Monday, September 17, 2012

Math is the Science of Pattern

Every semester when I start a new math ed. course with a new group of students I increasingly see the value of exploring and including the ideas associated with pattern in the course. When you stop to think about  it there is almost nothing random about math, in fact, trying to come up with complete randomness requires the sue of sophisticated computer models.

There are several different definitions of "pattern"; pattern as a design, pattern as a model or something to be copied, and pattern as a regular sequence or set of events. It is this last definition that is most relevant here. If we can help children see patterns between different mathematical entities it will help them remember, recall and make sense of what they are learning. We can do this from the earliest stages when children learn to count by 2s, 5s and 10s. What makes this type of activity even more worth while is to count by 5s starting at 3 or count by 10s starting at 7. Whenever i do this with my students I can see them initially stumbling and going slowly. Then, as they see the pattern emerge they speed up and end up rattling the number sequence off.

The Fibonacci number pattern identified by the squares above and dun flower to the left is a classic number pattern that occurs all over the place. It can also be demonstrated in the Sierpinski triangle, a classic fractal, as well as in Pascall's Triangle.

Here's another amazing number pattern. Add 1+2 (=3)+3 (=6)+4 (=10) +5 (=15) +6 (=21) +7 (=28) +8(=36). These are called triangular number because they make triangles (imagine 1 + 2 next to each other like steps etc). Now add consecutive triangular numbers together and what do you get? Yes, a square number. Imagine turning 3 upside down and fitting it together with 6 to make 9.

Math is, indeed, the science of pattern. 

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