In what way can homework influence the development of emotional intelligence?
Emotional intelligence comprises many different attributes, attributes that are important in having insight into others and oneself and acting intelligently upon those insights in ways that make us interact with others in a more satisfactory and productive manner. It might seem somewhat counter-intuitive to think an activity done on one's own would help one develop emotional intelligence, but it can.
Let's take the attribute of perseverance. Perseverance is an aspect of emotional intelligence that is of high value. When we are able to persevere, we can complete tasks in spite of obstacles and encourage others to do so as well. People who quit at the first obstacle are unable to recognize and address their emotions regarding their work. Overcoming obstacles to complete homework teaches us perseverance.
Another aspect of emotional intelligence is self-discipline. We are almost valueless without this since a lack of self-discipline can prevent us from doing whatever we need to do or cause us to give in to impulses that are harmful or otherwise counterproductive. Self-discipline also makes it easier for us to get along with others, as most people find a lack of self-discipline to be a very unattractive trait. Completing one's homework teaches self-discipline.
There are also specific kinds of homework that could promote the development of emotional intelligence, for example, being assigned to read a novel or a non-fiction text might help us better understand ourselves and/or others. Empathy is a strong feature of emotional intelligence, and those who read literature have it to a much greater degree than those who do not read.
So, you see, whether you are sitting in a room by yourself grappling with algebra problems or at the library reading about World War II, you are exercising your emotional development muscles!