You need to use bindValue instead of bindParam.
When you use bindParam, it binds the variable provided to the parameter, not the value of the variable.
So, if you do:
$x = 5;
$stmt->bindParam(1, $x, PDO::PARAM_INT);
$x = 6;
$stmt->execute(); //executes with 6 instead of 5
It's actually executed with 6 rather than 5. To do this, the method must have a reference to the variable. You cannot have a reference to a literal, so this means that bindParam cannot be used with literals (or anything you can't have a reference to).
$x = 5;
$stmt->bindValue(1, $x, PDO::PARAM_INT);
$x = 6;
$stmt->execute(); //executes with 5 instead of 6
Then:
$stmt->bindParam(1, 1, PDO::PARAM_INT);
//invalid because there's no way to pass a literal 1 by reference
$stmt->bindValue(1, 1, PDO::PARAM_INT);
//valid
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