Here at Math Medic we are huge fans of Peter Liljedahl’s book ““Building Thinking Classrooms””. And from the many, many emails we’ve received from you all, it sounds like you are too! The most common question we’ve gotten is about how BTC (Building Thinking Classrooms) and EFFL (Experience First, Formalize Later) fit together and can be jointly implemented in your math classroom. We’re here to share our ideas with you.
To start, let’s talk about the similarities in the two instructional models. The big idea of EFFL lessons is to empower students as mathematical thinkers that can make sense of concepts for themselves, with the support of their peers through discussion-rich group work. Our goal is to create experiences that allow student-generated, rather than teacher-generated, ideas to build the foundation for deep conceptual understanding. Our student-centered classrooms focus on problem solving, communication, and deep conceptual learning rather than passive information transfer or rote memorization. We want students to be able to think, rather than just execute a procedure. The BTC framework also has student thinking at its core. The 14 teaching practices described in Liljedahl’s book are strategies for orienting every part of the classroom experience (layout of the furniture, where, how, and when tasks are given, assessment, interactions with peers, etc.) toward that goal. Both models rely on rich tasks that get students to think. Using the language of BTC, the activity portion of an EFFL lesson would be an example of a curricular task.
The biggest difference between the models is how the task is presented. EFFL lessons are done primarily on paper, where the activity consists of carefully sequenced questions designed to get students to build a conceptual idea from the ground up. They generally start with questions that activate prior knowledge and then slowly build in complexity. Students must communicate first to each other as they try out ideas and then in writing as they describe ““how they know.”” The activities are written to be low-floor, high-ceiling tasks. In the BTC model, questions aren’t given all at once. Students are given an initial prompt verbally, then work on that prompt at whiteboards (or any vertical non-permanent surface). Students can get the next prompt from either the teacher, or preferably from their peers, as a way to foster autonomy and mobilize the knowledge. In an EFFL lesson, interaction between groups happens primarily during the debrief, as students attend to, build on, and challenge the ideas of their peers.
In both the EFFL and BTC model, the goal is to increase student thinking and foster students’ autonomy as problem-solvers. To that end, it is helpful to look at what the research tells us. Thankfully, this is the work that Peter Liljedahl has done for us, and then succinctly compiled into a set of 14 teaching practices. We won’t talk about all of them here, but we do wish to share several BTC strategies you can incorporate into your EFFL lessons.
Use Visible Random Grouping (VRG) to make your groups. I have used this strategy since reading Peter’s book and I love it! I like that students have opportunities to work with many of their peers and that complaints about who is in their group have essentially disappeared, since they know they will likely be working together for one day only.
Defront the classroom. This is another easy-to-implement strategy. Instead of having the pods of desks all face the front, turn each chair so it faces a different direction.
Only answer ““keep-thinking”” questions. You’re in luck on this one. Monitoring students during an EFFL lesson consists of asking assessing and advancing questions only, not answering students’ ““Am I right?”” questions (stop-thinking questions) or their ““studenting”” questions (proximity questions).
Use check-your-understanding questions. Peter’s chapter on assigning homework provides a compelling rationale for why we give 3-5, ungraded, check-your-understanding questions at the end of every EFFL lesson, and why full solutions are available to students online. Ideally, we give students time in class to complete these questions.
Give the task verbally, with students standing loosely around you. The box at the top of every EFFL lesson introduces the context of the lesson. Instead of having the groups read this on their own, consider starting the class with everyone standing by the board near you and you giving a synopsis of the context in your own words. I do this often and my level of enthusiasm when briefly explaining the task can greatly affect how quickly students get to work.
Use ““notes to your future forgetful self””. In an EFFL lesson, we create a summary of the learning as a class in the QuickNotes. This takes up a very short portion of class, and occurs after student ideas are consolidated in the debrief. Consider how you might transform these to be more student-led. Instead of everyone writing down the same key ideas, have students decide for themselves what the important take-aways are, paying special attention to the margin notes made during the debrief. The ability to write meaningful notes is an acquired skill, so you will need to train students in this at the beginning of the year. Using a graphic organizer may also be helpful. Be aware that student-generated notes will likely take up more class time. Peter suggests planning at least 10 minutes for this portion of the lesson.
Have students work at vertical non-permanent surfaces (VNPS). This is a bit more challenging with the format of an EFFL lesson, but we’ve heard some great ideas from you all about how you do this. Some of you have mentioned taping a copy of the lesson to each whiteboard. Others have suggested cutting up the lesson and giving students the next question once they’ve completed the previous one. If you’re more experienced in facilitating BTC style lessons, you could modify the EFFL lesson to include only 2-3 essential questions, which are given verbally, and remove some of the scaffolding. This may require combining some questions or rewording them. Since student work is on separate whiteboards rather than the front board, your debrief can include traveling to different groups’ whiteboards and writing the margin notes in a different color on the students’ workspaces.
No matter where you are in your journey toward building a thinking classroom, even small changes in your practice (like how you make groups) can have a BIG impact on students’ willingness to think in your math class. If you’re a Building Thinking Classrooms expert and also using EFFL, we’d love to hear from you about ways you’ve adapted or modified EFFL lessons to incorporate BTC best practices.