About this school: Chris Luzniak teaches 12th grade pre-calculus at the Urban Assembly School for Law and Justice (SLJ) in Brooklyn NY. A high school of just over 400 students, SLJ draws students from all over the city, either through random assignment or through application. No exam is required for entrance into the school.
About today’s class: Mr. Luzniak often uses hypothetical examples of students’ or teachers’ work to prompt discussion and debate. In this class, on properties of the unit circle, Mr. Luzniak puts up a “Try now” with example work by Ms. Smith. On a unit circle that has several given points (written in black), she has indicated other points that relate to the given points. Her work is in red. The students’ task is to determine whether Ms. Smith’s work is correct or not. They first work in pairs to analyze, discuss, and debate, and then Mr. Luzniak brings the class together and asks students to state and defend their findings. (He uses the language of “claim” and “warrant” from debating.)
As you watch the video, consider the following questions. It may be helpful to watch it more than once.
The Classroom Setting:
How is this classroom physically arranged?
What is the teacher’s role in this class?
What is the student’s role in this class?
What does this classroom sound like?
How would you describe the culture of this classroom?
How do you think it feels to be a teacher in this classroom?
How do you think it feels to be a student in this classroom?
Argumentation and Critique:
Watch for a moment when students are making an argument and justifying it.
Watch for a moment when the teacher is facilitating debate.
Listen for, and jot down, specific words that students use in making mathematical claims and justifications.
Watch for a moment when students are building on the work of other students.
Watch for a moment when students are critiquing the work of other students.
Write down a few adjectives that you think describe the most striking moments in this class.
What characteristics of this “try now” work encourage argumentation and critique?
What counts as getting the “right answer” in this class?
How does the expectation that students will have to state and defend their arguments change the nature of group work?
How do you think Mr. Luzniak prepares for classes of this kind?
Putting Argumentation into Practice:
In the video, Mr. Luzniak mentions that initially he was scared of opening up debate after students had made their claim and warrant, and he, rather than students, followed up. What are the risks when opening up a class in this way?
Mr. Luzniak’s instructional style taps his knowledge of debate and role as debate coach (for instance, having students stand to give their claim and warrant, as they would in a debate). Teachers have differing styles and backgrounds: how could you adapt some of these ideas to your own teaching style?
Make a list of things you like about this class and this teacher’s practice, and make a list of things you question or wonder about. Discuss both lists with a colleague.
In the video, Mr. Luzniak says that he introduces argumentation, logic, and debate structures to his students from the first weeks of the school year. (This video was recorded relatively late in the school year.) These structures include things like using precise language, summarizing, building on the work of others, understanding reasoning and proof, and disagreeing productively and respectfully. How could you fold ideas like these into your class experiences at the beginning of the year?
If a colleague were to come to record your classroom tomorrow, what kind of argumentation and critique would he or she see and capture on video?
What small change could you make this week to foster or improve argumentation and critique in your class?
What longer-term change could you make?
What might keep you from making these changes? What might help you in making these changes?
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