Reflection: Student Feedback REALLY BIG IDEAS! Graphing vs. Substitution - Section 4: REALLY BIG IDEAS! with an Example from the Quiz


We can never predict precisely the threads that may arise in any given year of teaching.  At the start of this year, I wouldn't have predicted how the word "easy" would become a focus of my thinking about how kids learn.  But it keeps coming up, and it's worth considering how to leverage a word that students so often use in a way that helps them get the most out of this class.

When students learn something new, they will often call it "hard," and I often show them that difficulty and "newness" are not the same thing.  I've come to frequently say things like, "I'm going to show you something new right now.  Most of you probably have not seen this before, but that doesn't mean it's impossible to learn."  I'm reminded of the title of Duncan Watts' provocative book, Everything Is Obvious (Once You Know the Answer).  That book is about how common sense will often fail us.  My job as a ninth grade algebra teacher is often to make students feel like a new idea is common sense.  Taking one topic at a time I try help my students transition as smoothly as possible from the realm of the confounding to the obvious.

That's why I've taken to using the language of my students.  Like I did today, I'll students to consider a set of similar problems or exercises, and then to tell me which they think are "easier" than others.  On the inside, it pains me a little, because I'm wishing for a little more nuance from my kids, but this is a way to access their thinking.  We're building metacognition by using the language my kids use, and ideally, it students to think more deeply about why they perceive what they do.

  "Easiness" as an Informal Mathematical Principle
  Student Feedback: "Easiness" as an Informal Mathematical Principle
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REALLY BIG IDEAS! Graphing vs. Substitution

Unit 9: Systems of Equations
Lesson 11 of 20

Objective: SWBAT solve systems of equations exactly (with substitution) and approximately (with graphs).

Big Idea: If you’re going to have a variety a tools, it’s a good idea to have a good idea of what each is good for!

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