Peter Liljedahl’s Building Thinking Classrooms is full of fantastic work. So much so, I’ve got 4 podcast episodes talking about it. I don’t agree exactly with everything he says, but studying it was very much worth my time, and is probably worth yours.
Right out the gate, I couldn’t agree more with his insistence that math classrooms need to be thinking classrooms. Students need their intellect and reasoning to be engaged to actually learn, particularly in math. If an assignment can be done without thinking–that is following predetermined steps where the only prerequisite for use is their base memorization–then that is not a thinking assignment. Generally speaking, if giving the student a calculator would trivialize the assignment, that is not a worthwhile assignment. Consider that anything worthwhile a ‘mimicking’ assignment can deliver, a thinking assignment can do while actually building the reasoning skills that will later trivialize problems written to trip-up the mimickers.
Students that build their answer-getting skills through reasoning instead of mimicking don’t need additional help with word problems, let alone whole units devoted to solving them. They don’t need yet another acronym, mnemonic, or list of steps to memorize because they’ve been thinking and reasoning the whole time. They don’t need to learn how to make the math apply to a specific context because all their learning was already in context.
I could go on about this, as thinking and reasoning through math is kind of my whole schtick, but then I wouldn’t get to talk about those lovely ‘vertical non-permanent surfaces’. Which is a lot of syllables to describe what is often a vertical whiteboard. It doesn’t have to be a whiteboard, just vertical and erasable.
There is some simple but fascinating and powerful psychology behind this.
Point one: why vertical?
This is, depending on your perspective, a slightly devious but highly effective way to hijack peer pressure to work in favor of the learning instead of against it. When writing on a horizontal surface, the student will only be concerned with what their immediate neighbors can see. But vertically, where anyone looking around the classroom can see at a glance who is engaged and who is not, it becomes socially painful to disengage from the learning. This is particularly helpful in student group dynamics for reducing the incidence of the one student doing everything while the others twiddle.
Point two: why non-permanent?
Students hesitate less to put their thinking down if they have reassurance they can erase it. Having utilized peer pressure in point one, the erasability is our pressure valve. Putting your thinking where your peers can see it creates a certain vulnerability. Not all students will care, but many will. Especially if they aren’t confident yet in the subject matter. Being able to erase your thinking, particularly when you later realize you were wrong, eases that sense of vulnerability. It removes the demand that what you write be perfect. This is particularly good, since in a well-designed task we expect students to make mistakes as they learn.
Point three is less universal, but is still powerful when it applies. By physically changing the learning space to accommodate vertical non-permanent surfaces, the classroom becomes a distinctly different place from past classrooms, specifically past classrooms that may have spent the entirety of their time mimicking instead of thinking. A different environment sends the subconscious signal that we are doing things differently here.
Now, all that said, I don’t think vertical non-permanent surfaces are a magical cure-all or that they should be used all the time. Not all good work is group work. Teacher facilitated instruction, particularly when using Problem Strings (my fav!), is still a powerful tool.