Math Geek Mom; Squares and Diamonds

In geometry, we study the “Euclidean motions in a plane”, which include translations (sliding a figure across a plane) as well as other motions, such as reflection and rotation. I found myself thinking of the motion of translation recently when I met someone who works in special education, and we began to discuss the idea of what it means to say that someone has a learning disability. Of course, I have come to prefer the label of “learning difference”, because that is what it really is.

Imagine two square figures, both of the same size. One of these figures is resting on a side, while the other, poised like a diamond, rests on one of the corners. If you think about it, there is no way to use the motion of “translation” to get the two congruent figures to line up exactly on top of each other. To do so, one would need to rotate one of the figures, which is not part of the motion of translation. Simply sliding either of the figures in the plane will never allow the square to become a diamond, and would never allow the diamond to rest on its side.

I think of the many students with learning differences that I have taught over my more than twenty years of teaching college, and this seems to be a good analogy for how a teacher needs to think of teaching students who are diamonds and not squares. The usual approach, which works on most squares, just may not work for diamonds. And yet, I am intrigued by the fact that we say that anyone who does not learn like a typical square must be “disabled”. Could it not be that those with learning differences are actually in possession of special skills that allow them to see the world in a more insightful way? Could those with learning differences actually have skills and abilities that the world desperately needs, but which are so unusual that the teacher used to teaching only typical students can’t relate to them and leverage them for their own benefit using typical approaches?

I think of one woman I know who had a very difficult time with standardized tests throughout college, but earned almost a perfect grade point average when her master’s program asked her to write papers. Her talents for writing were hidden when she was tested in the traditional way, especially in large science classes, but, when allowed to come to light, allowed her to shine. Today she works with people struggling to regain their lives after serious injuries, and has been a powerful influence in the lives of many people on such journeys. Because I know her story, I make it a point not to give multiple choice tests in my classes.

I remember one parent saying that we don’t really want “normal” children, because none of us think of our children as “normal”; we all think our children are amazing. Just how they are amazing differs from child to child, but none of us wants the world to see our child as completely unexceptional. After all, in our eyes, they are unique and precious.

The special education teacher I met recently summed this idea up by sharing a quote on the vocation of the “intervention specialist”. By John Fischer, an American pianist, sculptor and composer, it reads “The essence of our effort to see that every child has a chance must be to assure that each has an equal opportunity not to become equal, but to become different-to realize whatever unique potential of body, mind and spirit he or she possesses”

To all the wonderful diamonds out there that I have had privilege of teaching over the years, may you always continue to shine!