When we left off, we were talking about the double-slash, a form of notation I’ve developed that helps students attain greater focus when simplifying algebraic expressions.
With greater focus, students make fewer mistakes. With the double-slash at their disposal, students avoid the mistake of combining terms that should not be combined. In the following example, students use the double-slash twice to simplify an algebraic expression:
+ 8 – 2(3x – 7)
= + 8 // – 2(3x – 7)
= + 8 // – 6x + 14
= – 6x // + 8 + 14
= – 6x + 22
By cordoning off the section with the distributive property: – 2(3x – 7), the double-slash allows students to see it distraction-free. With this heightened level of focus, students are more likely to work out the distributive property correctly, then continue on, simplifying the whole expression with no mistakes.
In a sense, the double-slash gives students a chance to “take a mental breath” before proceeding, similar to the way that a period ends a sentence and thereby allows a whole new thought to commence. So when students take up the next part of the problem, they are not affected by the + 8 that lies to the left of the double-slash.
Through this example we see that teaching students to simplify algebraic expressions involves art as much as science. The “art” aspect of algebra instruction requires us to take into account how students think, how they get distracted, and what kind of visual set-up makes correct thinking more likely to occur. With this awareness, teachers can develop strategies, like the double-slash, that maximize students’ chances for success and minimize their chances to go astray.
I use the double slash for a wide range of situations. In the next several posts I’ll describe a variety of situations where it has proved helpful. I also encourage you to look for situations where this notation would be useful. Feel free to leave comments on this blog if you would like to share any.
Final comment: as a tutor I am working with students who face significant challenges learning math. You may have students who have no need for notation like the double-slash. If so, that’s fine. I’m not trying to force anything on anyone. I am merely offering this strategy as another tool in the math teacher’s “bag of tricks.”