Reflection: Discourse and Questioning Complex Solutions to Quadratic Equations - Section 2: Discussion: Graphing Complex Solutions

I've been having a bit of trouble getting my students to engage in class discussions.  It tends to be the same handful of students who speak up, while the rest just listen quietly, and I often don't have any idea who understands and who doesn't!  To combat this, I decided that I needed to move into the background so that the class couldn't rely on me for an explanation.

After making sure everyone understood the question (why are the solutions symmetric in the plane), I drove home the point that they all needed to be able to explain why.  Then I told them I wasn't going to explain it and walked to the back of the class.  And it worked!  One student asked if he could try, then another jumped up to add to what he had said.  When the class turned to me to see if I approved of the explanation, I just shrugged my shoulders and said, "Don't look at me.  Is it correct?  Do you understand the explanation, and do you think it's true?"

Interestingly, the students were pretty tough on one another.  In the end, they went all the way back to the quadratic formula, they argued that the solutions would always be complex conjugates (although they didn't know the name for them), and they gave several different explanations for the symmetric placement in the plane.  Good questions were asked, and some of the quietest students began to speak up.

I think that they had more confidence asking questions because there was a better chance that the person at the board was wrong.  When Johnny doesn't understand the teacher, he assumes the problem is with Johnny.  But when Johnny doesn't understand Josie, he assumes the problem is with Josie, and he may be more likely to ask her to explain herself or to explain why he thinks she's wrong.

Getting the Conversation Started
Discourse and Questioning: Getting the Conversation Started

Unit 2: The Complex Number System
Lesson 4 of 16

Big Idea: Students investigate the geometry of the complex solutions to a quadratic equation in a dynamic setting.

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Subject(s):
Math, complex conjugates, Algebra, Quadratic Equations, Algebra 2, master teacher project, complex numbers, Imaginary Numbers
45 minutes

Jacob Nazeck

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