The ability to solve equations is a foundation of algebraic instruction and algebraic thinking. The student who is able to demonstrate a mastery of this skill is well on the way to success in understanding algebra and achieving success in higher mathematics courses. In this video, Brad and I will show you how we have presented this concept successfully in our own middle and high school classes. Our students have exhibited a high level of mastery of this concept both in their conceptual understanding and their computational expertise.
Brad and I begin our instruction in solving equations by establishing a solid foundation for understanding how the equal sign functions in mathematics in general and in algebraic equations in particular. You will see us initiate our lesson by asking students to solve equations that are presented in parallel conjunction with a visual model of a balance scale.
As a teacher and an expert in the needs of your specific students, you will decide how much of a foundation already exists in your class and how much still needs to be developed. Thus you may leave the visual model sooner or later depending upon your students’ conceptual development of equation solving.
This foundation is not only necessary for your students’ understanding of equations, it will also provide invaluable assistance to their teachers in future higher mathematics courses who build upon the foundation we establish. Often students demonstrate some success in mathematics until they reach the secondary level. This can be attributed to the fact that some of them do not really understand mathematics at the elementary level but are simply mimicking our models and processes without conceptual fluency. As these mathematical processes become more involved in middle and high school, their lack of understanding leaves them with skills that are little more than trying to master algebra by rote procedures. While this worked on simpler or shorter problems in the past, it leaves them wandering without a compass in the rugged algebraic landscape.
One of the components of teaching mathematics using Conceptual Layering is the presentation of concepts using positive whole numbers. Only when students have demonstrated an understanding of the concept are fractions and negative integers introduced. During the course of this training video, we will focus on equations that utilize positive whole numbers to develop the concept. Many of the worksheets in the accompanying PDF handout provide students with opportunities to practice these same concepts with more challenging numbers.” The vocabulary of additive inverses, multiplicative inverses, subtraction, division property of equality, and combining like terms are all covered in this video.