A basic mushroom growth experiment is feeding some mushrooms fresh water. Feed another group of mushrooms water containing organic materials. Measure the growth rate every other day and compare the results. The soil or base for both mushroom groups should be the same and expose the containers to the same amount of light.
For peroxide-cleansed mushrooms, start with mushrooms in a high-nutrient soil. Because mushrooms do well in warm, moist environments, keeping out mold and other competing life is difficult. Peroxide does not kill mushrooms but wards off mold. Feed a control group of mushrooms basic water and fertilizer while the peroxide-treated group receives the water-fertilizer combination as well as having peroxide poured on the matrix in which the mushrooms grow. Run more than one group, putting varying amounts of peroxide on different groups. This helps to determine the most effective amount of peroxide for maximizing growth.
Mushrooms grow well in hot, humid environments but rarely enjoy direct sunlight. Testing how different types of light effect mushroom growth is an interesting experiment. Create a series of boxes for mushrooms. All the boxes should contain the same growing matrix, get the same amount of water and be sealed. One box totally blocks all light, another has a clear top letting in all light while the third has a tinted cover letting in some light but not full sun. Take measurements every few days to decide what mushrooms are growing the most quickly.
Another light project requires making a series of boxes. One box lets in no light, a second exposed to natural light and the third to UV fluorescent light. Treat all three boxes the same other than the light exposure. Measure the growth rates and see which grows the most rapidly.
Place mushroom spores in different growing bases or matrixes. One could be fresh soil, another hardwood and a third soil with decomposing plant parts. This gives the mushroom different fuel in addition to the water and fertilizer. Take measurements. The mushrooms grow better when placed in a closed environment but experiment with open air as well, as long as all matrixes are treated the same.