The Expertise of Those in Authority

As some of you may already know, my school is fortunate enough to be located across the street of a major university specializing in agriculture and engineering. TAMU is a wonderful resource with many experts in a plethora of fields. We public school teachers are lucky enough every semester to get these professors, researchers, graduate students, and in-service teachers into our classrooms.

What do you though when one of these experts disagrees with the fundamentals that you teach, or presents a different mathematical concept to your students? Are these experts automatically correct because they are “higher on the food chain” than us public school teachers?

This doesn’t happen very often, but this present school year has continually brought up the debate about simplifying algebraic expressions containing exponents, particularly those with negative integers. My whole life I have believed the following:

(–3)^2 = 9 but –3^2 = –9

This has been questioned by different authorities in the science and mathematical realm. They are exerting that –3^2 = 9. I am totally baffled!

As my students work on Cognitive Tutor, the software doesn’t allow 9 as an answer to –3^2. At first they are frustrated because of the misconception. It’s a good learning lesson for my students. I ask them that if they were to follow the order of operations, would they apply the exponent first, or calculate the negative multiplication?

I believe that young people should have healthy respect for those in authority. At the same time, I am glad that I live in a time and place where we can also respectfully challenge and question experts. Every once in awhile, I am wrong and have to go to my students and confess. Hard to believe, I know! :-) On the plus side, this allows for rich discourse to occur in my classroom.

So, the next time someone tells you that half a tablespoon is equivalent to one teaspoon, my advice is to do your research and decide for yourself!