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Patterns and Missing Pieces

Fractal, Spiral, Geometry, Perception

One thing both Zull and Zadina talk about are how much the brain "loves a pattern"!  From birth, the brain is constantly scanning for patterns, and it prefers complete patterns.  This helps us in math class because math is ALL ABOUT PATTERNS!

Mesh, Pattern, Grid, Grill, Line, Metal

Zull states "If we expose students to incomplete images, charts, or graphs where progressions are not finished, students become motivated to work on them." (p132)

Does your brain automatically try to place the puzzle piece where it belongs in the picture below?
Puzzle, Concept, Design, Plan, Team

Incomplete patterns are something that I have seen motivate students time and time again.  Math guru and blogger Dan Meyer (http://blog.mrmeyer.com/) advocates to use that motivation by providing problems without all necessary information.  As he puts it - "be less helpful".  By providing only the framework (image or context) and the question, students are forced to think deeply about the problem and what information they need in order to solve the question and finish the pattern!  Students with disabilities find these types of questions especially accessible because it's less about finding a specific answer with numbers that may seem complicated, and more about discussing the problem or pattern.  This is a marvelous way to engage students using their brains as the motivator!

Dan Meyer also engages the students' natural curiosity to illicit interest in solving mathematical problems.  A wonderful example of how he works:
http://blog.mrmeyer.com/2013/teaching-with-three-act-tasks-act-one/

For example, when you look at the picture of the coins below, what do you notice?  What do you wonder?

Achievement, Bar, Business, Chart, Coin

I love that patterns are so interesting to students!  I knew that it worked, (to provide incomplete information) but was not aware of the brain connection.  Now that I understand how motivated the brain really is, and how rewarding the brain finds completing a pattern, I am convinced more than ever to continue using incomplete patterns as part of my teaching toolbox!

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