How to remove event listener within a class?

Question

Say that I have a class with the some methods such as:

addClickListener(e) {
    var self = this;
    e.addEventListener('click', function() {
        self.moveCharTo(e);
    }, false);
}

removeClickListener(e) {
    var self = this;
    e.removeEventListener('click', function(){
        self.moveCharTo(e);
    }, false);
}

calling removeClickListener does not remove the event listener. Is it because self is being changed each time? Is there a way to assign self in the class constructor and then refer to it inside the anonymous function in the listener parameters?