How do we learn patterns? Usually as young children we first look at logic patterns. After all, making categories—doing classification—comes before numeration. We have to be able to tell which things are blocks before we can learn to count blocks.

One kind of logic pattern deals with the characteristics of various objects. Another kind deals with order: there's a sequence of objects and a pattern in the attributes the objects possess. We see this type of pattern on aptitude tests. There are three figures, for instance, and we select one of the multiple-choice answers to mark which figure comes next.

Here are two activities—each with a different kind of logic pattern—that require you to identify and use attributes of objects. (Don't forget to read the activity background for more ideas on classroom use and connections to standards.)

• In Guess My Button the computer has secretly chosen a button. Can you figure out which one it is? What fits? What doesn't fit?

• If you see a line of people do you think you could discover a pattern? Figure out who should come next in a sequence of People Patterns.

You can easily adapt activities like these for a wide range of grade levels. For younger students, use fewer and simpler attributes. For older students, use more and subtler attributes with more distracters (i.e., irrelevant attributes) thrown in.

Reasoning about sequences of attributes reinforces understanding of number and function. Reasoning about attributes also leads to better understanding of logic, both the common-sense logic students use in every class and the more formal logic they need in higher grades to learn about proof.

These days, however, we need formal logic for more than proof. Every time we search a database, we construct logical expressions with Boolean operators such as AND, OR, and NOT. People Patterns and Guess My Button are the kinds of activities that will help students communicate with machines more effectively.

NCTM Standards (1998) contain numerous references to patterns. In grades preK–2, for example, all students should

• sort and classify objects by different properties;

• order objects by size or other numerical property (seriation);

• identify, analyze, and extend patterns and recognize the same pattern in different manifestations;

• describe how both repeating and growing patterns are generated.