Reflection: Developing a Conceptual Understanding Review or Move On (to the Quadratic Formula) - Section 3: Review & Work Time


Several times throughout this course, I've sung the praises of this kind of class period, where all students are working on whatever they need to work on and helping each other move toward mastery.  My role is to be there to answer questions and improvise mini-lessons and small-group discussions as necessary.  Today's class was no exception, and I'm once again reminded of why I always look forward to these lessons.

The most thought-provoking moment of the day came when a student was working on solving a moderately difficult quadratic equation, and after isolating zero on one side, she wondered whether or not she could factor the resulting expression.  She knew she could use the discriminant, but she couldn't come up with that word, and she couldn't remember exactly why the discriminant was useful, so she tried to ask me a question about, "you know, that b squared minus four a c thing."  I said, "Come on, I know there's a word for that...!" and she responded, "I know, but what is it?"

Does this happen all the time?  How many of my students can say, "y-equals-m-x-plus-b", or "a-squared-plus-b-squared-equals-c-squared", or "rise-over-run", without remember the word for each concept?  And if we can't recall a word for a concept, then does that change our ability to apply it?

I continue to believe that the constructivist approach is best - develop an idea and make it your own, then give it a name - but I also find myself wishing that students could come up with the word more often.

Even when I do front-load vocabulary (by placing it directly in the learning target, for example), students can have a hard time using it.  Right now, my kids are getting pretty good at factoring, but they're easily tripped up by the instruction: "Factor this expression."  Several times, I've had to say something like, "Ok, here's this thing you know how to do, and going from this form of an expression," (I'll point to a trinomial), "to this one," (point to a pair of binomials), "is called factoring."

It's clear that knowing the words to explain one's ideas enables us to have new ideas.  As I look ahead to next year, I'm thinking of ways to better emphasize vocabulary without losing any of the conceptual mastery that I already work to develop in students.

  But, What's the Word for That Thing?
  Developing a Conceptual Understanding: But, What's the Word for That Thing?
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Review or Move On (to the Quadratic Formula)

Unit 10: Quadratic Functions
Lesson 19 of 21

Objective: SWBAT review the Unit 6 Learning Targets as needed for the exam, and if they're ready, to practice using the quadratic formula.

Big Idea: After two quick review tasks, today's lesson is all about giving kids time and space to complete the work of their choice.

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