Working with the definition of linear patterns

Non-traditional pattern is a collection of concrete or abstract objects that have at least one characteristic in common, and are arranged in a manner such that the characteristic of one given object can be discerned from the other objects in the pattern.

Linear Pattern – kid-friendly definition – a list of numbers that increases or decreases by the same amount between each number

Linear Pattern – my formal definition – sequentially arranged numerical values (or objects that can be quantified) whose absolute value difference between immediately previous and subsequent values, is equivalent.

What is different between the kid friendly and formal definitions of LINEAR PATTERN?

The fundamental difference is that the kid-friendly definition implies that a linear pattern must exist as a list of numbers. The formal definition allows a linear pattern to exist as a collection of objects, as long as they fit the given definition. In this way, the formal definition is more general and can be used in a greater variety of situations. The kid-friendly definition can be used in specific cases in which numbers are the objects in the pattern. This is most likely the type of linear pattern that they will experience in math class.  This definition does not however, necessarily cover geometric patterns that may exhibit characteristics of a linear pattern (say the number of sides of subsequent polygons increase by one each time).

How to get students to understand the formal definition.

I think that by introducing students to patterns, that exhibit a linear component (such as the examples explained above) but are not strictly numerical, they will recognize how patterns may linear but not necessarily contain numbers. If they are familiar with the kid-friendly definition, they should be able to adapt it to include these other example patterns.