Possibly the biggest challenge for anyone trying to teach with Eureka Math while also incorporating the Guidelines for Universal Design for Learning (UDL) lies in the reality that Eureka is designed to be very teacher-directed, which is in direct opposition to the core of UDL, where teachers are working to help their students become independent and self-directed. I have written in earlier blogs about teaching moves that my colleague, Irene Witt, and I have made to bridge the gap between these two opposing philosophies (Bringing UDL to bear on curriculum; Using UDL to revise Eureka). As I see it, our work has been to continue to expect our students to engage with the high-quality, demanding, complex problems that form the Eureka Math curriculum, while providing support and supports so students can access those problems with less teacher direction and more independence.
One key to achieving this balance has turned out to be what we call “templates,” or teacher-created graphic organizers. The first template came about by happy accident. Two years ago, while teaching percent, we required our students to use the percent equation (part = percent*whole), as indicated in the standards. Not only is this expectation all over Eureka, but it also serves, in one form or another, to answer every possible percent problem (or at least the ones in Eureka or the ones we teach at the 7th grade level). I noticed that one of my students had created a little grid on her paper that she was using to corral the three elements of each problem…and a template was born.
This template brings together all of the aspects that we consider critical to teaching percent effectively: options for representations such as providing space for a visual model, an explicit expectation that students will represent their work with an algebraic equation, and space both to solve algebraically and a separate space to answer the question, as the answer from the algebra might not be the answer to the question itself.
As time has gone on, we have created templates for every Module in Eureka. Here are some of the benefits that we have observed:
- The templates provide structure without being overly prescriptive.
- The templates rein in some of the “number vomit” that plagues many middle school students, without providing any answers to the problems.
- The templates serve to remind students of expectations around organization and mathematical communication while allowing students freedom and room to make mistakes–the percent template, for example, will not help a student who doesn’t know that the amount of change serves as the part in a percent change problem, but it will help students remember that they are comparing a part to whole in every problem.
We have augmented the templates, in some Modules, with notes that help students make the connection between a variety of problems and the shared structure that underlies all problems of that content. For example, again in percent, we created a notes sheet, part of which is shown below, that connects every type of percent problem we teach in 7th grade with its correspondence to the shared structure of the template. We believe that making this connection reduces students’ sense that they are being barraged by a mishmash of disconnected problems and, instead, encourages them to see a common structure, which is at the heart of mathematics.
Using these templates has allowed us to reasonably expect our students to become more independent in their work, as the “resource” of the template sets clear expectations for a structure students can use to attack any given percent problem. The template provides an entry point or a way in, which allows students to give problems a try without direct teacher guidance every step of the way.