How do I cook rice properly when making rice pudding?

I recently made rice pudding and I used short grain white rice (3/4 cup) and cooked it with 1 1/2 cups of water. Everything worked okay except that some of the rice stuck to the bottom of the pot and started to brown. The recipe said to bring the water to a boil, stir in rice, and simmer for 20 minutes. I did all of this but it still stuck. I'm wondering if I used enough water, cooked the rice for too long, or had it at too high of heat. I know I followed the recipe correctly. What is the right temperature for simmering rice? My oven has 9 heat settings including low and high. I had it simmering at about 6 so can you tell what I could have done differently? I would like to make this again, but hopefully without one quarter of the rice sticking/browning on the bottom of the pot.