespeare probably attended it from the ages of 9 to 15 or so, from 1573 to 1579. However there is no documentation to prove that he even went to that school, never mind when. We can only guess from what was typical and from the fact that he had a good knowledge of…
We are not sure that he was. Some scholars have speculated that Shakespeare's dad may have been too poor to pay his school fees, and so Shakespeare did not complete grammar school. But we do not have any school records at all for Shakespeare so we cannot confirm any of this. We only assume he went to school at all because he seems to have had familiarity with the curriculum.
As there was no such thing as "high school" back in Shakespeare's time, it is certain that he did not "graduate". However, Shakespeare did attend Stratford grammar school from the time when he was 6 or 7 until 13. His father pulled him out of school at age 13. Yet that isn't to say that Shakespeare was later self taught and learned by other means.