Teachers in the Churchville-Chili Central School District always are searching for new and better tools to help students learn.
Math can be daunting for many, especially algebra with its abstract concepts of equations and solving for variables like X. Last year, the district introduced a system of learning that uses manipulatives to help students grasp complex mathematical problems more quickly.
Manipulatives — concrete objects that can be touched and moved, and aid in counting, equations, fractions, multiplication and other math tasks — help students visualize complex math concepts. Teacher Brittany Fitzgerald is using manipulatives to introduce her seventh-grade class to algebra.
“Equations are like balances — each side must be equal to the other,” she told students in a recent class while she moved red cubes representing positive integers to both sides of a scale. “If I replace the cubes on one side with this single unmarked blue figure, which represents a variable called X, then we know that X is equal to the total number represented on the cubes sitting on the other side.”
The math progresses from simple to challenging as the lesson proceeds. Green cubes are added to represent negative integers; yellow figures represent (-X). Soon, students are able to solve 2(2x + 3) = x + 12.
After this introduction, students gradually use the manipulatives less frequently so that they can solve equations using paper and pencil. Manipulatives can help them master the abstracts of algebraic concepts.
Churchville-Chili teachers use manipulative math tools like these in the Middle School and Ninth Grade Academy. The approach, Hands-On Equations, is validated by research and testing, and the district sees success at the ninth-grade level.
Students are quick to adopt the method. Comments include, “This is much easier. Very hands on, more visual”; “I can actually see the answers with this”; and “I can solve harder, more complicated equations than I could solve before.”
“Many students find that the visual representation makes algebra simpler to understand,” Fitzgerald said. “It is an easier way for them to solve problems and to check their answers. It is already making a noticeable difference for students in my classes.”