The In-Crowd: A Study of High School Students' Problem Solving Techniques When Calculating the Area of Irregular Polygons

Abstract

This research investigates student preferences of approaches and techniques used when calculating the area of irregular polygons. On a more conceptual level, this study was designed to analyze whether students demonstrate appropriate problem solving skills or simply the memorization of a single procedure. It was hypothesized that high school mathematics students would tend to choose one method and use that method regardless of its efficiency. To be more specific, it was hypothesized that students would choose the to use the addition method (breaking the polygon into smaller familiar shapes with known area formulas) more than the subtraction method (enclosing the shape in a rectangle and subtracting the area of the empty space) or any other method. The results of this study suggest that, as predicted, students do not use the most efficient method for calculating the area of an irregular polygon 72% of the time. However, further analysis reveals that students most often choose to employ methods other than the addition or subtraction method. While less than half of participants were able to use those other methods correctly, approximately two thirds of those who used the preferred methods (addition or subtraction) obtained correct answers.