In my opinion, the problem is not the geometric product, but having three products (inner, outer and geometric). I have explained GA using a single product, and

In my opinion, the problem is not the geometric product, but having three products (inner, outer and geometric). I have explained GA using a single product, and I think it is much clearer. Of course, the inner and outer products are also very useful, but I introduce them only at the last stage, as some extra notation, not to help understand new concepts.