Finding Elegance in Equivalence
This post was featured in an episode of This Week in Ontario Edublogs (July 11, 2018), beginning at 34:42 . Over the past week, we have been piloting diagnostic questions with students to get an idea of their understanding of equivalence. We gave students a series of questions, all having to do with the understanding of what the equal sign represents. One question, though, really challenged my idea of what "higher order" strategies we were hoping to see in our students. Here's the question: If 4x + 8 = 52, what is 2x + 4? Take a moment to figure it out. What is your answer? How did you come to that answer? If you're like my colleagues and myself (and most of the students of whom we asked the question), your instinct might have been to solve for x using the first expression, ...and then substitute that value for x in the second expression: So in this case, 2x + 4 = 26. As students advance to higher order strategies when learning math, we ...