I have completed my first term in the Mathematics Learning & Teaching (MLT) program at Drexel. The course I took was about using consistent language to describe varied phenomena from across algebra. Associativity, commutativity, identity, and existence of inverses apply equally well to addition of real numbers, addition of functions, and addition of matrices. Associativity, commutativity, identity, and existence of inverses (except for zero!) all apply to real numbers. However, with function composition and matrix multiplication, inverses become scarcer and commutativity fails for both operations. To hear more of what we talked about, you can watch my final project video.
My main takeaway from the class was a desire to have my students to see the unifying principles that apply across algebra. When we write $x(x+3)$ as $x^2+3x$, that's distributivity. When we add fractions with a common denominator, that's distributivity. When we FOIL a radical expression, that's distributivity! Students should feel that what they learn in one chapter carries over to the next chapter.
In terms of my three personal goals for the MLT program, this course has come closest to informing how my practice serves all my students in their lives outside of mathematics. If students are able to recognize similarities in different mathematical situations, they may be better able to recognize similarities and patterns in other places. I believe this is true, and it's a connections I want to draw tighter still.
You're always welcome to drop me a line and let me know your thoughts or how you serve your students.
I started this blog to share my transformation from math nerd to math nerd who loves to share math with young people. I teach high school in Philadelphia, Pennsylvania. Your comments are always welcome.