Here’s the thing: Technology has drastically altered how learning happens, and it will continue to do so. Depending on their circumstances and their interests, students now come into classrooms with greater quantities and variations of prior knowledge than ever before. 

This is because some families have access to online or in-person tutoring opportunities, or students themselves might be pursuing independent interests that give them more exposure to math concepts and their real-world applications. It could be via YouTube or any of the many other platforms that allow kids to explore content on their own. But all together, this creates a major shift for contemporary education, and from here on out, we will likely have increasing amounts of variability in how much kids know before coming into our classrooms. Not only at the beginning of the year but every single day.  

That dramatically changes the usefulness of typical diagnostic exercises and whether I’m actually getting meaningful data about what my students learned from daily instruction. So, I’ve opted for what I call a “formative instructional approach,” which takes this wide range of variability into account. In this approach, students come into class and immediately have the opportunity to show how they’re incorporating prior knowledge and insights by applying them to the material of that day’s lesson. That gives me the opportunity to assess their current conceptions from the quality of their work – not just whether they got the right result – and teach directly in response to the questions and observations their work is communicating. 

To shift towards a formative approach that truly allowed me to meet students where they are, I needed to rethink my instructional routines. Over the years, I’ve developed this instructional sequence to put the priority of formative instruction into practice.

1. Asynchronous learning 

I’ve embraced the art of making short, activity-focused videos that students watch outside of class and can reference when they approach their homework. A key here is that each video is new material, focused on the big concepts behind content we haven’t covered during class time. It’ll be about five minutes long, and while I might demonstrate a procedure, I always emphasize that I don’t want students to simply replicate that procedure. I want them to take the big conceptual ideas, make some notes, and apply those understandings to a few tasks before we tackle them as a full group in our next lesson. Their approach – one that brings in their current conception of what they already know and shows me what connections they still need to make – is the real value here.

2. Daily gallery walk 

The very first thing kids do when they come to class the next day is put their work up on the whiteboards. So immediately, we’re starting every class with a gallery walk as a built-in, expected part of our routine. Students are up and out of their seats and moving, observing, and discussing one another’s work. Then in small groups, each student has a chance to share their thinking by presenting either their own work or a peer’s work. Each person in the group, usually 4 students, takes turns until everyone has had a chance to speak. I find this way of starting our class time together so powerful because every student is delving into self-evaluation, analysis, and collaboration right away, instead of the typical “warm-up” activity.

An added component here is that I make sure to reward mistakes. Because in all the times we’ve done this activity, no group has ever paused and had a meaningful discussion over work that’s completely correct. The liveliness, questioning, and curiosity that are so crucial to activate with our students tend to come from discussions around mistakes. So I reward the students that created opportunities for everyone in our class to learn by putting up their mistakes on the whiteboards.

3. Deciding what’s next

During the gallery walk and the small group presentations, I can do individual check-ins with students about the understanding I’m seeing in their work. I can also listen to the different group conversations and see if shared observations, or misconceptions, emerge. From there, I’ll get a real-time sense of whether direct instruction is a valuable use of our time together that day or if it’s time to move us into learning communities. 

When there’s a really clear misconception showing up across the board, or the understanding of the core concepts from the video seems a bit too surface level, I can teach directly to those needs. But typically, I can spend about five minutes of our class time on direct instruction and move on because of how pinpointed the previous instructional routines allow me to be. 

Then we move to learning communities, they’re very similar to “thinking classrooms,” with one notable exception: I’m a firm believer in intentionally mixing up the collaborative groups. Every year, I see students develop a real sense of one another’s strengths and growth areas. So rather than assign groups at random, I organized our learning communities into strategically heterogeneous groups that acknowledge those different areas of strength and where each student is on their own route to mastery.

Empathetic explanation is a core value of our learning communities. That means every student is encouraged to think about how someone else might respond to a prompt, and it motivates a real curiosity about others’ thought processes. That means students who might have a clearer understanding of some concepts, or who might be completing tasks at a faster pace, are motivated to engage with peers who might be struggling or have misconceptions. This is important not only because it might be helpful to share their own understanding, but because they know they’ll benefit from broadening their perspective by understanding and working through their peers’ mistakes. As a result, students start engaging with one another’s approaches more like pathways to be explored, rather than mistakes to be corrected.

4. Tracking progress

I build in a lot of collaborative experiences for students to share their approaches and understandings and engage with one another’s perspectives on our content. But collaborative success, while crucial, doesn’t always neatly translate to independent success. Students still need structures that hold them accountable for what they learn inside of those collaborations with peers. That’s why we end each lesson with some kind of mastery check, usually a five-question quiz, and time for reflection using their individual progress trackers (click below for inspiration). 

After we’ve spent the majority of our class period emphasizing understanding and making each others’ thought processes visible, it would be strange to suddenly only focus on the right answers. So as I’m grading students’ quizzes with them, or as they’re grading their own, we’re still asking, “Well, what was the mistake here and what does that tell us?” And that’s the conversation they continue having with themselves in their progress trackers, taking a metacognitive look at their own learning and performance on the mastery check. So as we close out our time for that class, each student can check in with themselves, taking ownership of their learning.

5. Deemphasizing getting it right on the first try

We never get this sequence right on the first try. At the beginning of a new year or a new semester, we have some pretty significant traffic control issues as we get used to this routine, figuring out our pacing as a group and practicing a sense of agency in moving from group activities to individual practice, mastery checks, and reflection. We have slow choppy steps moving around the gallery walk, and slow choppy steps settling into how each part of the sequence feeds into the next. 

So on top of meticulously planning out this sequence, previewing it for each new class of students, and staying the course together, I start each school year modeling for my students that it’s OK to do something imperfectly. What’s more is that, together, we can offer one another all the grace we need to practice, make mistakes, and carry the insights we gain moving forward into the next learning opportunity. I hope you’ll find some inspiration here as you experiment with your own instructional routines in the years ahead.