Reflection: Trust and Respect Creating Linear Equations in One Variable - Section 4: Group Problem Solving


I have long been a believer in "circling up" and using classroom time to build soft skills and strengthening my relationships with students.  This year, some colleagues and I are exploring restorative justice, and through PD and conversations, I've refined some ideas and strategies for making the most of this time.

One simple and powerful idea is to read a passage with students and then to talk about it.  Today, as we moved into our unit on problem solving, I ran a circle in all of my classes.  As I'll show you here, this circle ended up incorporating beautifully into the curriculum, but that's not the only reason I did it: students are almost two months into freshman year, and this is a great opportunity for us to pause and talk about what's working and what isn't, and how we can do our best moving forward.  Independent of curricular connections, I believe deeply that this sort of experience enhances student access to the curriculum, and that this work is imperative in schools working to improve their overall culture.

For the reading, I chose a passage from the book Creative Confidence.  While not specifically directed toward teachers, this book was an invigorating read that gave me a lot of ideas for my own classroom, and I recommend it heartily.  Here's the passage I read for students as we started our circle: The Failure Paradox from Creative Confidence.

After reading, I asked students to share whether they agreed or disagreed with this passage, and I invited students to share stories from the year that might show whether or not they had taken these ideas to heart.  In each class, the conversation proceeded a little differently, but in all classes, students said they believed that it was true and wanted to a better job persevering to learn new things.  On its own, I was happy with how the circle went, and in the days since teaching this lesson, I've watched my students grow more willing to give things a try.

Here's what I'm particularly excited about, however: this reading fit perfectly into the curriculum!  As we get started on creating equations, I like to show students how to use guess-and-check to solve problems.  Students learn how guessing and checking can form an intermediate step on the way to understanding a problem well enough to create an equation that represents it.

To begin, I wrote the words "GUESS AND CHECK" on the board, pointed to them, and asked, "Is this a legitimate way to solve problems?"  I knew that by asking the question that way, students might doubt it a little bit, but that gave us the opportunity to talk about Thomas Edison.  "Did guess and check work for Thomas Edison?" I asked.  "Did he invent the lightbulb in one try?"  Moving on to applying this strategy, students recognized that a wrong guess is an opportunity to learn something more about the problem, and they were proud to be able to relate to this famous inventor.  Indeed, as the Failure Paradox states, the most ingenious breakthroughs come from trying and failing over and over again, without giving up!

  Trust and Respect: Thomas Edison, Guess and Check, and "The Failure Paradox"
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Creating Linear Equations in One Variable

Unit 4: Creating Linear Equations
Lesson 1 of 8

Objective: SWBAT create linear equations in one variable, and use them to solve problems.

Big Idea: We start with a focus on matching words to equations, and establishing guess and check as a viable strategy.

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Math, modeling, Algebra, equation solving, conceptual approaches, word problems, writing equation
  43 minutes
u1 l33 group work
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