I'm not sure what you've learned yet, so some very basic materials science and thermodynamics:
Consider just water and ice for a second.
Changing temperature of water or ice or steam requires heat to be added or removed.
Changing a state from solid to liquid to gas (ice, water, steam) requires extra energy. This is why a teakettle will generate steam for a long time, with water at exactly boiling temperature and steam at exactly boiling temperature, before running dry. You can also have a mix of water and ice that is exactly at freezing temperature, without sufficient extra heat left to either melt all the ice or sufficient "coldness" of the ice to freeze all the water.
When you stick two objects of different temperature next to each other, they will try to become the same temperature. When you try to stick ice on a surface, it could melt for two reasons.
1. the surface is warmer than the ice and cooling it to ice temperature won't happen before all the ice melts.
2. the air is warmer than the ice and slowly melts it. This is more complicated, but the simple version is that when air changes
temperature it tends to move, so the air won't be cooled to ice temperature, instead new warm air will arrive to slowly add energy
to the ice until it melts.
How fast this occurs is based on something called "heat conduction". The easiest way to understand this is to think about an oven.
When you stick your hand in a hot oven, you don't burn yourself unless you leave it in for a long time and your hand actually cooks.
If you brush your hand against a metal rack though, you'll burn right away. Metal has a much higher heat conductance than air, it
will want to "even out the heat" much faster than air will.
So for your project, what you want to do is keep air temperature constant, make sure the surface you are putting the ice next to is
constant (probably room temperature, same as air), make sure your ice cubes start out at the same temperature (pull them from the
same freezer) and are the same size (more ice takes longer to melt).
What should happen is higher heat conductance surfaces should melt the ice faster. There is a bit of a danger though that if the
surface is too small the ice will instead cool it to freezing before it melts, and then all you are measuring is air convection melting.
If you had some way of keeping the surface at a known temperature it would be a better test. Or you could "bake" the surface in an oven
so it is considerably warmer than room temperature, giving it more heat to transfer. Not all surfaces may survive this though. Talk it over with your instructor.