The times when I notice the changes that are happening in our craft over our implementation of the common core standards do not occur with a frequency I would hope for. One of those moments occurred as I am cleaning out my digital closet: I found some notes I had prepared for my algebra students my first or second year of teaching. The standard stated
19.0 Students know the quadratic formula and are familiar with its proof by completing the square.
What I did: Under the guise of direct instruction I wanted to give the kids an “easy” to follow, step-by-step to start with the homogeneous set of a quadratic equation in standard form and through the process of completing the square to arrive at the quadratic formula. So, I created a fill in worksheet that the students and I went through, then I gave them the mathematical equivalent of sentence frames to reproduce the exact steps we had just covered. I would then reward the students for being able to fill in the blanks and follow the brightly illuminated path to solution.
The predictable outcome: The notes and student work look like this
Each step was part of a PPT presentation and the students were to copy those steps and listen to the rationale of those steps. This kind of teaching makes me shutter at this point in my career, the cold detached nature of completely irrelevant math facts, in a complicated manner to find an equation that the students either already knew or could find in a few minutes on their phone. The blank stares, the constant yawning, the glossy eyed students staring back at me as I dutifully taught the lesson in the manner I had been instructed made me think I was doing my job right. At one point, I was even complemented on the lesson and the “good lesson” I was giving on this difficult standard. This problem struck me then, as it does now, how sterile math had become, and this is the example I often think of when “I teach high school math. I sell a product to a market that doesn’t want it, but is forced by law to buy it,” said Dan Meyer.
What is this approach missing: I usually don’t like to repeat the same negativity without offering any solutions, but this one is screaming at me so loud I do not hear new thoughts creating in. The biggest problem I have with this particular piece is the lack of student buy in to the problem. As I stated earlier, the sterility of the presentation of the problem and the lack of student experience to make this a relevant problem are slap you in the face obvious.
What I am missing: The problem I have had since digging this up is creating a relevant scenario that would get the students to buy into how we start with one and end up at the other. The idea I feel coming on is literally a map with the steps are the part key you must solve to get the next piece of the puzzle, and creating a positive interaction to see where kids stand…however, this isn’t a context where the math naturally arises, so it looses a lot of its power. I am coming up blank with a good idea on a way to make this happen, but I will keep looking for ideas.