Independence: before they can learn, children must be allowed to try

To encourage childhood independence, a good rule of thumb is the following: When they want to do it, let them try! Even though a toddler will initially put his shoes on backward, or wash only the palms of his hands and not the backs, parents shouldn't complain (or try to take over the task).

Learning to be competent and independent takes a long time, and children must be free to mount - and master - one step before going on to the next.

One place where learning can always be encouraged is the kitchen. Today cooking is a family affair. A boy or girl who grows up to be confident in the kitchen makes a wonderful roommate or marriage partner. It makes sense to let a small child try his hand at ''kitchen things'' as soon as he shows any interest.

Most preschoolers begin by wanting to wash dishes. Part of this stems from their fascination with water games, but it can be a learning experience, too.

Simply fill a dishpan with warm water, suds, and plastic items (don't include cutlery, breakable dishes, or glassware); let small children kneel on a chair; and give them a sponge. Prepare for water on both the floor and your children (you might want to dress them in their raincoats), but it's a small price to pay for a first ''cleanup'' lesson. As time goes on, you can also teach them to rinse, dry, and put away the items.

By the time children are 3 or 4, they will probably want to prepare some of their own food, and you should certainly let them try. Sandwiches are fun and easy, especially if you assemble all the ingredients.

Show your children how to wash and blot the lettuce; let them spread peanut butter or mustard with a blunt-edged knife. And don't criticize if first efforts produce holes in the bread; preschoolers can't automatically exert the right amount of pressure.

Children can pour cereal into a bowl for breakfast, too, but lifting and aiming a milk pitcher may be beyond their present skill. The first appliance they use will probably be the toaster, so be sure to show them how it works, caution them about touching it, and stand by until you are certain they can handle it alone.

These first kitchen experiences will probably result in spills and messes, but parents should remain cheerful and encouraging. An atmosphere of goodwill will whet a child's interest in perfecting one task and learning the next.

As children grow, they can peel vegetables for salads or soup, use the hand mixer for cake batter, make milkshakes or fruit drinks in the blender, and eventually follow a recipe. When they've progressed this far, you can allow them to use the stove and oven, provided you are present.

Start with just one burner and pan (perhaps for hot chocolate) and show your child how to adjust the burner control and turn the pot handle to the inside of the stove. A good beginner project for the oven is a batch of cookies or a brownie mix; demonstrate the use of potholders and how to set the oven timer. Let your child do as much of the actual work as possible, getting involved only if there's a problem. You'll feel as triumphant as he or she does when the family admires the finished product.

When introducing children to kitchen tasks, remember to emphasize the following:

1. Hands should be washed before beginning. This is a basic element in food preparation, and it ought to be learned right away.

2. Cleanup is mandatory. No child should be permitted to cook (even if it's just making toast) without wiping crumbs and replacing butter in the refrigerator. 3. Mistakes are OK. Even adults occasionally ruin a meal, and children should feel free to fail now and then. If a burned pan of cookies is overlooked, a pint-size cook will try even harder the next time.