I really like your idea for a science project, I think it is very interesting and something that most adults probably don’t think about. In my opinion, the best way to design this experiment would be to look through your 6th, 7th and 8th grade math textbooks and pick out a few problems from each. Perhaps choose 10 questions from each grade level, and try to vary them so that you would cover all the topics learned in the year. Then you could administer your math test to a group of adults, 8th grade students, high school students, and elementary school students. You could grade the tests and determine which group did the best. The 8th grade students would be your positive control group, meaning they should do very well because this test was designed to be something they will understand. The elementary school students would be your negative control group, because they should not have learned these things yet and should therefore do very poorly. The high school and adult groups would be the experimental groups because you are not sure how they will do. I think it would be interesting to look at high school students and adults because that will tell you how long people retain their middle school math knowledge. Be sure to keep track of the ages of all your test takers. Also, it might be interesting to keep track of the occupations of the adults who take this test, so you can see which occupations retain middle school math knowledge the best (perhaps engineers and teachers retain it better than lawyers and writers).

If you want to perform statistics on your results, I think a one tailed student’s t test should work, making your comparison to the 8th grade test taker average. You want to see if the others scored significantly lower than this group. If you enter your data into excel it should be able to make these calculations for you. Good luck with the science project!