In both of the EdX courses I took from Stanford, the professors often mentioned how important working with others and discussing justifications can be. I believed it worked– for others. It was one of my “I am awesome and independent” moments. Sure, I would encourage my students to pair up and talk about the questions and answers that came up in class, but it was never something that I had intended to practice myself. This changed Monday, when I swore during my Intro to Probability class.
We were asked how many permutations there were in the stringing of a necklace, consisting of three different-colored beads. We easily came up with six. Next, we were told to discuss within our table groups how many possibilities there were without repeats (Since the necklace would connect, rotations would fall into the same permutation). I came up with two. My partner claimed that there was only one. We argued a bit, then I finally raised my voice and said, “No. See, there are three rotations of this one [where I gestured to my model], and three reversed rotations of that one, and unless you flip the necklace– Shit!” My partner and professor grinned and some of my classmates snickered. My prof then waited as I explained to the rest of the doubters how there was only one unique way to string the necklace.
By justifying my reasoning that there were two options aloud, I was able to hear the flaw in my logic that my partner had seen. I was also able to solidify my understanding of the problem by tailoring my justification to make sense to other students who I had previously agreed with.
Communication is something my prof frequently encourages during class. There is a very small portion of class time spent watching him write on the board or explaining concepts without us interrupting with questions and comments. When we bring something up, he immediately asks us what our interpretation of the issue is and to try to come up with an answer in our own way and at our own pace. Class discussions continue to play an important part in my learning. When I believe I understand a concept, I can turn and explain my thought process to my partner, who then peppers me with questions about every step I’ve made. This helps me find and understand my mistakes and gives me a chance to practice my own teaching skills for the future. When he grasps something first, he’ll explain step-by-step, then ask me to re-explain it to him in my own way, to make sure I ‘get it’. These activities have deepened my level of understanding for the subject and helped me to double-check my work and fix mistakes early on.
While class discussion may seem overrated to introverts and independents (like me), it is a key element in the learning process– particularly due to the requirement of putting thoughts into words and listening to what comes out. I highly encourage classrooms to become less listen-and-repeat and more discussion-based. I was very surprised at how much of a difference it has already made in my education.
Dividing by Zero 