Algebra is that branch of mathematics which deals with solving equations, using letters to represent unknown quantities. The difficulty with algebra is that for most students the many letters and symbols create an abstraction that is hard to see through clearly. After all, when you see a bunch of x's and y's and other expressions involving a host of mathematical symbols, your footing can quickly be lost and your head could start reeling off track. To ward off this experience, which I call the "algebra syndrome," students must be taught algebra in a way that removes any unnecessary abstraction and paves a clear-cut road through the mist of confusion.
If students are shown ways to deal with the unavoidable abstractions in algebra, then they learn quickly to adjust for them and are not intimidated when they encounter an expression or problem that they have never seen before. By learning some tricks or short-cuts, students gain confidence and are better prepared to take on the challenges that algebra will invariably present. In one of my ebooks, I talk about some novel ways of handling and solving equations using the "light switch property." Another shortcut I teach to solve equations is called the "bridge-toll method." By giving meaningful names to abstract methods, the teacher lets students visualize the procedure and think about it in a way that makes it more concrete. After much of the abstraction is removed, students gain algebra mastery in a short span of time.
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