My 15 month old has tantrums?

At the moment he is testing his limits and boundaries. What you do now can have a huge impact on what kind of child he will turn out to be. I am personally, against using physical discipline, but that is each parents choice. I think you are on the right track. My nephew went through a similar stage, and is now a charming, mild mannered boy. There are heaps of ideas and guides out there, it's just a matter of finding one that works for you and your family.