It seems that Peter Liljedahl's "Building Thinking Classrooms in Mathematics" ideas are taking the mathematics community by storm. If you aren't already familiar with Liljedahl's work, you can read a nice summary written by Liljedahl himself in the footnotes below1.
I recently had the good fortune of being in the audience during one of Liljedahl's talks, in which he reasoned that many of the 14 practices he suggests create more equity and access in the classroom in addition to more thought. I'd like to share a few of those ideas about equity and access here.
Each time we strategically group students, despite our best intentions, we allow for implicit bias (or even explicit bias!) to creep in. We ensure certain students aren't in the same group, or we inadvertently put the same two students together time and time again. As Liljedahl notes, when we use random groupings, our expectations about which groups will work well together are often false. And here is the beauty in visibly random groups - meaning, we show students how the groups are randomly formed using programs such as Flippity2 - students who would normally assume we put them in a group due to their lack of ability - a common misconception in our at-risk populations - simply can't make those assumptions anymore.
I know what you're thinking - really, I'm supposed to risk that student being placed with that other student. Yes! Give it a try. As teachers, we need to be willing to give our students the opportunity to prove us wrong, over and over if need be. Why else do students need school if not to improve at the things that need improving? This includes working with others.
One of my favorite parts of Liljedahl's work is how he defines the attributes of good thinking tasks: a) low floor, b) high ceiling, c) huge degrees of freedom, d) fixed constraints, and e) inherent abmiguity. When it comes to accessing mathematical content, it can't be stressed enough just how important a low floor is. Tasks that have a low floor give all of our students, regardless of experience or background knowledge, a place to begin. Compare that to traditionally high floor tasks and you can quickly imagine just how different the classroom experience is for your students. Tasks with a low floor create more confidence in the classroom, more effort, and ultimately a culture of problem-solvers.
Importantly, good thinking tasks also have a high ceiling that push our students to new levels in their thinking. It's a beautiful thing to witness. See the footnotes for examples of good thinking tasks3.
Within their writing about equity in the classroom, Hanover Research4 notes that one of the best practices we can use is to seek multiple persepctives and different answers to questions. This aligns so well with the Thinking Classroom approach. Students are given a good thinking tass, put into visibly random groups, and work together on the task. When your class operates that way, you can't help but invite multiple perspectives and different answers. Sure, some of the strageties that your students use will make your head spin, but that's kind of the point! The next time your head spins in that way, see it as evidence you're achieving a more equitable classroom.
Pete Grostic, Ph.D
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3 Good thinking tasks from Open Middle