A Grand Unified Theory of Remediation in Math Class
How to support students without just throwing them on computers.
Lots of people who are not teachers responded to the "learning loss" from the pandemic by saying that teachers need to provide remediation or acceleration or whatever. No one seemed very interested in the nitty gritty of how to do this, and so lots of schools responded by throwing kids who are struggling in math onto IXL or some other online math platform for 30 minutes a day and calling it good. I ranted about how much I hate that stuff last week. This post is my attempt to offer a coherent alternative to what remediation can look like that both works for students and is sustainable for teachers.
There are lots of ways to do this wrong. The "throw kids on a computer" approach is hip right now, but it's not the only model out there. Ten years ago I worked at a school where we gave students big cumulative tests, had "data days" where we picked the questions that students struggled the most on and planned mini-lessons to reteach those skills, or set aside a day to do a whirlwind reteach of random stuff. That didn't work very well because the lessons stood alone. Even if students got something from the lesson, they didn't revisit the concept and forgot it again. Other models rely too much on individual pullouts and are hard to schedule and grueling for teachers. Then there's the computer-based stuff, which tends to be unfocused and work randomly on skills from past years that might not be relevant to where students are headed in the future.
Here's what I tried to do last year, and am building on this year:
Prioritize
I can't remediate everything. I pick the most essential skills, do them well, and leave the less essential skills behind. In 7th grade that means I don't care very much about adding and subtracting mixed numbers or long division. It means I really really really care about solving one-step equations. If you only have time to remediate one skill, pick the most important one and spend a lot of time on it.
Connect Skills to Grade-Level Content
I can reteach skills all I want, but if I reteach them and students never use them again they'll be forgotten. Instead, I identify the foundational skills that lead to grade-level content and reteach them right before that relevant content. If I want to reteach rounding, I should do it right before my unit on area and circumference of circles so students can put it right to work. Adding integers works well right before a unit on rigid transformations. Simplifying fractions works well right before a unit on slope.
Plan Ahead
If I'm going to reteach one-step equations before our unit on two-step equations in 8th grade, I shouldn't wait until the day we're about to start to teach a quick mini-lesson. Learning takes time to sink in. I'll be better off carving out time for a few mini lessons over the weeks before the unit.
Get Feedback and Adjust
If I plan in advance I have time to make changes based on what students know and don't know. Each mini-lesson I can think about what went well and what didn't, and adjust accordingly. I'm often surprised in both directions — at what students know that I thought they would struggle with, and what they've forgotten that I assumed they'd remember. If I plan ahead, I have time to act on this information.
Concepts and Procedures
I design these as mini-lessons, 10-15 minutes each. I start with an introduction to the concept, using representations to help students visualize what we're doing or giving a concrete anchor problem they can use to make sense of the concept. Then I move to procedures. Concepts are important but procedures are what will lay a strong foundation for grade-level learning.
Practice
The second half of the mini-lesson is practice. I'm loving mini whiteboards right now because I can see which problems are hard and adjust the difficulty as we go. A little practice goes a long way toward making things stick. Then, students will get a chance to use the concept in the coming days or weeks as it comes up in class. Finally, throw a bit more practice into our weekly sets on DeltaMath to help make it stick.
Here's what I like about this model. If you have lots of time, you can make some solid progress on key skills. If you don't have much time then pick one key skill, carve out time for a few mini-lessons, and prepare a bit of followup practice. I don’t need weeks of extra time to make it work; even little bits carved out here and there add up, and if it’s only a skill or two that’s fine. Even that could make a big difference with one key grade-level concept.
The hardest part is planning in advance and choosing what to prioritize. That's the kind of work that would be really valuable for a district math specialist or math department lead or instructional leader to support teachers with.
This model isn't perfect. There are some students who need individual attention, or content that meets them where they are. But for a large group of students I think this model can make a big difference. In addition to helping students learn, chunking remediation into small pieces connected to course content makes it feel way less soulless and way more purposeful than most of what schools are doing right now.
I think this is especially useful as a "grand unified theory" in that it's easily extendable across levels. I teach undergrad stats classes in a model where I often can't assume students are comfortable with useful background math skills (e.g. calculating percentages, interpreting interval notation or inequalities, working with the equation of a line), and one class period a week is supposed to be dedicated to shoring up those skills. And this feels like basically the right framework for that, too! I'm not going to teach everything that the students would see in a full remedial course, just the bits that are directly useful for stats (or *sometimes* broader quantitative reasoning). I try to start covering something in that support section a couple of weeks before we'll use it in the "main" class, but I do a lot less rigid planning of the support section to respond to where students need review and practice. And the biggest change I've had to make over the past couple of semesters--definitely what I'm still working on most--is providing enough procedural practice (and spaced well) for those mechanics and the concepts to really stick.