A Brief Blog on Algebra

Students are introduced to algebra concepts from very early grades. Problems that ask for a missing addend, as an example, are a form of algebra. In later grades that missing addend is replaced with a variable. One important aspect of algebra that is introduced from the earliest grades is the meaning of the equal sign. Students often develop an understanding of the equal sign to be synonymous with the word "is." That understanding is not correct and can lead to misconceptions and struggles with learning more advanced algebra concepts. The equal sign indicates equal values on both sides. Each side can use different representations for a value, but the total value on each side must be equal. For example, in the number sentence 3x5 = 12+3, two different operations are used but each side maintains the value of 15. In the number sentence 3+5+2 = 4+4+1+1, younger students may focus more on the number of items on each side of the equal sign, whereas they should focus on the total value on each side of the equal sign. A math balance can be a great tool for helping students to understanding the meaning of the equal sign. I also like using the Pan Balance - Shapes and the Pan Balance - Numbers on the NCTM Illuminations site (Interactives) for emphasizing this concept. The Pan Balance virtual tools can also be helpful in supporting students as they transition from numerical equations to algebraic equations - all connecting back to the meaning of the equal sign!

Students often struggle to see the real-life application of algebra concepts. Solving for an unknown variable can be applied in a real-life context through word problems. Algebra concepts can also be applied to coding, as equations and problem solving are the basis for coding.

Understanding and application of algebra concepts is fundamental for higher level math not only because of the foundational concepts provided, but also because of the critical thinking and problem solving that can be fostered with applying concepts.