Patterns and Inductive Reasoning

     We see patterns every day in all aspects of our lives everyday, from the woven fabric of your clothes, to the street-lights, to the aisles at the grocery story. While patterns often hold together parts of our daily lives, they are also the essential keystone to mathematics. Dictionary.com defines the word "pattern" as, "a combination of qualities, acts, tendencies, etc., forming aconsistent or characteristic arrangement." Without patterns, we would have no idea how to solve even the most basic problems because we would not have the ability to carry the knowledge from one problem to another.
     Inductive reasoning is the tool we use to transfer patterns between different situations by making generalizations about a certain pattern, then recognizing those generalizations in another problem, then applying and modifying techniques in order to solve the problem. A good example of the inductive reasoning process can be seen in this worksheet, Number Patterns Worksheet. This worksheet uses skip counting, or arithmetic sequences,  starting with counting by doubling to establish a pattern of counting by other numbers than one. It gets progressively more difficult and incorporates subtraction. This worksheet is a great example of both patterns and showing the inductive reasoning process because students have to assess the problem, determine the pattern, then move on to a more difficult kind of pattern using the same techniques.
     Patterns are an essential part of mathematics at all levels, and teaching kids how to observe patterns and recognize their differences is a tool that will help them succeed in all levels of math, as well as other subjects.