I do not teach special ed., but I can help a little with your question. Crossing the mid line of your body helps build pathways in the brain. You can do exercises with your children that require them to cross the mid-line. ie.. touching the opposite elbow, crossing one foot over the other walking sideways etc. There is a lot of brain research out there. You may have hear of "Brain Gym." They have a website you could google and get more info. I hope this helps some.
Some children actually have a problem "crossing the midline" of their bodies (an imaginary line down the center of the body from head to toe). They cannot reach across their body with their right hand to pick up an object that is on their left, or vice versa. They get "stuck" in mid reach & will have to switch hands. This can also apply to the legs, but is more noticeable with the hands/arms. Not being able to cross the midline may affect a child's ability to read, write, participate in sports & physical activities, etc.
As the previous poster noted, this all has to do with "brain programming", etc. Brain Gym exercises that involve crossing over to touch the opposing shoulder, elbow, knee, toe, heel, etc. can help "program " the brain to do this. You may have to physically assist the child to make the movements across the midline.
If the child is very young, you can try table exercises to cross the midline. While sitting at a table, have them pick up a marker, toy, cheerio, etc. that is placed on their right, but gently restrain the child's right arm and make them use their left. If the item they are reaching for is an item of great interest (favorite toy or treat), they will make a greater effort to get it. Again, you may have to physically assist the child to move the arm across the midline.
Another suggestion is drawing large lazy figure eights (the infinity sign, or an 8 laying down). This can be done on a chalk board, in the air or on large piece of paper. I have also had my students walk along a figure 8 I drew on the carpet. It was interesting to see them stop at the crossing point and turn right & walk a circle instead of crossing the line!
Too often, children do not do activites which require the use of their two hands working in conjunction with one another. For example, our current fads in technology such as texting, computer and video games, rely on the hands only working for a goal to be achieved on that particular side of the body. Children, as a result, are unable to ride a bike as young as they used to be, reach for things using the hand on the opposite side of the body and coordinate to catch and throw balls. Some things you should keep in mind is to encourrage your children to manipulate steps (do not put both feet on the same step in order to get down), reach for things on the opposite side using the hand farthest from the object. DO NOT allow children to play video games for extensive pedrriods of time. Use it as a reward and limit it to 15 minutes daily.
Children should be coloring, playing with play dough and doing activites that enable upper body strength.