Terminology
Experts in the field of mathematics (or maths) education in the UK have been using the term "dyscalculia" for decades. In the U.S., we've begun using the word to describe math learning disabilities relatively recently, although all the terms and acronyms are synonyms - MD (math disability), MLD (math learning disability), SLD (specific learning disability) in math, and dyscalculia. When I began tutoring students with math learning challenges as a former Montessori elementary teacher, I had a firm foundation in what Montessori calls "sensorial" learning - also described as hands-on, tactile, or multi-sensory. We used a variety of Montessori-specific materials: bead bars and chains to teach multiples and squares/cubes of numbers, abacus-inspired bead frames for addition, subtraction and multiplication, arrays for multi-digit multiplication, binomials and trinomials, fraction insets for teaching equivalence and the four operations with fractions, and tiny cubes that represented decimal fractions - all color coded.
I found surprisingly few resources to help me scaffold and supplement the Montessori math approach - or any other instructional approach for that matter, so I began an exhaustive search for techniques to teach students with special needs. This effort uncovered a few gems that helped my neurodivergent students tremendously and greatly improved the quality of my instruction.
Most of these resources come out of the UK from Ronit Bird, Steve Chinn, and Jane Emerson, but not all. Chris Woodin is an MLD expert in the US who has made his work widely available in a curriculum bank on his website and Helmy Faber, who wrote a helpful book called The Math Handbook, is in Singapore. More details about some of these experts to come in this article, but first, let's define and identify MD (math disability), MLD (math learning disability), SLD (specific learning disability) in math, and/or dyscalculia.
Identifying Dyscalculia
Dyscalculia is a learning difference that affects an individual's ability to understand and work with numbers. It impacts everything from school to daily living - calculating tips at restaurants, estimating costs at the grocery store, telling and calculating time. It's estimated that between 3 and 7 percent of people live with dyscalculia.
People with dyscalculia are challenged from the beginning, starting with counting or cardinality, skip counting, and understanding place value. They rely on a ones based way of thinking to solve math problems, and tend to overlook the relationships between math facts. For example, in one of the assessments we use at Mindguide for incoming students, The Dyscalculia Assessment by Jane Emerson and Patricia Babtie, students are asked to solve simple addition problems requiring doubling. Most dyscalculic students will start counting from one and progress forward to find the sum of, let's say, 6+6. When asked for the sum of 6+7 immediately afterward, they will again start counting from one, rather than reasoning that 7 is one more than 6, so 6+7 must be one more than 6+6.
Students with dyscalculia may not make a connection between a numeral, like 2, and the quantity it represents, like two apples, or understand that four apples are double two apples. Because of the ones based way of thinking, it's difficult to skip count (by 2s or 5s, for example), understand place value, or find the position of a number on a number line. Some individuals with dyscalculia may have trouble with spatial reasoning and understanding spatial relationships, measuring, or reading charts and graphs. Here is an expert reviewed list of signs from Understood.org.
Because a strong sense of numeracy or number sense remains undeveloped in the early years, when computation is expected of these students, they don't understand the rules. Math fact recall is slow and frustrating. Subtraction, along with counting backward, is difficult and multiplication and division facts remain elusive. These difficulties persist with every passing year, creating anxiety and damaging self-esteem, unless research based intervention is provided. Dr. Sheldon Horowitz from the National Center for Learning Disabilities talks about the different elements of dyscalculia here.
Experts and Resources
In my search, I found Ronit Bird, author of The Dyscalculia Toolkit, Overcoming Dyscalculia & Difficulties with Number, and The Dyscalculia Resource Book, all of which inform our teaching practice at Mindguide. They are practical manuals of teaching activities and games aimed at teachers and parents of dyscalculic students. Listen to Ronit's explanation of the signs of Dyscalculia here and watch some video demonstrations of the games she developed on her Youtube channel.
Christopher Woodin, Ed.M., is a specialist in the fields of mathematics and learning disabilities who has been with the Landmark School in Beverly, MA since 1986. He has developed a curriculum bank which he makes available on his website for free. This was an invaluable resource for me in my growth as an interventionist. From "Decoding Drake's Dream" in Harvard Graduate School of Education magazine: " Woodin calls this method whole-to-part learning because the emphasis is on understanding the relationship between the question and the answer rather than on being right or wrong — a notion that flips traditional classroom dynamics on their heads." The idea that math is either 100% right or 100% wrong is one of several math myths I unpack in my course about ending math anxiety. If you're interested in learning more about math anxiety - which is different from dyscalculia, sign up here.
Since I was in the world of dyslexia remediation, I came across Marilyn Zecher, M.A., CALT, who started off as a language tutor and created math training with similar apparatus (beads on strings rather than bars, fraction sets, base ten materials) for students with dyslexia with a special focus on the multi-sensory aspects of dyslexia remediation and the importance of language in teaching math. She expounds on her particular contributions in this interview with the Pennsylvania Training and Technical Assistance Network (PaTTAN).
Examples of Intervention
What can be done to help? Students with dyscalculia won't discover math rules through exploration, they need explicit instruction that highlights and explains concepts clearly and directly. Complex ideas need to be broken down into smaller, more manageable steps. Each learner is different, and will ideally have an individualized learning plan tailored to their specific needs. Repetition is key, and the practice of interleaving concepts - practicing several math concepts repeatedly within a lesson rather than focusing on one concept at length - helps ASthem retain previously learned ideas.
As outlined by all the experts above, students with dyscalculia benefit from a multisensory approach using sight, touch, and movement to help them retain mathematical concepts. Concrete manipulatives like base ten materials, counters, fraction sets, and beads on a string/bead bar all make abstract concepts more tangible. In this video, my student uses beads to find the next ten when counting by sevens. She finds thirty five, then moves five more beads over, and sees the remaining two, to arrive at 42, continuing to 70.
This doesn't necessarily teach the multiplication facts, but does help students associate numbers with their factors, and this particular exercise reinforces finding the components of ten while crossing through the next ten: 35 + 7 = 35+5 = 40+2 = 42. This is one of several ways to use bead strings in a linear fashion, as opposed to arranging bead bars in an array. Thanks to Marilyn Zecher, M.A., CALT for putting loose beads on a string, rather than having them bound tightly in bars (as in Montessori) or in shorter rows as on an abacus.
This is one small example out of thousands of individual lessons that offer the kind of instruction these neurodivergent learners need. This kind of instruction can extend all the way through Algebra. Beyond concrete tools, visual aids like diagrams, charts, graphs and students' own drawings help them organize and understand mathematical processes. Ideally,algorithms and rules are introduced after concepts are practiced using concrete materials and visuals - although there is often a fluid back and forth for reinforcement and practice.
There is hope.
Living with dyscalculia can be agonizing for both children and adults. Parents and teachers can support their unique learners by understanding their specific challenges and using a method that starts with concrete tools, progresses to representational images, and then connects abstract thinking in signs and symbols (aka the CRA method). It will take time. It will take patience, creativity and compassion. And most importantly, it can help a wounded learner develop a deep sense of confidence and competence in their mathematical abilities. If you are searching for answers, traditional methods are failing your child, and your child needs support, reach out to me for a free consultation by filling out the form on the Mindguide website.