Analyzing Geometric Patterns

Friel S.N. & K.M. (2009). A Framework for analyzing geometric patterns tasks. Mathematics Teaching in the Middle School. 15(1), 24.

This article begins by impressing the importance of students thinking algebraically in the middle grades. It explains that thinking algebraically is essentially recognizing patterns and devising functions to express those patterns. In the middle grades, students work largely with patterns that grow, and using geometric figures is an effective tool for helping students recognize patterns of growth and develop their functions. The authors of this article developed a framework for helping students find patterns and functions. First, they discuss patterns and develop rules to match their patterns. Then they record their information in tables. Finally, they organize their information from the tables into graphical representations.

I always struggled with figural reasoning when I was a student of mathematics. I could figure how many smiley faces were in the 10th stage, the 43rd stage, the millionth stage - but when they asked for the nth stage they lost me. For this reason, I would use the information in my future classroom to help students understand what the nth stage really is - it is the result of some pattern they have found, translated to a numerical formula. I think that using geometric figures is an excellent way to teach and reinforce algebraic thinking because not only does it provide a visual for the students when seeking patterns, it helps them connect algebra to geometry. For these two reasons, I would definitely use this information in my future classroom.