Teacher A and Teacher B: Seeing the Possibilities of Universal Design for Learning 3.0
by Nesta Marshall
It can be said that teaching is an art because teachers can be eclectic in shaping and refining their instructional approaches using a variety of research-based strategies, mentor-informed tools and action-oriented guidelines. One noteworthy set of guidelines is Universal Design for Learning (UDL). The guidelines support teachers in incorporating the UDL concepts into their practices while also offering viable ways for teachers to support learners. UDL 3.0 is the current version that has value-laden principles and meritorious themes for promoting student learning and student efficacy. It was developed in response to the robust appeal from educators and researchers to “address critical barriers rooted in biases and systems of exclusion for learners with and without disabilities” (CAST, 2024).
UDL 3.0 centers around three big considerations when designing instruction: include multiple ways for engagement, multiple means of representing information, and multiple ways for all to interact and communicate. The guidelines embody the notion that instruction and its delivery, curriculum, information resources, technological devices, assessment and the learning environment, including physical spaces, allow students to have equal access to learning.
In this blog, two themes will be presented for enhancing teaching practices and creating a learning milieu that support greater learner accessibility to and ownership of math tasks.
Theme 1: Promoting Interdependence and Collective Learning
This theme “emphasizes the value of collective learning and interdependence, encouraging environments where collaboration and shared knowledge-building are central to the learning process.”
One can posit that a classroom environment where collaborative discourse and co-constructing knowledge are promoted does not exist in a vacuum. The learning milieu must espouse a sense of belonging that spans the range of students’ learning capacities including low floor and high ceiling engagement. Of equal import, the classroom community should be a place where culturally-sustaining math teaching is esteemed. Moreover, multilingual learners should have “supported opportunities to express themselves” in English and their home language.
Theme 2: From “Expert Learner” to “Learner Agency”
The goal is to shift from “expert learners” to fostering “learner agency,” which centers on developing learners who can actively co-create their learning environments.
This theme is tied strongly to recognizing students’ assets and optimizing student learning by promoting multiple approaches towards sensemaking. This can be achieved by looking at a student at work, promoting usage of manipulatives and having resources available to support challenges. In this type of strengths-based classroom, opportunities for creativity, rigor, equity, student autonomy and self-advocacy position students to have voice and choice in their learning. As Hammond (2025) notes in her article, agency can be developed when teachers integrate a “cognitive apprenticeship” model, support student examination and revision of how they see themselves as learners, and offer regular opportunities for student reflection.
Keeping these two UDL themes in mind, let’s take a look at two different classrooms of two different teachers, Teacher A and Teacher B.
Teacher A
In a Grade 6 classroom, twenty four students were deepening their understanding of the Cartesian coordinate plane by plotting points across all four quadrants. After reviewing the coordinate plane, and explaining how to plot the negative number coordinates, Teacher A gave directions for students to plot sets of ordered pairs and connect the points to create pictures on their graph paper. Students worked individually at their desks with no noticeable on-task dialogue happening among them. Several minutes into the task, a student approached Teacher A, and requested a ruler. The exchange between them was as follows:
Student: Can I have a ruler?
Teacher A: Why do you need a ruler?
Student: I need one to do the picture.
Teacher A: I don’t see why you need a ruler. Everyone is doing it without a ruler.
Student: I’m not everyone.
Reluctantly, Teacher A handed the student a ruler from her desk drawer. She remained at her desk. Just before the class dismissal, she asked volunteers to show the pictures that they created.
Teacher B
Teacher B’s twenty-four students were doing the same task as those in Teacher A’s class. There were clusters of four desks. Math manipulatives and tools (e.g., geoboards, rubberbands, rulers of varied lengths, colored pencils) were easily-accessible. There were options for the coordinate grid (e.g., varied-sized graph paper, pre-printed grid with a plastic sleeve for dry-erase purposes, large laminated grid, digital grids). An active word wall with lesson-specific vocabulary (such as origin, ordered pair, x-axis, y-axis, x-coordinate, y-coordinate, quadrant, coordinate plane, integer) with correlating pictures and examples was provided, along with student-created glossaries in English and their dominant language. After an interactive mini-lesson, students were given a menu of tasks that consisted of: 1) writing the ordered pair for 6 out of 8 points, 2) choosing 6 out of 8 ordered pairs to plot and label, 3) creating shapes or objects using a set of points provided or their own points, 4) making a map and labelling the points to show the location of at least five items in a place that they chose. Two students’ requests to review a short video demonstration on plotting points was granted and commended.
At the back of the classroom, a small group of students created a coordinate grid using the floor tiles. They took turns calling out a point and positioning themselves to represent its location. Jack and Bella compared how they each plotted (-3, 2), and Bella realized that she moved three units down from the origin and then jumped two across to the right. Jack explained that the first number in the ordered pair was located on the horizontal number line. Another student, Jamie, listening in on their conversation, recognized that he used the correct directions for the x,y on the geoboard, but thought that the origin started with the number 1; so his point was (-4, 3). As Teacher B circulated, she asked all three students how they might remember where to start and which direction to go. Jack showed that he used arrows to recall the direction (-3←, 2↑). Jamie shared an idea for a rap: “To the right and climb up are positive moves; To the left and climb down are negative moves, That’s how we groove and prove”. Teacher B encouraged them to add their strategies to the Strategies for Using the Coordinate Plane chart.
As Teacher B continued to circulate, she saw Malachi and Gus drawing a rocket ship on a large laminated coordinate plane. While looking at where the corners of the rocket ship’s engine landed on the grid, Malachi and Gus thought that the repetition of numbers in the ordered pairs (-5, 1; -5, -1; 5, 1; 5, -1) was “cool”. Teacher B probed, “What do you notice? What patterns do you see? Does the pattern work for other sets of ordered pairs? When does the pattern work? Can you make a rule?”
For the lesson’s closure, Teacher B asked, “What was important to know about the ordered pairs and why? If given this task again, what would you do the same or differently? What new idea or strategy did you discover? Where might labelling points be useful?”
Clearly, Teacher A and Teacher B tell the story of two teachers, two classes and two different instructional approaches. Having Teacher A’s story as a counterpoint and something to ponder (including the ‘ruler’ episode), let’s unpack how Teacher B integrated the two UDL themes into her practices.
Interdependence and Collective Learning |
Learner Agency |
| During the lesson closure, there were opportunities for metacognition. reflecting on ‘the what’, ‘the how’ and ‘the why’ of the task helped to consolidate learning. | Students had the freedom to make choices by selecting tasks from a set options; flexible learning was purposeful in making a map based on their everyday experiences. |
| The desk cluster arrangement and access to math tools, manipulatives, and resources facilitated the co-creation of knowledge. | A variety of multimodal (e.g., tactile geoboard and kinesthetic labelling of points using the floor grid) and multisensory approaches (such as musical rap) was showcased and affirmed. |
| When students were asked how they might remember how to plot and name points, the teacher created an inclusive math community (Lambert, 2024) where students clarified ideas, contributed skills and shared strategies. | There was an openness and responsiveness to students’ input for attaining the goal of the lesson and building new knowledge when discovering the mirror image of points on the x-axis and y-axis. |
| Student-to-student feedback served as a vehicle for addressing misconceptions and deepening conceptual understandings based on students’explorations as seen in comparing their labelling of (-3, 2). | Self-advocacy was honored and supported when students got the go-ahead to use a technological aid to guide their processing of the lesson’s content. |
At any given time, an educator can intentionally or unexpectedly or unwittingly mirror Teacher A’s instructional practices. If this is your case, a good place to start could be to learn from Teacher B (who is Teacher A reimagined). Consider the maximal positive impact that such a strategic, student-empowered, resource-rich, collaborative-focused instructional approach would yield. Let’s then avail ourselves of the teacher-ready resources, like UDL 3.0, that would arm our students with their metaphorical ‘ruler,’ and help us to create a learning environment that engenders productive learning outcomes in our students’ lives in the classroom and beyond.
References
CAST. (2024). Universal Design for Learning Guidelines (Version 3.0).
Hammond, Z (2025): Rebuilding Students’ Learning Power with Learn-to-Learn Skills in Cult of Pedagogy.
Lambert, R. (2024). Rethinking Disability and Mathematics: A UDL Math Classroom Guide for Grades K-8. Corwin Press.
Math for All: Making Rich Mathematics Accessible to All Students in Grades K-8.
University of Colorado Denver (2024). Teaching & Innovation Blog.
The contents of this blog post were developed under a grant from the Department of Education. However, those contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.
This work is licensed under CC BY-NC-SA 4.0 
Math for All is a professional development program that brings general and special education teachers together to enhance their skills in
planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.
