This has been a question of much controversy, not really for training professionals, but more amongst semi-educated workout enthusiasts. The answer lies in the fact that the average male has 10 times more testosterone than the average female.
If you are the norm, your fear of "getting big" won’t materialize. Having said that, I suggest you train within the generally accepted hypertrophy zone, which is 8 to 12 reps. We all need to gain muscle mass simply due to the fact that eventually our bodies will begin to atrophy with age, so the more overall mass and strength we have the better off we will be in the long run. To make a long story short, high reps of 20 or more, is really not as effective as lifting a bit heavier with the recommended number reps. Don’t worry, you won’t "get big," just better!