A Balancing Act: Making Sense of Algebra

A Balancing Act: Making Sense of Algebra

Sue Pawula

Summary

            This article demonstrates ways that students can use balance scales, bar diagrams, and shared mathematical reasoning to develop deeper understanding of equality and variables in relationship to equation creation.  Students need to develop their skill using numbers in computational procedures and operations through making sense of problems, reasoning abstractly, and modeling their thinking using graphs, tables, diagrams, and more.  They need to explore the structure of the numbers and create dialog to justify their thinking as well as analyze others reasoning in a respectful way.  Understanding equality, by making sense of problems, justifying their reasoning, and considering others tendered solutions, allow students to gain a stronger hold on how to use and interpret the equal sign when they see it.  By showing their reasoning using a variety of different visual models, they also aid others in their class through access to diverse solutions that might be the particular lenses that these other individuals can see and learn more effectively through.  Compensation strategies were also discussed to help students build mental computation fluency as well as reasoning abstractly and quantitatively.  Final focus of the article was student knowledge development on interrelationships among variables as well as the effects of operations on the variables.  Overall skills were focused on helping students become better mathematicians in equality and build deeper understanding of variables and their relationships in equations.

Reflection

            This was a very intriguing article to read since many of the practices discussed in it are also practice in the early elementary classrooms.  The idea of using scales with objects on them to show students what it means to be equal is a very powerful visual.  Also, the use of the bar graph to depict the differences in the number values is another visual that is meaningful and easier to draw as the numbers become bigger.  Justifying answers and being able to explain and defend how they came up with their answer can help many other students, as well as developing the ability to listen to someone else’s reasoning of how they developed their answer and view it through another mental construction, is so valuable in providing students with a variety of strategies to use when solving real life problems.  Finally, letting students “play” with the variable can be like letting them play at putting a puzzle together.  That can be such a difficult skill for them to make the associations necessary to understanding.  Building deeper understanding of equality and variables will give all students a strong base on which to build their Algebraic foundation skills.

Gavin, K. G., & Sheffield, L. J. (2015). A balancing act: Making sense of algebra. Mathematics Teaching in the Middle School, 20 (8), 460-466.