Learning from Mistakes

Learning from Mistakes

I tried something new in my intermediate algebra class. Over the last 3 classes we covered absolute value equations, absolute value inequalities, and graphing absolute value functions. I tried to tie these ideas together through the magic of Desmos, and although it started strong, it could have ended better.

We began with the equation \left \| x-2 \right \|+1=5. Students solved this by hand and we went over the solution. Then I had students use Desmos to graph y=\left \| x-2 \right \|+1 and determine where it intersected the graph of y=5. Students observed that the x-coordinates were the solutions of the original equation. Students, in groups of 4, went on to solve six equations in this fashion, including equations that would have been extremely difficult to solve.

We regrouped as a class and reflected on this strategy, and the level of understanding was strong.

Next we moved on to absolute value inequalities. We discussed how the same approach could yield the endpoints of the intervals. Students first solved the absolute value inequality \left \| x-2 \right \|+1<5 by hand, then we examined how we could obtain the solution from the graph. Together we worked through two more examples, first solving by hand and then by using a Desmos graph. Here’s where it started to go badly.

I’m not sure if I just was not getting the idea across, or whether there were students not paying attention, but there were many students who were solving the inequalities by hand rather than using Desmos as I had instructed. There were constant questions from students trying to solve, by hand, inequalities that we had never learned to solve by hand like \left \| x+6 \right \|>2x-9 or \left \| x-4 \right \|<\left \| 3x+7 \right \|. The questions seemed to make the class a little chaotic, and I felt like the end of class was confusing for some. I spent 15 minutes after class clearing up some misconceptions, and those students seemed to have things under control.

I think my approach was a good one, and will continue to use it with equations. We won’t see inequalities again for several weeks, and hopefully this will be more accessible to my students by the time we get there. I will spend 15 minutes of the next class going back over this material, and hopefully it goes well.

If I am going to be the best teacher I can be, I know I have to be open to the idea that not every idea will work perfectly and be willing to take a hard look at what I could do better. That’s the growth mindset at work, and I feel I have learned from this experience.

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