While the sinful heart is always in play in our lives we cannot deny there can be other factors that will promote anger in a child. These have to be examined in light of his or her regeneration and cannot be dismissed or ignored. The world our children live in is much harsher, colder than the one you and I grew up in and I would also say it is a lot more dangerous.
One possible reason for a child to be angry is difficulty in school. Children who struggle to learn battle more than just poor grades, they also are confronted by their peers who can be so cruel and mean. Slow learners are made fun of and ostracized and school becomes a place of emotional torture for some.
Children who are not gifted with an ability for sports are also ridiculed. Some kids are just not agile or built to play sports! One of my sons had the height for basketball, but nothing else that he needed to be a good player. As hard as he tried he was more of a hindrance than help on the court and it was discouraging to him! No one likes to be the last one picked in gym class or for a sports team. When other players equate your reason for living with your ball handling skills it can be very upsetting.
Children who are overweight, underweight, or with distinguishing features also have a hard time in school and anger can result. As I said, kids can be very cruel and when a child is the daily recipient of cutting remarks and other hurtful things anger becomes a lifestyle for them.
Is the child overtired? When a child is tired it is a sure thing that crankiness will be the result. It is not reasonable to expect a young child to be shopping at midnight on Thanksgiving night! Yet I saw too many kids out with their parents getting "the deals" that could not wait, kid howling in the cart and parent yelling at them to "shut up."
Is the child hungry, or bored, or in some other discomfort? Yes, these are all reasons kids get angry and there are heart attitudes to address in each one.
The child who struggles in school for academic reasons; in addition to getting the child the help he or she needs I would suggest dealing with the heart issues as well. This child knows he is different, he knows he can't keep up and it is a cause for embarrassment for him. He does not understand that he is fearfully and wonderfully made (Ps. 139) and that God did not make a mistake when He put him together. You will have to deal with the issues of self-pity and possibly sorrow without hope (what the world calls depression) in addition to the outbursts of anger. Taking each sin issue and dealing with it on the heart level will help you and your child to understand that the anger problem is not only external, but internal first.
What an opportunity to help your child understand the message of the cross! Teach him to live his life to glorify God in whatever ways he can. Not everyone is intended to be an Einstein and that is ok! He needs to focus on glorifying God with his thoughts, beliefs, and desires and as he does his school work for the glory of God instead of A's and B's his attitude may change.
When the kids in his school or neighborhood are cruel and mean he has a great opportunity to demonstrate Christ-likeness toward them. Teach him to live out 1 Peter as he suffers.
For you have been called for this purpose, since Christ also suffered for you, leaving you an example for you to follow in His steps, who committed no sin, nor was any deceit found in His mouth; and while being reviled, He did not revile in return; while suffering, He uttered no threats, but kept entrusting Himself to Him who judges righteously; 1 Peter 1:21-23 (NASB)
This is a valuable lesson to learn at a young age! This change has to begin in his heart before it will be visible in his life. Continue to encourage him to show love to those who don't deserve it as Jesus has done for him.
You must confront the sin of the child biblically. Keep addressing the root of the issues you see, not only or even primarily the behaviors. Ask questions instead of making statements at them. Seek to learn what they are thinking about, ask them what they believe to be true about something or someone who is troubling them. What do they believe to be true about themselves? These questions can open doors for you to see in your child's heart and develop biblical strategies for change on that level. Just like adults they must also be transformed by the renewing of their mind (Rom. 12:2).