Math Thinker

I’ve been experimenting with the use of Algebra Tiles. I like the idea of visually representing values and variables. When I was learning Algebra in middle school and high school many of the things we learned seemed so abstract. I always felt like we were learning rules about abstract things, but in Catholic school we had no exposure to mathematical concepts such as the Properties of Numbers, the Properties of Rational numbers. We were drilled on how to do the ‘mechanics’ of math, addition, subtraction, multiplication and division plus a thing or two on how to use the same operations on fractions. By the time I got to high school I didn’t know what hit me. The math teacher was speaking a muddle of a language that I could barely understand, and considering my upbringing and former educational experience, I focused only on memorizing equation types. It was a very short sighted and limited way of learning. I know it was awful, but I really do think that the words of that fifth grade teacher (I wrote about her briefly in a previous post) really stuck with me. She sent this message that basically told me that it was okay to give up. I should understand now that she was only human and she had her own fears when it came to math (she was a Baby Boomer teacher and most likely grew up during the Donna Reed age where understanding and mastering higher math wasn’t a goal expected of most women).

I muddled my way through Algebra and then found my way into a Calculus class. Our teacher in this class was a very caring and methodical woman who really had a passion for her discipline. She even took us to see “Stand and Deliver.” Incidentally, Jaime Escalante became a sort of role model for me and his work actually inspired me to become a teacher myself. However, by the time I got to Calculus, I still had a really bad or superficial understanding of some of the number sense basics (Integers, Rational Numbers, Properties, Operations, etc.). I wonder how I was able to even manage a C in Calculus.

I actually created a set of my own “eTiles” for Powerpoint. I’m including images here.

Ooops…. the operation should read 2x²+4x+12. Ahhh the joys of using graphic tools that don’t have superscripting. Thanks to my commenter for the correction.

I wasn’t sure how to represent negative numbers so I did so by circling the depicted value with a dotted red line. It might be embarrassing to admit this, but I feel a sort of healing and relief as I worked to develop these visual images. Perhaps actually creating these pictures help re-reinforce the concepts I probably did get, but only half way.