I have always been taught that you use gears to maintain a specific leg cadence i.e. number of leg cycles per minute, shifting up or town to maintain that cadence. Some cyclists are "spinners" high cadence riders others are more "power rider" using leg strength to compensate for a lower cadence. Higher gears should in fact increase your speed at a given cadences once you get more wheel revolutions per leg stroke by using lower gears on hills you can maintain your cadence.
Here are two good websites with explanations in depth. www.livestrong.com/article/389622-what-gea