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Supporting High-Quality Inclusive Math Instruction in Co-Taught Classrooms

By Cathy Buyrn, M.Ed.

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By Cami Williams, M.Ed.

The goal in every math classroom should be to instruct students in a way that they all reach proficiency, regardless of racial, ethnic, linguistic, gender, socioeconomic, or disability status. This is what equitable learning in the classroom is all about – planning lessons that are accessible to all students. How can a teacher do that?  

Teachers that take a Visible Learning approach to their instruction promote an equitable learning environment. The heart of this approach is a shift in vision for both the teacher and the student. With Visible Learning, teachers are asked to view learning through the eyes of their students and students see themselves as their own teachers (Almarode et al., 2019). We will explore three math instructional strategies that embrace the intentions of Visible Learning and, when implemented with fidelity, help cultivate an equitable learning environment. Those three strategies include facilitating student conversations about the math, using student mistakes as learning opportunities, and presenting multiple representations to scaffold conceptual understanding. Being intentional about including these approaches in each lesson helps students understand their responsibility in their own learning.  

Veteran special educator, Tanisha Facey, details how she promotes an equitable learning environment in her math resource classroom. She gives a peek inside her classroom, sharing what works for her within these three strategies and the challenges she is facing with a new placement in an urban middle school. Let’s meet Mrs. Facey and dive into how to reach more students with Visible Learning through three math instructional strategies.

Math discourse gives students a chance to explain their thinking and understanding of a problem or given concept. Teachers will be able to identify misconceptions, if any, that may not be evident in their paper/pencil work. Facilitating meaningful discourse also allows students to not only share their thinking, but to listen to and consider other students’ points of view. This can be done by allowing students to work together to troubleshoot and problem solve when they are unsure of how to proceed. Providing sentence stems to students can help facilitate these conversations in small groups but it is equally important to monitor and plan for the questions that are asked during instruction. Mrs. Facey shares with us how she finds space during her lessons to facilitate these conversations with her students.  

Just as there are multiple modes of learning – kinesthetic, visual, auditory, etc. – there are multiple ways math concepts and procedures can be presented to reach more students. When students are shown multiple ways, it allows them to determine which is the most comfortable fit for how they comprehend the information. The representations fall into three categories, in no certain order, pictorial, abstract, and concrete. As with instruction in general, you want to use these multiple representations to meet students where they are or to deepen their understanding. An equitable learning environment starts at a place where most students will be reached to lessen the chance a student is left behind. Mrs. Facey talks about her approach to providing multiple representations to her students to ensure their understanding of math concepts and procedures.  

How are mistakes (those of the student and teacher) handled during instruction? This is an important thought to consider and strategically address. To help students engage in their own learning and model independent work endurance, try using mistakes as an opportunity to share metacognitive strategies with students so they may explore their reasoning skills.



• Use Think-Alouds during instruction to show reasoning and troubleshooting errors
• Ask students
• What strategy did you use? Why?
• How did you begin to think about this?
• Is your solution reasonable?
• How can you determine if your solution is reasonable?
• What parts of your work are you most sure about in this problem? Why?

Mrs. Facey talks with us about how she makes sure her students feel comfortable sharing mistakes and using them as learning opportunities.

Mrs. Facey closes out our conversation with her perspective on co-teaching and what administrative supports she feels would be most beneficial to maximize collaboration between general and special educators to create equitable learning environments in the math classroom.  

While planning for the next math unit, consider choosing a focus in one of the three areas – math discourse, multiple representations, or mistakes as learning opportunities. Prepare each lesson for that unit to include opportunities for students to grow in the area of focus. Below are resources to support each area.  

References

Almarode, J., Fisher, D., Assof, J., Moore, S. D. C., Hattie, J., & Frey, N. (2019). Teaching mathematics in the visible learning classroom: Grades 6-8. Corwin.