A developmental psychologist who used the correlational method found that there was a positive correlation between children's self-esteem and their academic achievement

First, what does a positive correlation mean in this case? Second, how might these results be explained?

What will be an ideal response?

Answer: A positive correlation in this case means that children with high (low) self-esteem also manifest high (low) academic achievement. Results could be explained in a number of ways: (1) high self-esteem gives children confidence, so they try harder and achieve more; (2) high achievement boosts children's self-confidence and self-esteem; (3) some third variable such as parental involvement or intelligence might cause both self-esteem and achievement to be correlated.