3 things to add outside of what everybody has said about saddle height:

1) if you're new than you probably haven't developed high cadence pedalling techinque yet. it takes time and time is the only way to build it! practice practice practice. before you know it your avg cadence will increase from week to week on your rides.

2) one thing that works for me to smooth out my pedalling at higher cadence is to focus on keeping my heels down a little bit from wherever they were. it's a natural tendency to pedal "toe down" as your cadence increases. if i focus in keeping my heels down so my feet are flatter (note: by flatter i mean relative to the "toe down" position, not actually level) than what my feet do automatically, it's much more smooth and i actually have a higher power output via my powertap.

3) what also works for me in keeping a smooth rhythm if i'm riding tempo or doing an interval, i focus on the top half of the pedal stroke. i think it's Lemond(?) that says to think about scraping something off of the bottom of your shoe and pull your foot back at the bottom of the pedal stroke. for me it's the opposite that works better. i focus on pulling across the top as if i could pull my foot directly from the 9 o'clock to the 3 o'clock position. it makes more sense to think of it this way anyway because when people do one-legged drills - where's the dead spot? at the top! so why not focus on pulling your leg/foot across the top and this easily eliminates that problem and gives you a fluid pedal stroke.