Last week, my content seminar professor asked us to explore some different blogs of fellow math educators on the Five Practices for Orchestrating Productive Mathematics Discussions – which is a fancy way of saying, “Let’s talk!” A blog I found to be extremely interesting and helpful with understanding this process was Christopher Danielson’s, which you can check out on the following link: http://christopherdanielson.wordpress.com/2011/08/30/five-practices-in-practice/
The five practices are:
1.Anticipate 2.Monitor 3.Select 4.Sequence 5.Connect
So basically, you first anticipate the strategies you think your students will use to solve a given problem. Doing this allows you to be a step ahead in the classroom so you will hopefully know what to prompt and say next. Next, you monitor your students’ work. This allows you to see if what you anticipated was correct. It can also help you to start making mental (or physical) notes of who you will call on when it’s time for the actual discussion. Next, you select. This is where you make your final decision on who you want to have share their findings to the rest of the class. This is extremely important, because the rest of the students are (hopefully) listening and will be learning from their fellow classmates. Also extremely important, is sequence, or order. The order in which you have students present their findings is crucial in that you want student learning to be optimized. And finally, connections. It is extremely crucial that students make connections between strategies of what has just been learned, especially if that means explicitly pointing them out as teachers.
This really inspired me to want to have a great discussion in the classroom. I tried my hand (slightly) at this on Tuesday. It wasn’t planned, but I had read the blog recently and it popped into my head as something that might work with this particular lesson. We were doing an exploration activity that was aimed at getting the students to discover the direct relationship between angle measures and opposite side measures of a triangle. I went around from group to group and wrote down on a note card which groups had different findings, and I had the order that I wanted them to share. What I hadn’t accounted for was that I already had the students set up in groups and discussing it amongst themselves, so when it came time to discuss as a class – they were about all talked-out. This was a classic case of beating a dead horse. However, I definitely won’t let this stop me from using this strategy many, many times in the future. I am really excited to see what kind of discussions can come from this.
“Spoon feeding, in the long run, teaches us nothing but the shape of the spoon.”