Developing Mathematical Fluency (ePub)

While many persons see education as the process of acquiring knowledge that involves memorizing facts andprocedures, mathematics is not just a set of rules. An alternative way of thinking about mathematics is as theactivity of constructing patterns and relationships. In this view, mathematics is something people do. Knowledge isnot acquired but constructed by the individual as he or she solves problems. In today's fast changing society withnumerous new challenges, it is important that students give meaning to their mathematical activity and be able to solveproblems not seen previously. Mathematics is reasoning, not just memorization. While it is useful to know certain facts and procedures, it isessential that these facts and procedures develop with understanding. For example, a student who thinks in tenscan see immediately that 34 + 16 is 50 without going through some arbitrary set of steps by making marks onpaper. Mathematics is more like learning to find your way around a park with many trails. With experience thatinvolves exploration, a person can build a mental map of the park and move through the park without getting lost. Inthe same way children can build networks of schemes that allow them to cope with novelty and solve problems theyhave not previously considered. Just memorizing facts and procedures can actually be debilitating since it bypasses theimportant activity of building inter-connected mathematical ideas.