In general as the pressure decreases, so does the temperature required to boil a liquid. The boiling point at the top of a mountain is lower than it is at the bottom, because the air pressure is lower at the top. I used to live in Colorado, and when I was there I had to steep my teabag to make tea longer than here in NEw York. This is because boiling water in Colorado, which is about a mile high in elevation, is cooler than boiling water in New York, which is at sea level. Thanks for your question, hope this helps you understand boiling a little better.
Mom is right.
In fact, when you do this, the water will boil and freeze at the same time. The reason is that at room temperature, water molecules are constantly going into the air as vapor and moving back into the liquid water. When you heat water, you are making the vapor that comes off the water have a higher pressure. When the pressure gets as high as the pressure of the surrounding air, bubbles of vapor can form inside the liquid and push against the air. When this happens, the liquid boils.