We spent a great deal of time over the last month working on memorizing multiplication and division facts. We also ventured into the world of exponents (squares) and tessellations. I had planned on spending the remainder of the school year teaching Roman numerals and doing a quick review for CAT testing at the end of May.
Yet, with the results of Alex's comprehensive test, I changed course a bit. We would have to go back and review and master the concepts in which he was lacking. First up: addition equations. After working with my son the past two days, I have come to realize that Alex has the ability to read a math problem and know the answer, as long as the numbers are fairly small. Many individuals with a basic working knowledge of arithmetic can do this. Take, for example, 2+x = 4. Obviously, x = 2. But, one must learn the proper steps to arrive at the answer so that one has the skills to solve 4907 + y = 90,672. Alex is lacking a mastery of those steps. Apparently, he had been getting by on luck and chance, rather than a true working knowledge of the concepts.
Alex's fourth grade teacher was satisfied that he provided the correct answers to the equations with which he was working. She didn't apparently care how he came to the answer. The end product was more important than the foundation. This wasn't going to fly with me. Remember, a foolish man builds his house upon the sand, while a wise man builds upon the rock. The basic steps needed to solve algebraic equations serve as a foundation for higher mathematics. If Alex really wishes to become an engineer when he grows up, he can't glaze over these key concepts.
Therefore, we are working diligently to show work, even when it seems unnecessary. Alex is also learning to check his work, an idea that is apparently entirely foreign to him. "Plug it back in," I say. It will become our mantra.
I knew that there would be gaps in Alex's education. I knew we would have a rough road ahead. I just didn't realize how many potholes we would find. Granted, he wasn't passed along each year without learning how to read, but I have to wonder what other knowledge we may be missing.
Photo Credit: Mykl Roventine