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.
When students are are practicing their skills in Algebra class, some students will be unsure of how to solve a problem, and some students will be able to proceed confidently. The difficulty is connecting the confident students with the students who need help. I use the "Ask an Expert" approach to address this disparity of knowledge in my class.
Take a worksheet and divide the practice problems into four sections and clearly label them J, Q, K, and A. Take all royal and ace cards (sixteen cards total) from a standard playing card deck and give one card to each student. Have students get into groups of four according to the rank of their card: J, Q, K, or A. The students are given time to work on the set of practice problems. They should attempt all the problems, but they should give special attention to the problems with the same label as their card. After ten minutes, students get into their Expert Groups according to the suit of their card. In their Expert Groups, each student is responsible for explaining the problems they focused on in their first group. Give students five minutes in their Expert Groups, then have students provide you with the answer key and address any unresolved questions.
I really like this method of doing practice problems for several reasons.
This activity is easily adapted for different size classes and different types of problems. Here's a recent worksheet that I used the activity on.
I'd love to hear how you do skills practice in your classes. Comment below.
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.