It’s hard to explain. Honestly, when people ask, “Why should students learn to factor over the integers? Can’t they use the quadratic formula instead?” I can’t just say, “Factoring is faster.” Because it isn’t – yet. Not at first.
You see, factoring over the integers has a steep learning curve. When first introduced to it, the initial reaction is a blank stare and a furrowed brow. Which is completely understandable. The process takes place almost 100% in your head, so from a student’s perspective, it looks more like magic than math. “How did you do that? Where did those answers come from?”
Once you master it, however, the answer “Factoring is faster,” is absolutely true. To prove it, we’ve video-taped the process of finding the roots to the same quadratic equation using the 3 most common methods: factoring over the integers, using the quadratic formula, and completing the square. Watching them side-by-side, it’s pretty clear which method is best for the situation.
See? It took 3 steps to factor over the integers (Advanced students might even cut it down to 2.), and 7 or 8 for the other methods. With a difference of over a minute in time. Don’t you think that might be an advantage on a test?
That’s why it’s worth the extra work to learn it. Once you really understand it, the time and effort put into finding the roots of quadratic equations is greatly reduced.
And, no, it doesn’t mean students shouldn’t learn the other methods, too. Each method is particularly useful in specific situations and with certain types of equations (like complex roots and finding the standard equation of a conic section, for instance). That’s why it’s important to learn all three. Learning how to factor over the integers is simply the method I would recommend for general use in finding the roots.
What other “Why” questions do your kids ask? How did this video help you understand why we teach factoring over the integers?
Author: Elizabeth F., Writer and Teacher at A Grade Ahead