According to Piaget's theory of cognitive development, the ability to think about things that are not concrete, make predictions, and use logic to come up with hypotheses about the future is attained during the <em>Formal Operational Stage.</em> This stage starts at age 11 and goes through adulthood. Kids develop the ability to think about abstract ideas, make predictions, and think logically.
Algorithm could be described as a way of carrying out a process through following instructions strictly. It's a systematic way of going about a process.
The problem solving method that involves the systemic search is called An algorithm