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Probably the most important fundamental branch of mathematics is algebra. No matter what anyone tells you folks, if your kid is not good at algebra, there is no shot that he will excel in any of the higher branches. In fact, the famous calculus is really a form of "glorified" algebra and this is what I used to tell my high school students all the time. Therefore, if you want your kids to have a chance to study and enter the beautifully intellectual realm of the calculus, then be sure that they have the tools to master algebra.
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, students can visualize the procedure and think about it in a way that makes it more concrete. By removing as much abstraction as necessary, a teacher can give students algebra mastery in a short span of time.
See more at Cool Math Tricks and Algebra Shortcuts Ebook
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