Communication is a system of exchanging information using symbols, signs, and/or behaviour (‘‘Communication,’’2015). Mathematics necessarily involves communication, and according to the National Council of Teachers of Mathematics (NCTM, 2000), communication is a critical mathematics process for which all students must develop the facility to effectively engage in mathematics learning.
This article summarises and highlights the main points from Thomas et al., (2015) research that aims to relate mathematics, language, and literacy and to describe the difficulties faced by students with disabilities with math content based on the language demands of mathematics using universal design for learning (UDL) to examine the goals, methods, materials, and assessment of instruction for helping educators identifying potential barriers to learning and developing solutions to lessen the language demands of mathematics for the wide range of learners.
It is commonly acknowledged that approximately 6% to 7% of school-age children have a mathematics disability (Swanson, Jerman, & Xinhua, 2009). Interestingly, it has been found that more than half of the students diagnosed with a learning disability have some disability or difficulty in mathematics (Bryant, Smith, & Bryant, 2005). Although ‘‘difficulty with the language of math’’ (Bryant, Bryant, & Hammill, 2000, p. 175) is a behaviour recognised by many experts in the field, perhaps one of the least acknowledged and understudied impediments to learning mathematics is the relationship between mathematics and language (Donlan, 2007; Morin & Franks, 2010).
However, this research does still suggest a link between language and mathematical development, also assumes that students with both math and reading disability were less skilled at solving complex word problems and have a poorer understanding of key conceptual principles in computation than students with a mathematics disability only.
As such, language, including the language of mathematics, can be conceptualised as having both expressive (speaking, writing) and receptive (listening, reading) aspects. Understanding each of these components can help shed light on the critical role that language plays in mathematics learning and development, particularly for students with disabilities and those who struggle to learn mathematics.
There are many different difficulties students with disabilities and learners at risk for math failure may experience in mathematics that are related to language. From these challenges are:
- Receptive Language Challenges.
- Expressive Language Difficulties.
A universal design for learning (UDL) framework (Centre for Applied Special Technology [CAST], 2011) is described to help teachers ameliorate barriers posed by the instructional demands of mathematics to support full access to the general curriculum for the broad range of learners found in today’s diverse classrooms.
CAST conceptualised the UDL framework, proposing that the inflexibility of much of the traditional curriculum-imposed barriers for many learners.
Unlike typical curriculum modifications and adaptations, UDL is most effectively applied during curriculum design (Hitchcock, 2001), with a focus on considering goals, methods, materials, and assessment. The UDL framework consists of three key principles that are designed to help minimise barriers and maximise learning:
a) Providing multiple means of representation, this principle addresses the presentation modes of information and content for learning (the ‘‘what’’ of learning).
Examples:
- Presenting the information using multiple perceptual modalities, such as graphic, verbal, and tactile using graphic organisers, concrete or virtual manipulatives, and video screencasts that enable repeated access to auditory information.
- Providing a variety of representations and additional support may be necessary, options may include a traditional or technology-enhanced dictionary, a word wall, cue cards, charts of mathematical expressions and symbols, peer-mediated learning, and text-to-speech for mathematical language and notation.
- Pre-teaching vocabulary and critical prerequisite concepts including the use of demonstration or models in pre-teaching of vocabulary and concepts; highlighting or colour coding key elements in word problems or equations; providing guided notes, tables for assisting in the processing of mathematical content; and giving explicit prompts for each step in a sequential problem-solving process.
b) Providing multiple means of action and expression, this principle addresses how learners navigate and make sense of the learning environment and demonstrate their learning (the ‘‘how’’ of learning).
Examples:
- Using assistive technology that provides such adaptations as speech or switch activation, alternative keyboards, as well as virtual manipulatives (e.g., GeoGebra).
- Increasing opportunities to respond and interact with the language of math in supported environments such as technology-based practice and through peer-mediated learning and Scaffolds that can be faded as learners make progress support independence and can foster development and practice in critical thinking skills.
- Supporting students in both lower-level executive skills (to reduce cognitive effort and free capacity for higher-order processes), and in higher-level executive skills (including strategies for more effective processing may increase students’ executive capacity) (Geary, 2004; Jerman, Reynolds, & Swanson, 2012).
- Including checklists and graphic organisers, calculators to manage computation and reduce cognitive load and free capacity to enable focus on higher-level thinking skills.
c) Providing multiple means of engagement (Rose & Meyer, 2002), This principle focuses on motivation and engagement for learning (the ‘‘why’’ of learning) and acknowledges the high degree of variability in how students engage and experience motivation to learn.
Examples:
- Giving learners’ the choice in how learning objectives can be reached can help them develop autonomy. Learners attend more when the material is personally relevant. In math, real-world problems such as anchored math, situating students on opposing sides of math disagreements, and including culturally relevant instructional materials increase engagement and focus on critical thinking skills.
- Struggling math learners are often afraid of making public errors and therefore do not have the confidence to share their answers; an accepting and supportive classroom facilitates engagement (Carver & Scheier, 2005).
- Reiterating the goal; breaking the long-term objective into shorter, more approachable tasks; and teaching students how to establish and monitor progress toward reachable deadlines can help.
- Giving timely and specific feedback can promote effort and persistence for future success.
- Activities that encourage self-reflection include the identification of personal goals, and the use of checklists, diaries, and online options for self-management such as KidTools.
Finally, universal design principles have proven to be highly effective in daily life and calls for UDL are becoming increasingly prevalent in current policy and reforms, it is worth pointing out that the evidence base for UDL in mathematics content is still developing. Still, UDL provides a framework that can help teachers better align their instruction to meet students’ needs, including effective solutions for reducing language demands that may prevent students from making adequate progress in mathematics and for supporting the development of mathematical language and thinking within the learner.
References
Bryant, D. P., Bryant, B. R., & Hammill, D. D. (2000). Characteristic behaviors of students with LD who have teacher-identified math weaknesses. Journal of Learning Disabilities, 33(2), 168-177. https://doi.org/10.1177/002221940003300205
Bryant, D. P., Smith, D. D., & Bryant, B. R. (Eds.). (2005). Teaching students with special needs in inclusive classrooms. Upper Saddle River, NJ: Pearson.
Carver, C. S., & Scheier, M. F. (2005). Engagement, disengagement, coping, and catastrophe. In A. J. Elliot & C. S. Dweck (Eds.), Handbook of competence and motivation (pp. 527–547). New York, NY: Guilford Press.
Center for Applied Special Technology. (2011). Universal design for learning guidelines version 2.0. Wakefield, MA: Author.
Communication. (2015). In Merriam-Webster’s online dictionary. Retrieved from http://www.merriam-webster.com/dictionary/communication.
Donlan, C. (2018). Mathematical skills of children with specific language impairments: Testing developmental theory. Language and Culture in Mathematical Cognition, 131-144. https://doi.org/10.1016/b978-0-12-812574-8.00006-7
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201
Hitchcock, C. (2001). Balanced instructional support and challenge in universally designed learning environments. Journal of Special Education Technology, 16(4), 23-30. https://doi.org/10.1177/016264340101600404
Jerman, O., Reynolds, C., & Swanson, H. L. (2012). Does growth in working memory span or executive processes predict growth in reading and math in children with reading disabilities? Learning Disability Quarterly, 35(3), 144-157. https://doi.org/10.1177/0731948712444276
Rose, D., & Meyer, A. (2002). teaching every student in the digital age: Universal design for learning. Educational Technology Research and Development, 55(5), 521-525. https://doi.org/10.1007/s11423-007-9056-3
Swanson, H. L., Jerman, O., & Xinhua Zheng. (2009). Math disabilities and reading disabilities. Journal of Psychoeducational Assessment, 27(3), 175-196. https://doi.org/10.1177/0734282908330578
Thomas, C. N., Van Garderen, D., Scheuermann, A., & Lee, E. J. (2015). Applying a universal design for learning framework to mediate the language demands of mathematics. Reading & Writing Quarterly, 31(3), 207-234. https://doi.org/10.1080/10573569.2015.1030988
Comments