"The Big Five" model is a personality theory that describes personality using five basic traits. Openness to experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism make up this theory... an easy way to remember this is with the acronym OCEAN. 

How do these traits affect a way a child learns in school? It is necessary to examine each of the traits individually. 

Openness to Experience

Openness is a general appreciation for art, unusual ideas, curiosity, and imagination. This trait distinguishes people who are more imaginative from those who are down-to-earth. People who are more open tend to be more creative, more likely to be open to new and different ideas, and more in-touch with his/her feelings. 

People who score lower in openness to experience tend to be more closed-off. They are generally more analytical and resistant to change. They see imagination and art as things that are a waste of time. 

So how would this apply to a learning environment? A child who has a more active imagination will be more likely to create stories, be better readers, and develop better writing skills. Curiosity breeds good questions which causes a search for answers and when people a looking for answers, not just going through the motions, they are more likely to retain the information. 

People who score lower on the openness to experience scale are more likely to be concerned with grades. They are more likely to just work hard for the sake of hard work. 

Conscientiousness

Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. This trait shows a preference for planned rather than spontaneous behavior. Conscientious individuals achieve high levels of success through purposeful planning and persistence. They are also regarded by others as responsible and reliable. They can become compulsive perfectionists and workaholics. 

In a learning environment the benefits of being conscientious are clear. A person who is more conscientious and plans his/her work and practices self-discipline will be more likely to succeed. Those people are focused and aware of the work that needs to get done and do it in a timely and efficient manner. Teachers would generally describe conscientious students as the responsible students.

Extraversion

Extraversion is the tendency to seek out the company and stimulation of others. The trait is marked by pronounced engagement with the external world. They tend to be enthusiastic, action-oriented people, who love excitement. In groups they like to talk and draw attention to themselves.

Introverts lack the exuberence, energy, and activity level of extraverts. The tend to be quiet and low-key and not very involved in the social world. Introverts shouldn't be confused with depression or shyness, they simply lack the need for external stimulation that extraverts crave. 

In a learning environment, either extreme is generally considered negative, however usually people get more concerned when their child doesn't want to play with other kids. There is nothing wrong with not needing lots of time with other people but it is important to not let a child isolate. In school it is important that the pressures that come along with social lives don't get in the way with learning. 

Agreeableness

Agreeableness is the tendency to be compassionate and cooperative with others. The trait reflects individual differences for social harmony. Agreeable individuals, as the name suggests, generally get along with others. They generally have an optimistic view of human nature. 

Disagreeable individuals place self-interest above all else. They are not very concerned with others' well-being, and are less likely to extend themselves to others. They tend to be skeptical of people's motives and of human nature which can make them suspicious, unfriendly, and uncooperative. 

In the learning environment it is much more helpful to have agreeable people. Cooperation is one of the most important things kids learn in early childhood and so more agreeable children make for a better adjusted classroom. Also, if you have a classroom full of disagreeable people it will cause too much turmoil for learning to take place.

Neuroticism

Neuroticism is the tendency to experience negative emotions, such as anger, depression, or anxiety. Those who score high in neuroticism are highly reactive in stressful situations. They are more likely to interpret ordinary situations as threatening or minor situations as too difficult or as impossible. 

In a learning environment those highly neurotic people have a harder time adjusting to stressful situations. When presented with a difficult situation or a problem that they don't know how to figure out, they just break down rather than being able to handle the situation. They also get angry easily and don't know what they are angry at, themselves, the homework, the teacher, etc.