Grandma always said "Idle hands are the Devil's workshop" and I, for one, agree!  Active Engagement of our children is an excellent behavior reduction technique.  When children are not actively engaged they can get into a world of trouble.  Keeping them actively engaged in preferred activities can go a long way in avoiding problem behaviors.  While independent play is an important skill for children to learn, it also gives parents and teachers an excuse to not actively supervise.  This lack of active supervision (a key component for active engagement) can often lead to children engaging in problem behaviors. 

Take, for example, when you leave your toddler or preschooler in the living room while you are cooking dinner in the kitchen.  You may initially set them up with activities (coloring, puzzles, books, etc.) and walk away.  Since you are cooking dinner, your full attention is not on your child.  The next thing you know, your child has colored on the wall!  In my daughter's words (hands on cheeks) "Ah nah!"

A classroom example might look like this:  You have instructed your Kindergarteners to play freely (i.e. "free play") prior to morning instruction.  While your students are engaged in "free play", you continue to plan the morning lesson.  Your can see and hear all of your students; however, your full attention is not focused on the children.  The next thing you know, someone is crying.  Why?  Because they are Kindergarteners and when left to their own devices they will likely not engage in sharing behaviors (or a multitude of other behaviors).  The likely scenario?  Someone took someone else's toy resulting in that someone hitting the offending child who is now crying. 

ACTIVE ENGAGEMENT!  Yes, it requires much more from us as parents and teachers.  But it also reduces the chances for our children to engage in problem behaviors.  With active engagement, we can stop the behaviors before they start and teach appropriate behaviors in the moment.