Practicing Math Practice 3 With Our Master Teachers
When it comes to teaching lessons aligned to Mathematical Practice 3, our Master Teachers often find that less instruction is more impactful.
In order for a teacher to recognize that students are learning effectively, his or her students must be able to communicate what they understand and what they don’t understand independently of a teacher’s direction. Our high school Math Master Teachers meet up regularly to discuss Math Practice Standards. In February, they discussed Math Practice Standard 3. You will find that each MT has his own tactics to get students to communicate their arguments, strategies and understanding.
Here’s a refresher: CCSS.Math.Practice.MP3: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
This blog highlights:
1. Master Teacher Jacob Nazcek addresses MP3 in his lesson, “The Parallelogram Rule”.
“This lesson I selected to focus on MP3 and the parallelogram rule for the addition of complex numbers. In the previous lesson, we would have actually introduced the notion of adding two complex numbers – the real parts and the imaginary parts. This lesson really focuses on the development of the rule and the justification of the rule (hence MP3).
I’ll have a student come to the board and explain how to do the addition.
Then, when that student is done, I’ll ask someone else to come up and connect those lines and we will begin a discussion about how we can prove that this figure is a parallelogram. During this whole process I try to step into the background. I say very little. As students ask questions, I point those questions to the kid in the front of the room.
This kind of lesson I really enjoy. In some sense, my job is really “easy”. I ask some questions and walk to the back of the room and let the rest of the class question each other from there. It takes some effort to build up a culture where students are comfortable asking each other questions, disagreeing with each other in a respectful way and also the student at the board being comfortable saying ‘I don’t know. I can’t figure that out.’”
2. In the lesson, “Inequalities: The Next Generation” Master Teacher Tim Marley starts with common misconceptions for students, and uses this to engage them in justifying their answer (MP3).
Tim knows what tasks will trip students up. He knows what answers they’re going to gravitate towards and he uses that expertise on a regular basis as part of his instruction.
To start off this lesson, students are given a task worksheet with a simple problem to solve.
Then, they present their work. I tell them to use as many different methods as possible. Students are seated in groups. We talk about how this is different than what we have been working with. (polynomial functions / equations).
Every single student was convinced that this strategy was correct:
After that, I had a student come up and present their work. I asked, “How do you guys feel about this?” They were convinced that this was right. I had them test a couple of points. Test the point -4. They plugged it in and figured out that this works in the original inequality but not the new one.
The reason I picked this lesson is because making these arguments and critiquing the reasoning is really the most important part of this lesson. Thinking about their original reasoning and trying to come to terms why it didn’t work in this case.”
3. Master Teacher James Bialisk discusses his lesson, Mirror Task; Understanding Cognitive Functions and how, through MP3, students share out their thinking.
“Since we’re really trying to focus on MP3, I picked this lesson because this is a completely student centered lesson. It’s really student driven. They’re doing a lot of the work and it really works out nicely that way when they’re coming up with a lot of the math.”
“One technique I really like to use to get MP3, is as students are sharing – trying to have them to build off of each others’ responses instead of just sharing their own. So, when you’re doing a think, pair, share, you really want to get around and try listen for – what conversation is gonna be a good entry point for everybody and start there. And then ask for other students who might have more sophisticated responses to build off of that initial response. And so that usually works pretty well to get students not only listening to each other but also building off of each others’ ideas.
The nice thing about this lesson is that it basically runs itself once you get the students out there, get ‘em investigating. They have a good opportunity to really discuss among each other how to come up with these different expressions.
I use different turns of phrase to get students to build on each other, such as, ‘Can anyone add to that?’ It gives the impression that we’ve got something. We’re starting.
A nice way to facilitate some of those conversations is recording the essential vocabulary on the board. It brings out dialogue and questioning from the students.”
If students can learn to speak the language of math independent of the teacher and come to their own conclusions, whether they decide their conclusions are right or wrong, they are learning. As a result, they inevitably take more away from their classroom experience.