Arbitrary and Necessary

I was always aware of the difference between arbitrary and necessary realms in mathematics. As a student, I never understood why my teacher made me memorize formulas in a math classroom. It did not enhance my learning journey and made me spend less time practicing my logical and critical skills when solving a problem. As a math teacher, I need to make sure I am helping my students to practice their own awareness as this is a crucial skill in mathematics and problem solving. The article talked about a teacher informing their students that the angles of a triangle add up to 180 degrees. This example made me think about one of my lessons during my short practicum. I had to teach my students the quadratic transformations: stretch, vertical translation, horizontal translation, and reflection. However, my SA and I agreed that we did not want to tell our students what a, p, and q does in y=a(x-p)^2+q. Instead, we created an activity where students were able to investigate and play with Desmos, numbers, and tables of values to observe what each variable represents. Hence, this will drive students to use their awareness to come to their own conclusions. This also can be easily done through whiteboards. The day after I taught my students each of the transformations, I made them work in pairs and use the whiteboards to draw the graph of y=a(x-p)^2+q. The process of playing and struggling first before I gave them the lesson enhanced my student's understanding of this specific chapter. When I become a math teacher, I want to implement activities that will allow students to use their intuitive thinking to play and struggle before I give them my lesson. I believe that giving a lesson at the start of a class will allow students to practice developing their awareness instead of memorizing information.