Beyond Jumbled Letters: How Dyslexia Affects Learning Mathematics
Emma Koolpe
Illustrations by: Mara Russell
When I was in third grade, my math teacher introduced the concept of the dreaded word problem: “Each watermelon costs $2 and you have $10. How many watermelons can you buy?” This simple two-sentence problem took the concept of division and added words into the mix, which frustrated me greatly. I remember asking my teacher, “When would I ever need to know how many watermelons I need to buy? And, why would I ever need more than one? I like watermelon, but not THAT much.” I took these problems home to my parents, who would spend countless hours trying to explain the process to me. My parents and I had no idea why I was experiencing such difficulty in solving word problems; I seemed to excel at all other concepts of math, but a gap persisted when it came to translating written language into equations. It wasn’t until the seventh grade that we understood why: dyslexia.
Dyslexia is a learning disorder that affects one’s ability to identify speech sounds. A majority of the research and discussion regarding this phenomenon has focused on differences in reading and language-based tasks. For instance, functional MRIs (fMRIs) demonstrate that dyslexic and non-dyslexic people utilize different parts of the brain when reading. However, dyslexia does not just stop at language learning issues. Dyslexic and non-dyslexic brains also use different neurological processes to learn and understand math.
As the utilization of fMRIs has become more common and prolific, further studies have focused on identifying and understanding the differences between the mechanics of dyslexic versus non-dyslexic brains. Functional MRIs measure brain activity related to blood flow. When an area of the brain is in use, increased blood flow is shown by the fMRI [1]. As more oxygen is needed in active portions of the brain, the oxygenated blood in the area alters the local magnetic field and results in a change in signal that is detected by the machine [1]. Functional MRIs have shown that the main cortical regions involved in reading are the language-dominant left hemisphere: the inferior frontal gyrus, the superior temporal gyrus, and the medial temporal gyrus [2]. The inferior frontal gyrus is part of the frontal lobe and is used for complex thinking, processing speech, and language. The superior temporal gyrus is used in processing audible sounds, making it a major area involved in language comprehension, or, for example, when you put the sounds “th” and “at” together and get the word “that.” Finally, the medial temporal gyrus is used for memory processing and visual perception. Think of “sight words” (the, he, at, etc). When you are in kindergarten and early grade school, you learn the shapes of words, so you don’t need to read each sound separately. The more a child reads, the greater this bank of sight recognized words grows. When you go to read a word that you have seen before, the medial temporal gyrus activates and remembers the word, so you don’t have to start from the beginning and re-sound it out [2]. When all of these areas of the brain are activated together, a good reader can have phonological awareness (the ability to manipulate sounds and recognize the structure of words), rapid automatic naming (the speed to name familiar things out loud), and reading fluency (the ability to read words and connect the text with speed and accuracy to support comprehension). Functional MRI imaging of a non-dyslexic reader who is actively reading will show activity in these portions of the brain [2].
In dyslexic readers, activation of these cortical areas is decreased. Studies have shown that dyslexics struggle with phonological awareness due to low activation in the superior temporal gyrus, creating difficulties with access to and the manipulation of sounds. Dyslexic children show a reduction in superior temporal gyrus (used for comprehension of language) activation when they are given an auditory phonological awareness test and they display no activation in the temporal lobe [2, 3]. Also, due to both underdeveloped language centers and struggles with using the left hemisphere of the brain, dyslexics tend to compensate via increased activity in the right hemisphere. In contrast to non-dyslexics, dyslexics activate the right inferior occipital gyrus in a separate area of the right hemisphere when trying to read [4]. This part of the brain is mostly used for visual processing of faces [11]. When dyslexics read less efficiently with the right hemisphere, it has been shown that tutoring can help provide the tools dyslexics need to strengthen their foundations in reading comprehension. Tutoring can train dyslexics to use the left hemisphere of their brains for reading, as well as reduce reliance on their right hemisphere.
A common myth about dyslexia is that it is purely a reading disability. However, the frontal and temporal lobes are also vital to processing mathematics [3]. Math is an abstract subject, and it is taught to children beginning at a very young age. Dyslexics may struggle to convert words into mathematical symbols, like knowing that “three”, 3, 1+1+1, and 2+1 all represent the same number [5]. Both long-term and short-term memory are needed for learning and understanding math. In the long term, numerous concepts in math build upon each other and are used to perform more difficult computations [5]. For instance, if a student is given a problem of 2x=4, they will need to access the concept of division in their long-term memory to “undo” the 2x multiplication to solve for x. In the short term, memory is used to process a question, hold it in the mind, and follow a procedure to reach an answer [5]. Solving 2x-1=3 requires following more steps, as well as remembering the goal of the problem: solving for x. If a dyslexic student realizes that, when they add one to each side of the equation, they get 2x on the left and 4 on the right, they may forget the initial conditions and can have difficulty recalling what should follow in the process to achieve the answer.
The areas of the brain needed for reading comprehension are not only used for word processing, but also for memory storage and abstract understanding. In particular, the medial and superior temporal gyri have both been linked to memory processing, with the medial gyri used for long term memory storage and the superior gyri used for short term memory [6]. Because dyslexics have diminished neural activation in these areas, they also experience some difficulty in learning mathematics. This is often seen in dyslexics struggling to remember mathematical facts when attempting computations [5]. When dyslexics have challenges forming and recalling long-term memories, they have difficulty learning math facts by heart and remembering calculation procedures, even if they have mastered them. This demonstrates why dyslexic students tend to fail at generalizing knowledge throughout a subject: they are unable to make connections between concepts that will benefit them as the subject matter becomes more difficult. However, although dyslexics have difficulty accessing these facts due to poor long-term memory, they can compensate with strong problem-solving skills.
Poor long-term memory also contributes to difficulties in working memory. For example, envision a task where one has to do a series of steps in chronological order, such as doing laundry or calculating the tip on a restaurant bill. When conducting one of these tasks, one must remember each step to take in order to successfully complete it (e.g. putting the laundry in the washer, putting the detergent in, and turning it on). After repeating the process several times, one no longer needs to actively remember each task, as the process is now stored in the working memory. Those with poor working memory, such as dyslexics, have trouble storing and recalling simple steps. This is evident in mental and oral calculations. Because math facts are not easily memorized, more mental strain is required for simple calculations [5]. For instance, instead of immediately knowing that 12+5=17 because 2+5=7, a dyslexic person has difficulty breaking these numbers up into the smaller components and will instead count on their fingers or rely on a calculator to reach an answer. This slows down the process, leading to inefficient calculations [5]. Poor long-term memory also makes it more difficult to remember previous calculations, so when a new problem is presented, the entire process needs to be repeated [5]. For example, if the first problem required one to compute 5*8, a dyslexic person pauses and struggles to remember that the answer is 40. Now, when working on the third or fourth question, if the same computation is needed, a dyslexic person would not remember that they have previously calculated 5*8 in the first question and go through the entire process again. This is similar to when dyslexics read. If someone with dyslexia comes across an unknown word at the top of a page, it is mentally “sounded out.” If the reader then comes to the same word again, the whole process of sounding out the word is repeated.
As stated previously, dyslexia is a language disability. When learning a new language, whether it be Spanish, French, or in this case, mathematics, dyslexics have difficulties comprehending the new syntax [5]. This is because the cortical regions originally used for comprehending language are also not activated when a dyslexic studies mathematics. Math uses multiple words to convey the same meaning. For example, the words “addition,” “add,” and “sum” all mean the process of calculating the total of two or more numbers. The mathematical language also uses symbols (numbers) and words within the same sentences (word problems), and oscillating between numbers and words within a word problem can be extremely difficult for a dyslexic brain[5]. Take the word problem, “Joey is 37 and Karen is 12 years older than Joey. How old is Karen?” For a non-dyslexic, it is natural to understand that one would add 12 to 37 (37+12) to get 49. However, dyslexics have difficulty making this connection. For one, it is already difficult to read words, and adding the abstract component of symbolic numbers makes the task of solving this problem much more difficult. If this word problem were presented visually, the connection between the words to computation might be easier for a dyslexic to understand.
The final challenge dyslexics face in learning math is trouble with directional understanding, which is due to decreased activation in the superior temporal gyrus [2, 5]. The superior temporal gyrus decodes information in the brain. When information is decoded incorrectly, the output will also be inaccurate (Hudson, 2020). This is equivalent to comprehending language in the wrong order or writing things incorrectly, like 32 as 23. As one progresses in the mathematics discipline, computations change from a simple left to right calculation (2+3=5) to more complicated ones, such as 3+(5*3). To compute this example using the order of operations, one would begin with the multiplication inside the parentheses, 5*3=15, and then add 3 to that answer for 3+15=18. In this way, the first step is starting with the right and the second is starting from the left. If one were to calculate this example purely from left to right, they would get a completely different answer (3+5=8*3=24). This can become very confusing for non-dyslexics— let alone dyslexics— who have difficulty with directional analysis.
To help dyslexic students learn math, the way math is taught needs to be adapted. There are several methods teachers and researchers have discussed for teaching dyslexic children math. While every dyslexic is different, and practices and technologies are constantly evolving, helpful methods of teaching math to dyslexics exist. School systems tend to standardize their reading curriculum but vary in their instruction of math. Reading is taught through sub-skills that are learned and evaluated. In this way, a student’s strengths and weaknesses are shown frequently;therefore, an alternative teaching method can be introduced to help them. Teaching math the same way as language would help non-dyslexics and dyslexics alike. However, when math is taught, it is evaluated based on a level of achievement of doing harder and harder problems. After 2+2=4 is learned, the concept of 4-2=2 is taught. However, if a student does not understand why one can add or subtract numbers and simply memorize these facts, when faced with a more difficult problem like 24-22, they would not know how to solve it. If a child has “bad” handwriting or is a “bad” speller, they are not necessarily considered a “bad” writer, whereas students who do not understand a mathematical concept are often labeled “bad” at math. Breaking down math sub-skills, teaching students physically (using objects to show addition) and audibly naming steps in a calculation all help organize simple mathematics to build a foundation to complete harder problems.
Dyslexic students are auditory and visual learners, so demonstrating step-by-step computations, as well as having a dyslexic student explain these steps in their own words, is helpful for solidifying understanding of concepts. There are two distinct math learning styles for dyslexic and non-dyslexic learners: grasshopper style and inchworm style [10]. Grasshoppers are good at intuitive thinking and are able to visualize questions, but they struggle with the ability to follow procedures. Inchworms are very organized and good at working step by step, but they have limitations in visual and spatial reasoning, as well as difficulty forming an overview of problems [7]. To master math, one needs to move easily between these two styles of learning. This is where dyslexic learners struggle, as they tend to use only one of these thinking methods when understanding and performing computations [10]. When a learner is only using the inchworm style, they tend to focus on parts of the problem, isolating each step as it is presented in their minds. Grasshoppers, on the other hand, will estimate answers and “hop” to the end of the problem without fully computing the answer [10]. Whether you are a grasshopper or an inchworm, you are equipped with distinct strengths to compute and understand math. To be a good mathematician, one needs to be organized and able to visualize the process of a problem. Since most dyslexics struggle with using both of these methods at once, they are either very strong in algebraic analysis (inchworms), or mental arithmetic (grasshoppers) [10]. Those who favor the inchworm method should be encouraged to attempt to see an overview of the problem before solving it, whereas those who are grasshoppers should be motivated to write out their computational steps to find a solution.
Despite differences in learning styles, the gift of dyslexia is the ability to think differently. Dyslexics have excelled in making connections between different fields due to unusual combinations of ideas, compared to non-dyslexics [7]. Albert Einstein, a famous dyslexic mathematician and theoretical physicist, made connections in the world that others could not see. Einstein credited his discovery of the theory of relativity to conducting a thought experiment, where he saw himself riding a streetcar traveling at the speed of light. Although dyslexia is defined as a learning disability, I view it as an advantage. Dyslexics make connections and view the world differently than everyone else. Despite the different ways that my brain works, my love of math has carried from the days of struggling with word problems to the Symbolic Dynamical Equations course that I am taking this semester. I am not sure where my math major will take me after graduation, but I will inchworm and grasshopper my way in the real world to find out.
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