Patterns and the Induction of Rules

     Another type of concept learning or induction task is where you are given the first n, usually 3 or so, members of a pattern; and you are to discover the rule that covers the examples and predicts the future elements in the sequence. Usually the rule is some function of n.

     An interesting set of materials of this type that were studied with children were patterns which are generated from "geometric numbers."

     These are functions that not only have a simple mathematical form, but they also allow one to depict the function in a regular geometric form.The figure to the right animates the first 3 elements of one of these types of geometric sequences.

    The figure below summarizes the basic questions that were asked in these experiments.

 

 

 

 

Clicking on the figures below will open a page that shows cards 1 - 3 and card 9 so that you can try solving these rule pattern problems.


Pattern Problem 1

 Pattern Problem 2

Pattern Problem 3

Pattern Problem 4

Pattern 1

 Pattern 2

Pattern 3

Pattern 4
Clicking on the figures above will open a page that animates the first 11 elements of the sequence.


     Note that in order to answer these questions you probably found it useful (and probably even necessary) to think about the pattern using the geometric representation as well as a representation as an equation expressing the value as a function of n.

Induction,Concepts, Uncertainty
© Charles F. Schmidt