This is a big question and there are many and varied answers which correlate to it.
In my personal opinion I think that peoples behaviour can be modified through the guidance and instruction and an individuals characteristics can be transformed through virtues instruction and good moral examples within the society and culture that influence them.
Some philosophers reject the idea that human nature has an inherent inclination towards goodness. Hsun Tsu for example proclaimed that people were born with an evil mind and that if the mind received correct guidance and training these evil traits could be controlled and in turn may lead to goodness. He advocated that the mind was bad by nature but he did agree that personal experiences and interactions could possibly help to illuminate to a degree some of the inherent cognitive evil and be cured of this evil and embody human goodness.
From another angle the philosopher Meniscus believed that humans are born good and it is the situations and surroundings that corrupt the mind and cause individuals to react inn an evil way. No one acts in an evil manner unless first exposed to what is deemed to be immoral and again as in many areas of philosophy what is seen as immoral in one culture may not apply to that of someone from a different upbringing and culture.
Each of us as we grow we learn from parents, peers, teachers, TV and the society in general what is right and what is wrong and it is a subjective matter which path we choose to take. Goodness I feel can most defiantly be something that can be taught as is can be said the same of evil, an individual can make their own decisions from the information humans attain to make a conscious choice of what type of character they turn out to be, good or bad or even a combination of both of these factors.
I would like to conclude this section by quoting from Plato. He said that people are representations of things here on this earth and therefore are born without being either good or evil, but neutral of these factors. It is impossible for an individual to be truly evil because humans only represent the ideal evil. Nobody knows what evil is, evil is what we encounter throughout our life.
One may be perceived as a good person by a cult who beheads people in the name of a non existent God, while those who believe in this non existent entity could see this act as a symbol of virtue and respect such foul actions.
Can goodness be taught? Yes in some respects I believe it can but goodness can at the same time represent evil when viewed by a distant on looker who’s ideas reflect others disapproved notions.