More times than I care to count, my son would say to me after hearing an answer, “I wrote down [insert number], I just forgot the negative.”
I knew then we had a serious problem! Somewhere he had missed the important concept that negative numbers are different numbers. Eventually, number lines and graphing convinced him of this. But, that realization came in identifying the origin and going back to basics.
He didn’t like that solution one bit. As we reviewed key pre-algebraic concepts, we discovered more “negatives” in the form of learning gaps and lazy habits. He renewed his understanding of fractions and place values. I insisted he show his work and stop trying to work the problems in his head. In his mind, he was achieving the answer quickly. He didn’t realize that in skipping steps, he was missing the most important end result.
Going back seemed like a negative process for both of us. We wanted to move forward. We thought that was the only way to stay positive. Often in life our attitudes only adjust by reincluding long-forgotten basics. Somehow we find ourselves “two steps back” and not “one step forward.” But, those backward steps are critical for us to determine the desired outcome. Without them, we fall flat on our faces.