Yesterday’s class featured a discussion of absolute value inequalities, and using Desmos to explore problems through graphs. I knew that not all students were totally on board with this method for comparing two functions, but I felt confident that many in the class could now analyze an inequality problem using a graph.
So, the problem on the board when students walked in was intended to see if yesterday’s discussion could transfer to new ideas. Would my students now be able tackle a more difficult problem, or a problem with a similar theme from another chapter – like the polynomial problem I gave as a bonus? Would they impress me with their ability to analyze the inequality?
The first two hands raised to offer solutions gave close, yet incorrect answers, as they used Wolfram to “find” an answer – and incorrectly interpreted the output. Other students attempted a combination of factoring / dividing / shuffling of terms to gain some insight. But as these students have only some limited experience with quadratics, extending to the cubic was difficult.
But I’m not surprised, nor at all disappointed. My students have been trained very well in algebra as mechanical steps. The idea that we can analyze a scenario by looking at its graph is much more foreign to them. I only hope that I have started to chip away a bit and get them thinking about multiple perspectives. And by the end of class, I finally noticed some students toying with Desmos and looking at the given cubic. Tomorrow I’ll help them cross that bridge.