Like this:
$result = mysql_query ("UPDATE StudentInfo SET StudentNumber= '$StudentNumber', FirstName='$FirstName', LastName='$LastName', EmailAddr='$EmailAddr', PhoneNumber='$PhoneNumber' WHERE recordID ='$RecordID'");
or is this better
$query_str = "UPDATE StudentInfo SET StudentNumber= $StudentNumber, FirstName=$FirstName, LastName=$LastName, EmailAddr=$EmailAddr, PhoneNumber=$PhoneNumber WHERE recordID=$RecordID";
$result = mysql_query($query_str);
if (!$result) {
die('Invalid query: ' . mysql_error());
with the single quotes added