On the musing of Michael Pershan on Twitter this week I created a quick activity for my students to see if Venn Diagrams would help them understand solutions to systems of equations. I used the very excellent Desmos activities to help build my class’ understanding solutions to systems of equations so they already had some background, but I still felt like it was a worthwhile activity.
What I ended up giving the students to try needs to be developed some more. I began with a quick reminder of how Venn Diagrams worked and as a class we filled in a large Venn Diagram on the board with characteristics of dogs versus pigs. Then I transitioned to having them decide where solutions to different linear equations would go and what belongs in the overlap. The sheet I gave their groups to work on had three systems of equations. The first had one solution, the second no solutions, and the third infinitely many.
If I try this task again, I need to scaffold some more and plan for more classtime. This should be easier as the next time I teach it this idea will not be an on-the-fly based on inspiration from Twitter. I am thinking of something where a list of solutions are given to students and they have to decide where each belongs. This could emphasize not only what a solution to a system of equations is, but also how an ordered pair is a solution to a linear equation all by itself. Then in the next problem they could be given less info and would need provide more themselves.
I did not get as much discussion out of my students about what belongs where in the Venn Diagram and why as I would have liked, but it was a start. And the students had a chance to work together for the first time in class, which I was also hoping for. I saw various degrees of on-task behavior. I pointed out to the class what I liked and didn’t like about how they handled group work and encouraged them for next time.
I had some students who I had to move at the beginning of my middle block today because they were too disruptive yesterday. During the group task even though I had not placed them in groups they were disruptive again but did not misbehave during the other activities. I will need to talk to them about how when we do group work it does not mean that suddenly all proper class behavior goes out the window. I also had to move another student in my last block and that block struggled to get some chatter under control today. They were slower to transition activities correctly. I addressed it immediately and I will follow up with it again tomorrow. I am really hoping to avoid a situation like last semester where I start out connecting with a class and then I lose them and never really get them re-wrangled. However all of my classes were good. It was by no means a bad day.
Tomorrow they take a homework quiz with problems exactly from the homework assignments I gave this week that I did not check but did allow them to ask questions about. I am hoping this will work as a compromise between not checking homework and keeping them accountable for practicing the ideas from class. The first standard quiz is also tomorrow. I hope that this doesn’t end up being too much for them, but the quizzes are different in purpose, style, and import. But that’s how I see them and I am not sure if the students will agree. I am curious to see how it will go.
I am really feeling some of the time pressure from this class and the South Carolina EOC exam. I still do not think I have enough time to give them enough cycles of quizzes and learning before I need to give the Unit Test along with the department and be on pace to complete the curriculum. I know we like to say “we don’t cover curriculum” here on the math-twitter-blogosphere but to me right now it feels like a reality of the course I have been assigned. I don’t mean that in the sense of “Okay I talked about it so they should know it” but in that I have to teach a specific list of topics in a certain amount of time and if we don’t get through all if it then my students won’t be fully prepared for the test.
I’m not exactly complaining either, I’m just feeling a little pressure and I am worried about doing a good job. I definitely think there is a difference been the task of teaching math in this class context and the task of teaching math. I don’t know if that is going to make sense to someone else when they read it, but I have been struggling with wording this post correctly for over an hour now and have taken frequent breaks so I think it’s time to publish it and be done with it.
Thanks for reading.