In order for instruction to have an impact on learning, it needs to include research based practices. The use of manipulatives and UDL principles have been shown to improve mathematical achievement. 

Beal, C. & Rosenblum, L. (2015). Development of a math
     learning app for students with visual impairments. 
     Journal on Technology and Persons with Disabilities,
, 1–9.

Accessibility to math content for those with visual impairments can be especially difficult due to the complexity of math concepts and the high visual aspect of the content. The researchers conducted a small pilot study using a combination of a web based computer program and accessibility features on an iPad for students with low vision. While using the prototype app, those with low vision increased their engagement and math problem solving skills. Students were able to adjust font and background colors, hear text using VoiceOver, enlarge text using Zoom, and use hints and videos as needed to support content. The results of the study were favorable for engagement and attainment of math skills. The app,  Animal Watch IV Suite, is now available in the Apple Store.

Jimenez, B. A., & Besaw, J. (2020). Building early numeracy
     through virtual manipulatives for students with 
     intellectual disability and autism. Education and Training
    in Autism and Developmental Disabilities, 55
(1), 28–44.

The use of manipulatives in math instruction has been found to benefit students of various ages and abilities. This case study evaluated the effectiveness in using virtual manipulatives in teaching number sense, counting, comparisons, and estimation. The students demonstrated an increase in engagement and performance when virtual manipulatives were used during lessons. The students were also able to transfer their new math skills to new situations. The use of manipulatives as a UDL element can have positive implications regardless of a student’s cognitive ability.

Kaczorowski, T. L., Hashey, A. I., & Di Cesare, D. M.
     (2019). An exploration of multimedia supports for
     diverse learners during core math instruction. 
     Journal of Special Education Technology, 34(1), 41–54.

Multimedia tools for math instruction which are built using the principles of Universal Design for Learning can benefit all students including those with mild learning disabilities. The supports included pop-up window explanations, short instructional videos, colored markers and pens, and a variety of learning activities. The instructional tools increased student engagement with the material and increased math achievement. However, for students with mild learning disabilities, they still need explicit, direct instruction on how to use each tool and activity in order to benefit in their understanding and critical thinking related to math concepts.

Liggett, R. S. (2017). The impact of manipulative use on
     grade 2 math scores. Brock Education: A Journal of 
     Educational Research and Practice, 26
(2), 87–101.

The use of manipulatives can be used to increase achievement scores as well as teach problem solving skills to students of all ability levels. In a small study of second grade students, Liggertt found that those students who used manipulatives scored better on posts tests than those who did not. This finding was true regardless of gender, ethnicity and age. Since classrooms are composed of students of various abilities and disabilities, the use of manipulatives can be an effective instructional tool to learn mathematical concepts. “The fact that every classroom consists of students with different levels of ability to understand mathematical concepts means that teachers should focus on using multiple teaching strategies so that all students can benefit” (Golafshani, 2013, p. 139).

Peltier, C., Morin, K. L., Bouck, E. C., Lingo, M. E., Pulos, J. M.,
     Scheffler, F. A., … Deardorff, M. E. (2020). A meta-analysis of
     single-case research using mathematics manipulatives with 
     students at risk or identified with a disability. Journal of
     Special Education, 54
(1), 3–15.

The use of manipulatives in math instruction is considered best practice. They can aid in conceptualizing math concepts and performing procedural operations. Studies have found students identified with or at risk of having a learning disability, autism, or intellectual disabilities had positive results when using both concrete and virtual manipulatives regardless of their age. While younger students may prefer concrete manipulatives, virtual manipulatives are just as effective, and their use may be less stigmatizing for high school students.

Xie, J., Basham, J. D., Marino, M. T., & Rice, M. F. (2018).
     Reviewing research on mobile learning in k-12 educational
     settings: Implications for students with disabilities. 
     Journal of Special Education Technology, 33(1), 27–39.

A review of the research has found mobile technologies are effective tools towards implementing Universal Design for Learning principles into instruction and positively impacting learning across content areas, including math, for both students with and without disabilities. M-learning devices can support language and reading skills for students learning English or who have a reading disability. In addition, m-learning has been shown to have a positive impact on motivation and engagement with academic content. It can also provide choices in individual and collaborative learning.