CORE ACADEMIC QUARTERLY
CORE ACADEMIC QUARTERLY
Gaining proficiency in mathematics is dependent on the application of a variety of skills. Among these critical skills are reading, writing, sequencing, following oral directions, and memorizing facts and procedures. Language plays an important role in learning mathematics. Many students who have difficulty with math struggle due to language challenges. Dyslexia is a language-based disability as described in the following definition from the International Dyslexia Association (2002):
Dyslexia is a specific learning disability that is neurobiological in origin. It is characterized by difficulties with accurate and/or fluent word recognition and by poor spelling and decoding abilities. These difficulties typically result from a deficit in the phonological component of language that is often unexpected in relation to other cognitive abilities and the provision of effective classroom instruction. Secondary consequences may include problems in reading comprehension and reduced reading experience that can impede growth of vocabulary and background knowledge.
It should come as no surprise that students with dyslexia often struggle in particular areas when learning mathematics. Despite having dyslexia, these students are able to reason with math and successfully do higher levels of math (beyond elementary school). Many find their way to success with math through their own creative work-arounds. However, many students do not successfully find work-arounds and learn to approach math with a sense of dread and inevitable failure. There are many techniques that can help students with dyslexia overcome their challenges with less pain and with greater success.
Students who have dyslexia may also suffer from dyscalculia. Dyscalculia is a learning disability specific to math, separate and distinct from dyslexia. Below is a definition from the United Kingdom Department for Education and Skills (2001) as referenced by Chinn (2018, p. 2).
Dyscalculia is a condition that affects the ability to acquire mathematical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers and have problems learning number facts and procedures. Even if they produce a correct answer, or use a correct method, they may do so mechanically and without confidence.
While this article focuses on some of the challenges students with dyslexia face with math and includes suggestions for helping them overcome those challenges, a future Academic Quarterly article will focus on specific challenges with dyscalculia and provide recommendations for how to assist students with this difficulty.
According to Miles and Miles (2004), students with dyslexia often struggle with applying the following important skills when learning math:
Several of the issues listed above relate to limitations with working memory. There is a strong association between working memory capacity and mathematics performance (Berch 2011, p. 22). Berch describes an excellent assessment scenario (the Backward Digit Span task) to highlight the difference between short-term memory and working memory:
[A] random string of number words is spoken by the examiner (e.g., saying “seven, two, five, eight . . . ”), and the child must try to repeat the sequence in reverse order. Note that rather than simply having to recall the numbers in the same forward order (which is considered a measure of the short-term, verbal storage component per se), the backward span task requires that the child both store and maintain the forward order (i.e., verbal component) of the number words while simultaneously having to mentally manipulate this information to accurately recite the original sequence in the opposite order. It is this dynamic coordination and control of attention combined with the storing and manipulation of information in support of ongoing cognitive activities that I characterized earlier as being the sine qua non of working memory.
Berch provides an excellent chart in Perspectives on Language and Literacy (p. 24, 2011) of seven principles for addressing challenges with working memory that includes ideas on how to recognize working memory issues and types of memory aids to use.
Students with dyslexia often struggle with fluency with math facts. This struggle can impede learning of math concepts and skills because use of math facts is necessary for solving most types of math problems. The Institute of Education Sciences (Gersten et al. 2009) recommends regular short (10-minute) practice sessions with number facts for students struggling with math. Powell et al. (2011) found success with specific types of interventions for students with math difficulties who are struggling with recall and use of math facts (which they call “fluency with number combinations”). Their research showed success for students receiving explicit instruction on counting strategies coupled with regular practice with these strategies. Practice sessions lasting only a few minutes were as effective as well-designed 30-minute sessions. Counting-strategy instruction embedded within tutoring on word problems also proved highly effective.
Another effective intervention recommended on the Yale Center for Dyslexia and Creativity website (n.d.), shared by Chris Woodin, is using domino-type number displays to help students with subitizing. Subitizing is the ability to recognize quantities visually without counting the number of objects seen. For example, when we see a five pattern on a die, we instantly recognize there are five dots. Subitizing is an important mental building block for developing number sense in young children. It is also an area of struggle for students with dyslexia. In the images below, notice how patterns are used to make quantities easy to identify without counting.
Woodin explains that students learn to identify quantities in relation to “gestalts” of five and ten. Students can see the voids missing from five and ten and/or easily add on from five. Woodin’s use of graphic organizers such as these has helped students develop cardinality with numbers from one to ten (cardinality refers to the actual count of how many items are in a set).
Cheesman (2014) recommends several math apps that assist students with strengthening basic math skills, including the skill of subitizing. Her list of apps is shared in an “App Chat” on the International Dyslexia Association website. The recommendations avoid “programs/apps that require extensive reading, include in-app purchases, or contain distracting images and/or audio that may disrupt the primary task.”
Miles (2004) describes several aspects of mathematical writing and oral language that pose challenges for students with dyslexia:
Below is a chart of examples of types of vocabulary challenges in math (Ballard 2015, p. 51):
Miles (p. 55) also discusses the syntax of math sentences, describing them as “often tortuous and condensed.” She provides the following example:
‘The perimeter of a rectangular piece of paper is 4.8 cm.’
Brief and to the point? However, the first thing that we need to pick out is that it is a rectangular piece of paper; only then is the word ‘perimeter’ meaningful. Yet the word ‘rectangular’ is buried in the middle of the sentence.
The symbolic language of mathematics provides many challenges as well. Miles describes three key areas of confusion: Arabic numerals, algebraic symbols and sentences, and symbols other than numerals and variables. Given that each of these can present challenges and that mathematical sentences and problems typically involve all three mixed together, the level of challenge for students with dyslexia can be enormous.
Several other techniques have been suggested to help with reading and writing in mathematics (Chinn 2018; Gersten et al. 2009; Miles and Miles 2004; Dyslexia Help, University of Michigan 2020; Zecher 2017; Zwiers et al. 2017):
Students with dyslexia face many challenges in mathematics because math itself as well as the processes for learning math are language dependent. Students must continually read and write words, numbers, and symbols, each challenging on their own and extremely challenging when mixed together. Difficulty with skills such as subitizing can inhibit development of early numeracy. Limitations with working memory make it difficult to follow sequences of oral directions and solve multistep problems. Altogether, these challenges can be overwhelming. However, there are many techniques teachers can use to assist students with dyslexia and other math difficulties so that students can overcome these challenges and thrive in mathematics.
Ballard, D. D. 2015. Mathematical discourse, writing, reading, and vocabulary: Participant resource guide. Oakland, CA: Consortium on Reaching Excellence in Education.
Berch, D. B. 2011. Working memory limitations in mathematics learning: Their development, assessment, and remediation. Perspectives on Language and Literacy 37(2), 21–25. Retrieved from https://app.box.com/s/kw80f1h5rzk30lls5k6jk6dx9eaw7ads.
Cheesman, E. 2014. Dr. Cheesman’s app chat: Games to boost math skills. International Dyslexia Association. Retrieved from https://dyslexiaida.org/games-to-boost-math-skills/.
Chinn, S. 2018. Maths learning difficulties, dyslexia and dyscalculia (2nd ed.). London, England: Jessica Kingsley Publishers.
DyslexiaHelp, University of Michigan. n.d. Dyslexia and mathematics. Retrieved from http://dyslexiahelp.umich.edu/professionals/dyslexia-school/mathematics.
Gersten, R., S. Beckmann, B. Clarke, A. Foegen, L. Marsh, J. R. Star, and B. Witzel. 2009. Assisting students struggling with mathematics: Response to intervention (RtI) for elementary and middle schools (NCEE 2009-4060 ed.). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/PracticeGuides/.
International Dyslexia Association. 2002. Definition of dyslexia. Retrieved from https://dyslexiaida.org/definition-of-dyslexia/.
Lyon, G. R., S. E. Shaywitz, and B. A. Shaywitz. 2002. A definition of dyslexia. Annals of Dyslexia 53, 1–14.
Miles, T. R., and E. Miles, eds. 2004. Dyslexia and mathematics (2nd ed.). New York, NY: Routledge, 54–64.
Powell, S. R., L. S. Fuchs, and D. Fuchs. 2011. Number combinations remediation for students with mathematics difficulty. Perspectives on Language and Literacy 37(2), 11–16. Retrieved from https://app.box.com/s/kw80f1h5rzk30lls5k6jk6dx9eaw7ads.
Yale Center for Dyslexia and Creativity. n.d. Math: Counting & comparing. Retrieved from http://dyslexia.yale.edu/resources/educators/instruction/math-counting-comparing.
Zecher, M. 2017. Math Strategies for Students with Dyslexia. In International Dyslexia Association. Retrieved from https://dyslexiaida.org/multisensory-math/.
Zwiers, J., J. Dieckmann, S. Rutherford-Quach, V. Daro, R. Skarin, S. Weiss, and J. Malamut. 2017. Principles for the design of mathematics curricula: Promoting language and content development. Retrieved from https://ell.stanford.edu/sites/default/files/u6232/ULSCALE_ToA_Principles_MLRs__Final_v2.0_030217.pdf.
Issue 18 | Fall 2020
Jan. 27 | 4-5 p.m. ET
With Dr. David Chard, Dean ad interim and Professor, Boston University Wheelock College of Education and Human Development