## Reflection: Student Ownership Linear Equations: A Subtle Note, and Choosing Your Own Adventure - Section 2: Two Step Linear Equations: A Subtle Note

I have been fascinated lately by thinking about what students mean when they say that something is "easy".  For me, "easiness" conjures up an idea of efficiency and only having to think as much - and to work for as long - as I have to.  The more tools I have at my disposal, whether they're physical tools or mental processes (and this applies to all fields of study), the "easier" a task will begin to feel.  It follows that it might take some hard work of learning to get to that point where a cognitive task feels easy.

Many of my students quickly overlook the fact they had to engage in some learning process to get to the point where what they know feels easy.  What they know today is that they know the distributive property and how to apply it to solving an equation, and that it now feels easy for them to use that property as a tool.  I have to remind them that, sometime in the last few years, they went from being completely unaware that such a thing as the distributive property exists, to learning how to use it, to feeling like it's an easy tool to use.

Today, plenty of students will ask questions like, "Why would you solve an equation in that new way, when it's so easy to use the distributive property?"  As math teachers, we know how important it will be in the future for kids to be able to factor some term out of a polynomial expression and to cancel it by division.  My students don't have that long view, and although it might be worth making passing mention of that fact, it's usually not enough of a selling point to generate buy-in.*

So we must resort to being patient with kids, and making them feel like we're letting them in on a little secret.  Minds need time to change.  I show students this "new" method, and many respond with skepticism at first.  Slowly, however, they recognize that "new" does not have to mean the same thing as "difficult," and a critical mass coalesces, as one by one, students say, "Wait, actually, this IS easier!"

* This is to say nothing of another important point: that if kids know the process of distributing some term, but feel like just dividing by that term first is "hard," then they lack some important conceptual understanding of the structure of an algebraic expression and why the distributive property works in the first place.  Our job is to help everyone move toward that understanding.

What Does "Easy" Mean?
Student Ownership: What Does "Easy" Mean?

Unit 3: Solving Linear Equations
Lesson 3 of 12

## Big Idea: One method of differentiation is to let students decide on their own what they'd like to practice.

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Subject(s):
Math, Algebra, Linear and Nonlinear Equations, equation solving, Differentiated Instruction, formative assessment, progressive education, mastery learning
40 minutes

### James Dunseith

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