From a cognitive-development standpoint, this is called a concrete operational period, according to Jean Piaget.
(N.B: Some adults never progress beyond this phase, while 15% of kids may reach the following formal-operational phase at age 9!)
The child now (7-12) may factor in two dimensions of an object simultaneously. So, the longer cup may have less water because it is thinner. However, this is still hard for him/her to perform in the abstract realm, so, they are still uni-dimensional in that respect. Concepts and behaviors are still black and white. It is also hard for the kids in this stage to imagine and solve the structure of a mathematical problem. They cannot think contrary to facts. In other words, you can’t get them to use as a basis for an argument a question like what if the sky rains sugar instead of water?
Socially, Erikson felt that in this period kids develop industry or inferiority. According to his theory, from age six to puberty, children begin to develop a sense of pride in their accomplishments. If encouraged, they feel industrious and confident in their ability to achieve goals.
Based on these observations, we may recommend:
1- Using a lot of hands-on teaching, since they still have limited ability with conceptualization and abstract reasoning.
2- Continue the focus on memorization. If you want them to finish the Quran in 1-2 years, 12 and/or 13 seem to be the prime years for that. This suits some children and some families, not all. If you like a more gradual approach, you should have them start serious memorization at 7, accelerate at 10, and finish by 15-17. Not all kids are meant to memorize the whole Quran though; they can still be educated and pious. Invest in their strengths, not your dreams.
3- Use concrete props and visual aids, especially when dealing with sophisticated material. Use story problems in mathematics.
4- Use open-ended questions that will stimulate thinking and help the child reach the following stage faster. Example: “What do you think about the relationship between the brain and the mind?”; “What do you think about the relationship between prayful-ness and piety?” Make sure you know the right answers!
5- More explanations will be needed, but keep them simple, and even though they should be more detailed than the last stage, they still need to be uni-dimensional. Examples: we obey God because he created us; if we disobey Him, we get punished, and if we obey Him, we get rewarded in this life and in the hereafter. Too early to teach him that “the brokenness of the disobedient is better than the haughtiness of the obedient.” Break it down. Humbleness and obedience are good, while haughtiness and disobedience are bad.
6- Encourage and praise their accomplishments, while making them aware that there is always room for improvement. Continue to encourage initiative-taking and leadership qualities, yet you may also set limits, and make them aware that they will have to always report to someone. Even if there are no people above them, Allah always is. They have to adapt to being leaders and followers at the same time, because that is the reality of all people.
7- This is still a stage of belonging and affiliation to the group, and the child will develop more or less attachment to Islam through his or her experience at the masjid and with the community.