For a policy issued on a child, usually the parent is the owner and beneficiary and the child is the insured. Your parents may have changed the owner to you when you turned 18 or at some other point when they took care of the paperwork. With a tiny policy like those, the gift tax implications were probably non-existent.
Depending on the type policy and the dividend option chosen, the policy could have a fair amount of cash value. Probably not $1,000 but enough to make it worth cashing in. Assuming you have taken care of your life insurance needs through term insurance and have no need of the coverage, you have to look at a whole like policy like an investment.
What is the guaranteed interest rate? I've seen old policies that guarantee 4 to 6% interest rates. Those may be worth adding as much premium to as the insurance laws will allow. Then the cash value will grow at the stated interest rate. Growth of the policy in the past and in the future could vary widely depending on options chosen at issue. If the dividends were purchasing paid up additions, the death value could be well over $1,000 - so couldn't the cash value.
One option is to request an in force ledger from the insurance company (the individual agent can take care of this too if he or she is still around). This will tell you cash value, death benefit, projected performance on guaranteed and assumed interest rates, etc. If premiums have been paid to date, you can ask to see a premium vanish and see if the policy will still grow.