I think about missing prior learning way more today than I did a few years ago. I always understood in an abstract sense that students with gaps from previous years have a harder time learning. Still, I didn't appreciate the magnitude of the problem. If students don't understand the math that my lesson is building on they will learn less, every day. There's less for that knowledge to stick to in their mind and they are more likely to get confused along the way. So what do I do about that?
I wrote last month about how I try to address gaps in prior knowledge. The goal of this post is to step back and think about the underlying philosophy behind addressing those gaps. Here are six different things I’ve seen schools do:
Option 1: Look the other way
It might seem like I'm being sarcastic I'm here but I'm not. Lots of schools and teachers just avoid the issue. If you have a lot of students who aren't ready for grade level math it's a hard problem to solve and it can feel overwhelming. The school doesn't have a system and the teacher doesn't know where to start on their own so nothing happens. There are other ways schools justify ignoring the problem — some talk about how the curriculum spirals and students will see skills again so it's ok if they don't understand anything the first time. Don't do this!
Option 2: Offer support when students have a hard time
This is the premise behind lots of tutoring programs. If a student is having a hard time get them help on their homework or something like that. This is often what parents do, simply because they don't have the tools to do much else. Homework help might help students finish their homework but it isn't solving the basic problem: students aren't learning as much in class because they lack foundational skills.
Option 3: Just-in-time
It seems like this model has become more popular in recent years. Offer a mini-lesson or a bit of individualized help to students right before a unit starts or before some prior skill comes up. This often looks like some sort of warmup activity at the start of a lesson or a quick preview at the start of a unit. This is a good idea! I do this all the time. The issue is, just-in-time support often isn't enough. If you’re reminding students of a vocab word or something quick like the area of a rectangle then sure. But if students struggle with a bigger skill like solving two-step equations, just-in-time support isn't going to magically teach them during a warmup before a lesson on systems of equations. Starting a lesson with some quick review of prior knowledge is a good idea. There are lots of students who are a little rusty with a skill and benefit from that review. But if the student didn't learn the skill in the first place, just-in-time support isn't going to cut it.
Option 4: Start where they are
On the surface this makes sense. My students have a wide range of skills; what if I could meet each student where they are, beginning with what they understand? The problem is that schools don't have the resources to do this with humans so they put students on a computer program like i-Ready or Khan Academy or IXL. A great report just came out profiling these programs. The short version is that they don't work for the students who need that support the most. Kids find ways to game the system, or don't have the self-regulation skills to get much out of the program, or schools shove kids on the website with little supervision day after day. Even with thoughtful implementation the reality is that these websites aren't smart enough to figure out which concepts are holding kids back. I cannot emphasize enough how bad these programs are. Kids get questions wrong on the diagnostic on purpose so they get easy questions. Kids figure out that it gives them credit if they solve a problem once every two minutes so they time it to do the minimum work possible. Even kids who put effort in often don’t make much progress because they practice a skill for a day and then never revisit it. I’m not opposed to meeting kids where they are in principle but I haven’t seen a school with the resources to do it well for everyone.
Option 5: Start the year with a ton of review
This can work ok, but I have two concerns. First is about class culture. I like to start the year by learning new math so students can start to get comfortable with all of our regular classroom routines. Starting with review can make it hard to engage students who have those skills. I definitely mix in some review but I don’t want to only do review to start the year. My second concern is that starting with a ton of review might not be much help when students need those skills in March and April. It’s not a bad idea, but it’s not ideal either.
Option 6: Prioritize and plan with the end in mind
Options 2, 3, 4, and 5 should all play a role in schools. A bit of review at the start of the year is a good thing. It's good to give students help when it's clear they're struggling with something. Just-in-time review is helpful for lots of students. Some students who are really struggling will benefit from time working on their level if we can get a human to teach them. My primary approach is something different. I make a list of all the skills my students need to succeed in 7th grade math and I map out a progression of mini-lessons and practice so that students get the chance to improve with those skills before they come up in class. We start the year working hard on fraction multiplication and division because those skills come up so often in proportional reasoning early on in 7th grade. Rounding and decimal place value come up when we work with circles. That skill typically takes two weeks for students to get proficient. One-step equations are a big skill so we work on them for multiple months before we get to two-step equations. Angles are a quicker skill, so we spend a week before we begin solving problems with angles practicing those skills. It doesn’t take too much time. For the most part these are five minute mini-lessons, a bit of practice mixed in with other skills we’re practicing, and I figure out what students are stuck on and address that in the next mini-lesson. I'm not trying to address every single little thing students have missed. I'm prioritizing the most important skills, and I'm backwards planning so students have the chance to develop those skills before we extend them with grade-level work.
Keep It Practical
Whatever your approach to prior knowledge is, it has to be practical. Would it be great to give every kid high-quality instruction on their level every day? Sure, yes. But it’s really really hard to do that, which is why schools throw kids on i-Ready for 30 minutes a day in a room with 25 other kids and a paraprofessional and pat themselves on the back for meeting students where they are.
There are two big advantages to prioritizing and teaching mini-lessons with the full class. First, there are absolutely some students who need me to take a big step backward and work with them on their level. But there are also a lot of kids who will make good progress through whole-class mini-lessons, and I can filter out those kids and focus my energy on the students who need it the most. Second, while I understand the allure of individualized learning and starting where they are, that approach risks low expectations and an endless cycle where students never see grade-level content. My goal is to teach 7th graders 7th grade math, and that’s what my approach is designed to do.
Whether you agree with me or not, I think every teacher and school should step back and think about their philosophy. What’s yours?
I like 5 - prolonged diagnostic and intervention time