With that said, there is a very brief period of my day, entirely unrelated to my classes or my students, that is the source of a disproportionate amount of my stress. I am examining ways to mitigate this, but as of now I am unclear on what to do.
I had a conversation with a supportive coworker today that helped me to pinpoint some areas for improvement and shed some light on the reasons for my anxiety. It's going to be a process.
I'm also noticing an interesting phenomena in my Algebra II classes. I gave an assignment yesterday for students to practice solving equations with 1 variable. With no exceptions, my students fell into one of two categories: they either blew through the problems (accurately) and asked what was next, or they became hopelessly stuck on the first one and spent 15 minutes trying to solve it.
There was no middle ground.
Looking at the questions, they were remarkably similar to those given today by the Algebra 1 teacher to his classes as well as bearing a striking resemblance to the ones I gave to many of these same students in Pre-Algebra.
Why do we teach the same problems over and over again and why is there no retention of this information?
A good friend who is working on her doctorate reminded me that OF COURSE there is no retention of this information. The process of solving equations doesn't really make a ton of sense and is often put out to a level of abstraction that makes it difficult for students to relate to.
The process of solving an equation is disjointed and unconnected to any tangible concepts. This goes slightly better when we use a physical representation, such as a scale balance, but ultimately this process has the same faults.
I am doing what I can to put in more concrete questions and lifting the restrictions of "write an equation that represents this situation." Instead, my directions are that I want to come up with an answer that makes, using whatever process makes sense provided that it is mathematically sound and they explain it.
To illustrate this point, we did a series of problems today that read something like:
Stefan left school and drove to his friends house. Eugene left school 2 hours later. He drove at 40 km/h for 3 hours and arrived at the same time as Stefan. How fast was Stefan travelling?
The traditional process would want students to set up an equation relating the various speeds and times.
As a class, we talked about how they would solve this problem if they weren't forced to make a single equation. What if they solved it like they would solve any problem outside of school?
We solved it one piece at a time, picking apart what we knew and finding things we didn't. When we finished, I showed what the traditional process would look like and we talked about whether one was better than the other. One way was better for generalizing and was more efficient, but the other helped students to understand why we were doing what we were doing.
I prefer the second way as I would rather they have understanding, trusting that efficiency will come later. I wish I had more time. 40 minute periods are not enough...
I love the context approach! Making sense of a problem and a solution is so valuable (someone should write a list of these valuable math practices). How are they with a representational approach? I found this Twitter thread pretty enlightening:ReplyDelete