When we reach the midpoint of the school year, we consider student placement options for the upcoming year. Who’s performing at or above grade-level expectations and who’s not? Who’s ready for algebra, and who simply needs another year of arithmetic to be prepared for the rigor of algebra? Whether you're teaching accelerated Grade 7 students or Grade 8 students heading into high school, how do you know or feel reasonably confident that they will be successful in algebra the following year?
On Your Mark: Thinking about Algebra Readiness
Let’s discuss the basic concepts that must be mastered for algebra to make sense to students. The Oxford Dictionary defines algebra as “the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.” As a high school student taking algebra, I remember the adults close to me remarking about “math with letters” that they couldn't comprehend. If all those letters do is represent numbers, then proficiency with all things numerical should prepare us for algebra. Students need to have number sense to understand what numbers represent and how they are used to solve problems.
Get Set: Examining Algebra Skills Essential for Student Success
For starters, algebra-ready students have a solid mathematical foundation. They are fluent in basic operations and have a firm grasp on rational number operations, including a good understanding of the relationship between fractions, decimals, and percentages. They can identify and apply the properties of mathematics. Furthermore, students should be well versed in ratio and proportional reasoning and be able to recognize and interpret proportional relationships, including those that use a percentage as the constant of proportionality. They should be able to generate equivalent expressions and extend their understanding of independent and dependent variables into the development and solving of complex equations.
A fundamental understanding of geometry—shapes, solids, angles, and angle relationships—prepares students for successful problem solving in related algebra topics as well. No formula is too hard if students have a solid understanding of how to substitute values for variables and move around an equation using properties of equality. They must completely understand how the equal sign works as a fulcrum in a balance and how to maintain that balance in equations. The number line and the coordinate plane—plotting and graphing—should be second nature to algebra-ready students.
Let’s Go! Inspiring Future Mathematicians
Beyond covering our grade-level curriculum standards, what can we do to push students along the path to success in algebra? We can start by nurturing their “mathness.” Some kids come to middle school believing they are not “good” at math. At this level, we must impress upon them that everyone can be good at math—some just need a little more coaxing, and everyone needs lots of practice. We must have high expectations and give students many opportunities to discover math, apply different strategies, and dig deep into real-world problems. Above all, students should be independent problem solvers who can recognize reasonable answers and justify their thinking. Students who practice talking and writing about their math thinking are much more likely to truly understand the concepts. When they spend time analyzing their errors and the errors of others, they increase their own conceptual understanding.
Algebra is the gateway to higher-level mathematics. If students are ready for algebra, they are primed to be ready for anything math has to offer.
Want to hear more from Rebecca about algebra readiness? Tune in to our Extraordinary Educators™ Podcast. Or, learn more about assessing algebra readiness for your students.
