Building the thinking classroom in mathematics

I’ve known about Peter Liljedahl‘s work on thinking classrooms for a while. Since 2017, I’ve been using vertical whiteboards and visually random groups — the foundation of Liljedahl’s thinking classroom framework. My successes have been nothing to brag about, but they have done wonders for my teaching. This is why I was thrilled to discover that Liljedahl wrote a book on how to build a thinking classroom this year. I couldn’t help but get a copy and all but devour it.

I must say, what a great read! The book has a wonderfully simple structure to it. Each chapter starts with a common problem facing teachers (e.g. note-taking). Liljedahl’s then uses one the 14 components of the thinking classroom to address it. The writing — chock full of his research — is clear and accessible. I couldn’t help but to see myself, my classroom, and my students on every page. Liljedahl got me rethinking a lot of what my students and I do every day.

For example, my Algebra 2 curriculum is problem-centered. This is inherent in a thinking classroom, yes, but Liljedahl emphasized that the method and mode of delivery matters when it comes to the problems. He suggests that teachers give the task verbally while students are all huddled around a single board. He also recommends that teachers do it very early in the class period. I like both of these ideas, but have done neither of them in the past.

Also useful was reading his views on fostering student autonomy and mobilizing knowledge during a lesson. With the whiteboards, random groupings, and defronting of the classroom, I’ve had success in supporting students depend more on each other during lessons. It really is magical. Liljedahl did a great job of refreshing this for me and helping me see how I can be better at it.

I also appreciated his ideas on advancing competencies like perseverance, risk-taking, and collaboration. I expect my students to rely on these skills so much, but never actually evaluate them or systematically help my students develop them. Liljedahl suggests co-creating rubrics with students to identify growth areas in a given competency. These rubrics can be taped to the whiteboards so that both the teacher and student can use them to evaluate the work being done in class. Such a great idea.

His thoughts on formative assessment also struck a chord with me. They consisted mainly of listing out topics and having students track their progress on them throughout the year. The whole thing has a standards-based grading flare to it, which I have done before. But for years I’ve struggled with integrating my interleaved, problem-based learning system with standards-based grading. The two seem to be at odds with one another, but I’m not giving up hope.

His suggestions around note-taking caught my attention too. Working on the boards can be great, but distilling group learning into personal record-keeping and individual knowledge is hard for me. Liljedahl calls for a heavy dose of graphic organizers to help with this, but I’ve never had the discipline to follow through with them. Maybe I’ll experiment. A suggestion he had to help students be more aware of their note-keeping was to have groups write notes on the whiteboards for a given problem. This can turn into a gallery walk to help generate discussion about meaningful note-taking. Also interesting was the idea of giving students a task three weeks later that requires them to use their notes. This would encourage and incentivize more thoughtful record-keeping.

Despite the whole of the book being riveting, actionable, and forward-thinking, I have a few reservations and desires for more. At the end of each lesson/task, for example, Liljedahl suggests that the teacher summarize solutions and highlight big ideas for students. He calls this “consolidating” (great name, BTW). I get that it’s important for teachers to bring it all together because we can see the bigger picture, but it’s also important that students share their own solutions with the class. It is empowering and promotes agency and pride in one’s work. Lesson summaries aren’t always about content.

I also felt that his homework component was weak and mainly a dressed up version of what most teachers already do. He renamed it “check for understanding questions,” but it’s basically just practice. He made a case that the renaming of it is crucial, but I don’t think it makes that big of a difference. Over the long term, kids know what it is. With that said, I agree with him that we (generally) shouldn’t check this type of work nor give credit for it. To be meaningful, it should be student-owned and operated. By saying that, I feel like a hypocrite because I do give credit for my weekly DeltaMath assignments (essentially practice). At the same time, I don’t check or give credit for the daily, non-DeltaMath assignments I assign (a small mix of practice and non-practice).

His vision of grading in the thinking classroom was super interesting, but man was it ambitious! He honors the tension between students doing so much collaborative learning, but then using a bunch of individual tests to assess this learning. This feels disingenuous and I think he’s right. His research calls for a “data-gathering paradigm” whereby teachers collect lots and lots of data about a students’ understanding of content (instead of just things like exams, quizzes, and homework) to determine their grade. It goes back to standards-based grading, but this time the teacher triangulates data around observational, conversational, and product-based outcomes for each standard. Whether knowledge is demonstrated individually or in a group is also taken into account. It’s a highly complex structure that’s out of my league right now, but would like to test drive one day.

In terms of tasks, I was hoping that Liljedahl would go into more depth and show more examples of curricular tasks that can be used in a thinking classroom. I get that we should start the year with non-curricular tasks to build culture of thinking, but the curricular examples he showed were of the garden variety and kind of rudimentary (e.g. factoring trinomials). They didn’t help push me. Also, in terms of assessment, I wished he would have included some thoughts on structuring group quizzes or exams that utilize vertical non-permanent surfaces.

It was my impression that Liljedahl feels we should be using the 14 elements of his thinking classroom framework every day — especially the fundamental elements like the whiteboards and groupings. While I do love them as the foundation of one’s classroom (they are for me), in my experiences, it’s not a good idea to go hard with them every day. They’re radical enough to shock the system (e.g. the classroom), and necessitate different behavior from students, but when used every day, the kids grow tired of them. At least my did. Regardless of how interesting a task is or how engaging it is to work on vertical whiteboards, students need a variety of different approaches to learning. Things like speed dating, sit-at-your-seat whole class lessons, Desmos Activities, games, and plain old direct instruction have their place. They can and should be used under the right conditions. For me, my students are off the whiteboards 1-2 times a week in favor of more traditional learning experiences.

In the end, I think Liljedahl’s Building Thinking Classrooms in Mathematics does a lot for us math teachers. Not only is it highly readable and practical, but it gives us a model to break with the institutional norms that, in Liljedahl’s words, “have not changed since the inception of an industrial-age model of public education.” Given the nationwide return to in-person learning, it’s a book that can help us reimagine the math classroom for the better. It’s fearless and not afraid of upending a lot of what we take for granted — like students sitting at desks with notebooks in front of them. While these types of ideas weren’t new for me, they did refresh and reinforce a lot of what I’ve done in the past and help me continue to disentangle my own instructional struggles. This was extremely helpful at this moment. Couple this with how Liljedahl got me to see new possibilities for helping my students think, which included both small tweaks and sweeping changes, and his book is sure to be a reference for years to come.


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