You can help strengthen your child’s intrapersonal intelligence by:

Giving him a diary and encouraging him to write in it often. Holding goal-setting sessions and letting him decide how he can contribute to the family. He can set a goal to make the bed every morning, for example. Establishing a quiet time in the family schedule, immediately before or after dinner, perhaps. Encouraging him to express his emotions, asking him to explain how he feels about family, school, his friends, and so on.

Source: The Association for Supervision and Curriculum Development’s Professional Development Online