Foundations of Math: Teaching Students with Significant Disabilities

The Foundations of Math: Teaching Students with Significant Disabilities course is designed to develop educators’ knowledge of the mathematics they teach. This is accomplished by seeing math through the lens of a well-delineated number sense.

This course:

  • Focuses on research and practice that addresses the unique instructional challenges of teaching mathematics to students with significant disabilities and complex communication needs.
  • Provides teachers with the mathematical understanding needed to provide coherent, consistent mathematics instruction.

This course is for special educators, paraprofessionals, therapists, and related services personnel. It is designed for those involved in the teaching of mathematics to students with moderate to significant disabilities, including those with complex communication needs. This includes students who receive instruction in self-contained classrooms and center-based programs, who take the alternative math assessment, and/or are studying the Common Core Essential Elements.

Participants will:

  • Build deep foundational content and pedagogical knowledge.
  • Learn how to make solid instructional choices that positively impact students.
  • Connect procedures used in mathematics to conceptual understanding.
  • Build mathematical understanding and accurately assess learning for a range of learners.

At the heart of the training are the Components of Number Sense and the Prototype for Lesson Construction. Practitioners implementing skills and knowledge gained in the training should make multiple connections among the components of number sense and should approach lesson planning using quantity, mathematical structure, and symbols as presented in the Prototype for Lesson Construction.

Evidence Base

This course draws from research related to teacher content knowledge, how children learn math, and the connections between teacher content knowledge and student math achievement.

Mathematics in the 21st Century: What Mathematical Knowledge is Needed for Teaching Mathematics? - This course is predicated on research that identified a connection between teacher content knowledge and student achievement. 

Teaching Number Sense - Research on how students cognitively develop mathematical understanding from conceptual to procedural knowledge informs the Prototype for Lesson Construction used in this course.

The Learning Trajectories - The trajectories define natural developmental progressions that children go through as they develop mathematical understanding. This course shows how guiding students through these levels of thinking strengthens foundational mathematical understanding.

The Components of Number Sense - The Components of Number Sense provides a framework for teachers to utilize when planning and delivering math lessons. It allows for guidance and scaffolding of math concepts for both the teacher and student to deepen their content knowledge.

Mathematics for Children with Severe and Profound Learning Difficulties - This research provides insight into how students learn and how to approach instruction.

How to Receive This Training

You can choose to partner with Alt+Shift or attend a scheduled Statewide Event. Read more about each option below. If you’d like to be notified when the next statewide event becomes available, you can request to be notified.

Partner with Alt+Shift

Training is provided to ISD staff as part of an ISD partnership. Training is typically provided to the entire district, building, or program staff. This depends on the specific ISD's implementation plan. Training is one piece of the partnership. Strategic planning, implementation support, and capacity building are also addressed through the partnership.

Attend a Statewide Event

Statewide events are opportunities to receive training, but with limited opportunities for follow up support. Participants can expect to gain ideas and strategies that would be usable immediately in their practice, and to gain a better understanding of the nature of the training as part of an exploration process for sites considering a partnership with Alt+Shift.

There are no upcoming events for this training.

Implementation Stories

Alt+Shift asked partners around the state to share their implementation experiences and the impact on adults and students where they work.

Heather Gray

Special Education Teacher

The training challenged me to see the importance of math for my students. We now spend an hour daily on math. We have a half-hour math meeting focused on moving students along the learning trajectories followed by a half-hour math center time that provides more individualized instruction using the Essential Elements and individualized education program (IEP) objectives. The training has allowed me to see strengths in my students I was previously unaware of. The kids feel more confident, and I see less frustration when working with them on their individual goals. Our math meeting has high levels of engagement, and the kids are excited to participate every day. I have embraced the "repetition with variety" mantra. Math meeting is one part of the day I generally count on to go well.

The greatest implementation challenge is effectively differentiating for the wide range of skill levels we have in our classroom. Some students are ready to move on before others. Finding ways to make sure every student is met where he or she is at, and then appropriately challenged, is the daily struggle. Finding the right way to organize all the materials was another hurdle. I was able to organize all of the math supplies in a cart with drawers and label the drawers so I can quickly find what I need. The teaching assistants and even the kids know where to go if they need a number line, calculator, hundreds grid, clock, coins, objects to count, etc.


We've had so many magical moments this year where a student solves a problem independently for the first time. As a teacher, it is so reinforcing to me to watch students experience success and know what I'm doing is working. I think I will need to take some time this summer to reflect on what we accomplished and what can be improved for the next school year. How many of the Essential Elements did I end up covering? What activities can I design that incorporate even more exposure to other math concepts?

Continue the conversation with Heather Gray

April Perry

Special Education Teacher

In what ways have you implemented Foundations of Math?

I have started using the learning trajectories to assess students' math skills. I use this information to make decisions about lesson planning and goal writing. I have also used the learning trajectories website to find appropriate lesson plans to address deficit skill areas.

What impact has Foundations of Math had on you and those you work with?

Foundations of Math has helped us to understand the developmental sequence of math concepts. There has also been a shift from working on the recognition of written numerals to developing number sense. We found that many of our students could identify numerals 1-10, but they did not know what those numerals represented.


Describe one implementation challenge and how you overcame it or are working to overcome it.

Poor communication skills is a problem throughout our building. We continue to work with the speech therapists to develop reliable communication systems for our students. Within my own classroom, I have core vocabulary communication boards at each student's table. I also use fringe vocabulary during math lessons that relate directly to the math concept we are working on.


Describe one implementation success or highlight.

I have a student who began the year with many skills already in place. He could verbally count beyond 20, count backwards, identify numerals 0-10, and count small sets with 1:1 correspondence. However, he was struggling with producing sets made up of a requested number of objects. Throughout the year, we have worked on this skill using several different lessons from the Learning Trajectories website. Now, he is able to produce sets up to five objects.


What is your next step for implementing Foundations of Math?

I plan to continue to use the learning trajectories to assess student skills and to guide my lesson planning. I would like to incorporate more subitizing activities as well because I feel this is an area I have not routinely addressed with my students.

Continue the conversation with April Perry

What Others are Saying

We asked our partnership sites to share their experience related to the training.

Patrick O’Neill
Special Education Teacher
Benjamin White
Special Education Teacher

Additional Information

Foundations of Math

A Foundations of Math course was also developed for teachers who work in inclusive settings with students who study the Common Core State Standards. The pedagogy and philosophy are identical to Foundations of Math: Teaching Students with Significant Disabilities. However, this course does not include research, examples, and video of students with significant disabilities. Instead, it allows for planning and discussion related to students with disabilities who receive math instruction in general education classrooms or resource rooms and who are, or likely to be, working toward a high school diploma.

Visit the Foundations of Math page

Foundations of Math Handbook

The Foundations of Math handbook provides a course overview, descriptions of key concepts from the course, and answers to frequently asked questions.  It was written to help our partnership sites answer questions they were getting from classroom staff, building and district administrators, and parents.

Get the Foundations of Math Handbook