### Miguel Hernandez and Dr. Ivona Grzegorczyk

## Abstract

This project incorporates graphical visualization of polynomial functions. We use these graphs for solving polynomial equations. Students were first asked to explore characteristics of polynomial graphs, then students were asked to identify possible roots visually and write their own factored equations. Two groups of students used this method in different ways: first group started with graphing polynomial equations, then moved to solving polynomial equations using algebra, the other group began by solving polynomial equations algebraically, then were asked to interpret their solution using graphs to identify polynomial roots. I compared both methodologies and their effectiveness on student learning by applying appropriate statistical methods, based on data collected on student performance, using various assessments. This research is very important and timely, since high school students have problems with questions and mathematical problems related to polynomial equations and generally perform below the expectations on standardized testing. Students tend to have a difficult time understanding exponent rules and polynomial multiplication. For this reason, I strongly believe that providing students with visual representations of polynomial equations will help students make connections between algebraic and graphical polynomial representations.

Congratulations Miguel!

Why did the control group contain younger students? You have some interesting discussion at the end.

The results are very interesting. Good data analysis and presentation. Excellent job !