Episode 2 – What is UDL in the math classroom?

As  TK-12 math coaches one of the most common questions we are asked is, “What am I supposed to do with my students who are struggling? How do I differentiate for them?” Unfortunately, the answer is always pretty unsatisfying to the teacher: Avoid needing to differentiate in the first place.

Now what does that mean? How does one do that?

Universal Design for Learning or UDL.

Let’s start with some definitions.

UDL + DI = Success for ALL!

What is the difference between Universal Design for Learning (UDL) and Differentiated Instruction (DI)? How to they complement each other?

Both have the common goal of meeting the individual needs of students such that all students can access the same high-quality content. It is the role of the teacher to assess student progress during learning and then adjust as needed, provide multiple ways for students to develop and express concepts, and to emphasize critical thinking.

There are significant differences between UDL and DI, largely with respect to when and how student differences are addressed. In Differentiated Instruction the teacher modifies content and/or process in response to the student’s needs identified during the instruction. By contrast, UDL is a framework for the teacher to proactively customize/create the lesson for the broadest range of students from the beginning.

In other words, UDL proactively evaluates the classroom instruction and environment and provides access to the content on the front end; DI reactively evaluates individual students and retrofits and modifies on the back end.

This is a good time for a Venn diagram…

There are three principles of UDL. These three principles are in response to potential barriers that might get in the way of our students learning.

Goal: To create purposeful and motivated learners.
How: Stimulate interest and motivation for learning.
Goal: To create resourceful and knowledgeable learners.
How: Present information and content in different ways.
Goal: To create strategic and goal-directed learners
How: Differentiate how students can express what they know
Increase interest through individual choice and autonomy, relevance, and lowering affective filter

Sustain effort and persistence with goals and objectives, appropriate challenge, collaboration and community, and mastery-oriented feedback

Options for self-regulation via growth mindset, personal coping skills, and metacognition
Increase the variety in which the content is received by student: visual and auditory
Options for language, mathematical expressions, and symbols

Strategies to increase comprehension by transforming accessible information into useable knowledge
Provide options for physical action
Provide options for expression and communication using multiple-media, creation tools, and scaffolds

Provide options for executive functions: goal-setting, planning, graphic organizers, metacognition

But to implement these principles into your classroom, it does NOT require the teacher to learn a bunch of new techniques. Rather, UDL is a mindset in which the teacher intentionally creates variety and choice by inserting already familiar strategies into in the classroom.

Some classroom strategies of each of the three principles…

Recruiting interest
Alternative seating
Choice boards
Socratic seminar
Brain Breaks
Sustaining effort and persistence

Rubric for self-monitoring
Flipped learning
Peer tutoring

Desk dividers
Exit tickets
Three-Act math
Visual cueing
Language, mathematical expressions, and symbols

Word Wall – Cognitive content dictionary
Tape diagram
Math manipulatives

Warm-up problem (Application problem)
Anchor chart
Physical action
Act out a problem
Use online tools
Expression and communication

Oral presentation
Record on video
Math manipulatives
Executive functions

Goal setting
Anchor charts

Let’s wrap up this brief overview of UDL with the punchline…

It’s important to realize that UDL is not some new idea that you have to add to your plate. Really it is just an intentional mindset in which we are always asking ourselves, “Are we providing students a wide variety of classroom strategies in each of the three areas (or principles) to ensure that all students get their needs met? Moreover, are students given choice in these areas, so that they can do some of the choosing?”

Take a few minutes to explore these links:



  1. Great episode! In our classrooms, we’ve built some “toolkits” for the kids to use that contain all sorts of relevant manipulatives and other tools. Right now we’re doing geometry, so those include graph paper, tracing paper, scissors, colored pencils, straight-edges, etc. The kids love getting to discover what tools work best for them!

    Perhaps this would be getting into the weeds too much, but I’d love an episode–or at least part of an episode–where you walk through an entire lesson or two using UDL. Just to provide a complete picture of what such a lesson could look like.

    Keep up the good work, you two!

    1. That is not too into the weeds! It is a great idea! When we finished recording this episode, we had a distinct feeling that there should be a follow-up episode. You just gave us a great idea for what that second episode might look like. Thanks dude!

  2. Love this podcast! I appreciate you sharing the concept of UDL and would love a follow-up episode too! I’m also curious on how UDL can connect with assessments. I love that UDL gives students flexibility and options to show how they make connects but then I feel as teachers we get stuck giving student rigid, impersonal, and honestly boring tests. Ideally, if we use backward planning (which I see is connected to UDL) how can we also move to students showing their mastery – especially in secondary with hundreds of students.

    1. First…thanks for listening to our podcast. Second…thanks even more for contributing to the community with your comment. Third…
      Your focus on assessments is an important one! Why bother creating flexibility within engagement and representation, but then suddenly use a one-size-doesn’t-fit-all traditional assessment for students to express their understanding. I’m wondering if this might be where technology can help us.

      Often UDL refers to technology as a helpful tool for providing the variety for engagement (games, videos) and representation (virtual manipulatives, video tutorials). But, to your point, technology can help the teacher insert variety into his/her assessing hundreds of students. For example, students can use SeeSaw or FlipGrid to make simple videos demonstrating their understanding of a concept. Other students may use GeoGebra or Desmos to demonstrate the same concept. Finally, some students may opt to take the traditional test.

      How cool would this be if somehow the teacher could set aside two days for this type of “open” assessment. I’m thinking ultimately, the TWO days for this kind of assessment will actually save time for the teacher in the long run.

      Melissa…you got me thinking. Thanks!

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