In your query, you could do:
SELECT mystudents, mydate FROM mytable WHERE MONTH(mydate) BETWEEN 5 AND 9
This would select all students between the months of May and September.
If you didn't feel like parsing the date with PHP, you could also do this:
SELECT mystudents, mydate, MONTH(mydate) AS mymonth FROM mytable WHERE MONTH(mydate) BETWEEN 5 AND 9
Here mymonth will just contain the month value of the student's date and you don't need to do any further parsing with PHP (let MySQL do the work).
I think this is what you're looking for - this help?