I remember being told in education classes that it was important to differentiate. I’ve forgotten most of the details of that class, but I’ve seen the sentiment more times than I can count since then. It’s often used to describe lessons where each student has a problem exactly in their zone of proximal development, or a lesson that appeals to visual, auditory and kinesthetic learners in different ways, or a lesson that allows students to present their ideas through any of the multiple intelligences. I’m going to withhold my opinion on the research behind these ideas for now — that’s not my point. My point is simply that, even if these lessons are particularly effective, they aren’t worth the time.

I’ve come to the conclusion that great differentiation is actually really humble, and consists mostly of a few simple things. First, my students should spend significant time each class doing math — individually, partners, groups, whatever — giving me time to check in with and support students who need it, and making strategic decisions about where my time as the teacher is spent. Second, as often as possible, I should give my students opportunities to work on low-floor, high-ceiling tasks — tasks that have multiple entry points, and a great deal of opportunity for extension. These problems aren’t easy to find, but there are plenty of resources out there, and a few of these problems are worth a lot more mileage in class than a few dozen typical exercises. And finally, students need to be able to talk to each other in productive ways that support each others’ learning and create more avenues for learning than I can facilitate alone.

This isn’t all there is to it. I also need to scaffold language for English Language Learners and consider accommodations for students with disabilities. Small changes in the materials I put in front of kids can make a difference in their ability to access it. Some teachers have instructional aides or co-teachers to provide additional support. There are plenty more tricks I have yet to learn.

But my basic point here is simple. People who talk about differentiation — and especially people who run PD or write books about it — live in a bit of a fantasy world where teachers have the time and ability to, more or less, write multiple lessons for a single class. This sounds really nice. It honors the fact that all of our learners are different, and appeals to the belief that every student can succeed if they get that “just right” instruction. Maybe some of this is actually effective. But I really believe that the time spent doing any of that planning would be better spent doing any number of other things — tutoring after school, calling parents, spending more time anticipating student thinking, examining student work to see where students are. And more. The best differentiation is an engaging lesson with multiple entry points and opportunities for both me and my students to support everyone’s learning as flexibly as possible. The tools that go into that aren’t super flashy, but they lead to student learning, and leave me the time to plan another great lesson tomorrow.

Raymond johnsonNot only is the multiple-lesson differentiation strategy too time- and resource-consuming to be viable, I fear valuing that approach leads some teachers to think of differentiation as some kind of within-class tracking. I doubt that creating different educational experiences for groups of students in a class would escape all the problems we see with tracking when it’s done across classes in a school.

dkane47Post authorI like that perspective — many teachers really believe in learning styles, and telling someone not to do something because it wastes time doesn’t feel like the most convincing argument. Quick, convincing argument that relies on things that teachers already believe.

checkyourworkLove your post. I teach in a fairly affluent district and have a wide range of students in the same class. Many of my students, believe it or not, take math as an extra curricular activity (“Russian School of Math”) and others are two grade levels behind. As such the same work for all students really isn’t an option. However, I agree entirely with your post. Administrators would like to see me doing more small group instruction, but I resist. Even if my students know the rule, they don’t know everything, and I can usually find something interesting to think about or puzzle through. Also, I am usually the only adult in my room. So all students get the same instruction, and I aim to maximize students-doing-math time.

My question is more with pace of learning. Some students really do need less practice than others. Some students are ready to go on, and others are feeling whiplash. I don’t have any answers.

dkane47Post authorThat’s a really interesting perspective. I love your philosophy, and totally agree that unique circumstances require unique strategies. Sounds like a challenging job.

The pacing question is really tough. I don’t like giving students problems with the sole purpose of keeping them busy, but it’s often necessary to avoid chaos and leave myself the time I need to get to all the students who need it. I’ve ended up using a ton of problems from Five Triangles to find challenges for students that don’t take me forever to write — http://fivetriangles.blogspot.com/ but that’s imperfect also.

Five TrianglesRinging ears brought us here. We’ll add a different perspective on differentiation: it’s discriminatory and possibly illegal.

We are not putting into this category entrance exams for rigourous schools, “honours” classes, or students with IEPs, but within a single class, everyone everyday deserves an equal chance.

Put yourself in the position of the student who’s considered “in the stage of earliest development.” There’s simply no respectful way to put that. So that student gets the simplest problems, creating the lowest expectations, and possibly increasing the gap between him/her and the rest of the class. If we were the parents of said student, we’d sue the teacher, the board, and the district.

Would we win? Perhaps not, but it would be interesting to see what is revealed in discovery and the cross-examination of the differentiation-promoting education “pundits”.

That doesn’t mean a teacher cannot give hard problems; each student gets out of a lesson what he/she can. That’s the role of education, and neither to equally “engage” everyone at their level, nor guarantee an “A” for everyone.

AndyHey Dylan (and other commenters),

I strongly agree with the idea of certain types of differentiation as a form of tracking, or at a minimum, as allowing students to limit themselves from a broader education than they would have self-selected at the time. However, I struggle with multiple-entry problems and facilitating mathematical discussion. Is the breakdown of units into traditional groupings (teach polynomial unit, then factoring unit, then quadratic unit) part of the problem? Is it my own discomfort (or current ability to solve) the Five Triangles problems that makes me feel unqualified to teach others how to approach them? Is it my need to know how to do it myself first that is the real problem? Any insight would be great. Thanks!

dkane47Post authorThanks for this, Andy. I don’t have a tidy answer — I also struggle with Five Triangles questions and actually making this stuff happen in class.

I love your work on redesigning high school stats, and I think this is one possible perspective, but I think it has more to do with the lesson-by-lesson grain size. If each lesson practices one specific (usually decontextualized) skill, and the next lesson builds on that skill with something just a tiny bit more difficult or complex, we send the message that math is sequential, and is about following rules. Instead, we can start by saying “hey, there’s this funny thing called a quadratic, let’s learn some stuff about it”, and the first lesson takes a visual pattern perspective, the next an algebraic perspective, then we start making connections between representations and seeing what they have in common and building a broad base. Then over time kids gain flexible knowledge about this big idea, and students are constantly transferring concepts and building abstract ideas that they can apply in new contexts.

This can happen in a unit, or can happen in activities that spiral over the course of a year — I’m ambivalent there. But I think this “big idea perspective” is key to building these skills in kids, and I want to move my teaching in that direction.

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