Interview with Brian Butterworth
Photo courtesy of Stacey Bostrom Photography
Brian Butterworth is Emeritus Professor of Cognitive Neuropsychology at the Institute of Cognitive Neuroscience at University College London, UK, and my favorite dyscalculia researcher, scientist, and author.
Professor Butterworth’s dyscalculia research and work towards growing dyscalculia awareness has been immensely influential in my own understanding and education on this little-known learning disability.
Over the past several years Prof. Butterworth has graciously answered many of my questions, sent me research papers to read, and shared new resources with me and the Discovering Dyscalculia community. It was a great pleasure to finally meet with him in-person in London last year.
The second edition of his book, Dyscalculia: From Science to Education was recently published and I reached out him with some questions about this second edition. Below are his responses and thoughts about our current global situation surrounding dyscalculia research and awareness.
Dyscalculia: From Science to Education
Questions and Answers with Brian Butterworth about the 2nd edition of his book.
L. Jackson:
In the first edition of Dyscalculia: From Science to Education, you wrote about filling the gap between personal stories, teaching guides, and the science of dyscalculia. Can you say more about this gap and why you felt it important to connect these through your book?
B. BUTTERWORTH:
There are many books, courses and anecdotes by special needs teachers, psychologists, and sufferers that illuminate what it’s like to be a dyscalculic learner. These stories are valuable, and you’ll find them in my book. However, they can’t get to the root of the difficulty, and they are not designed to. Similarly, there are stories of practices that work for this or that learner, but the question is will it work for other learners? To get from personal stories to practices – assessments and interventions – that will work for most dyscalculic learners, properly designed scientific studies are needed. What I try to do in this book is show how the science is relevant to practice.
Unfortunately, many recommendations for assessment and intervention, including from official bodies, are not based on the science. This means that they have limited applicability. Following the recommendations that work for Johnny may not work for Jimmy.
However, there is no question that the insights of skilled and reflective practitioners can inform the science. In my own case, my science was informed by Dorian Yeo, and an exceptional teacher of dyscalculics, and by Diana Laurillard, a pioneer in the theory and practice of pedagogy.
There are innumerable (sorry for the pun) maths games available online that enable learners to practice concepts they already know. But the problem for dyscalculics, as Dorian pointed out, is that they don’t have these concepts, critically the relationship between sets and numerical symbols, and how operations on sets relate to arithmetical operations. So what is the best way to help them understand this? Here, having the right pedagogy is critical. Simple repetition with multiple choice answers doesn’t work. So what I recommend is Laurillard’s ‘constructionist’ approach, which incidentally mirrors neuroscience’s ‘prediction-error’ learning. The learner has a goal, chooses an action to achieve that goal, sees the effect of the action, and if it doesn’t achieve the goal, recalibrates the action to get closer to the goal. This is approach Dorian used in Dyscalculia Guidance with beads, number tracks and other concrete materials in carefully described games and activities. In the book, I describe a digital game, NumberBeads, based on this approach, which in several studies seems to work very well for dyscalculics and other early learners.
The really important thing is that any recommended method for assessment or intervention, should be supported by evidence, preferably by properly designed studies. In the book, I present evidence for each recommendation.
Of course, nothing is final in science, and better ideas and better studies will inevitably be produced. And described in a third edition?
L. Jackson:
What compelled you to write a 2nd edition of Dyscalculia: From Science to Education, just several years after its first publication? What is new in this edition?
B. bUTTERWORTH:
Much has changed since the First Edition in published in 2019. There have been significant advances in the science which I describe in the relevant chapters and some changes in the official recognition of dyscalculia. For example, both Scotland and the Republic of Ireland now have official definitions. Where dyscalculia was already embodied in law, for example in Italy’s Law 170 and USA’s federal Individuals with Disabilities Education Act (IDEA), the implementation has become clearer. There is now much more information on websites from official bodies, and other organizations, including those that can link to assessors and tutors. I list these in a new section on Resources. The psychologists’ ‘bibles’– DSM (Diagnostic and Statistical Manual published by the American Psychiatric Association) and ICD (International Classification of Diseases) have revised their criteria, and I have described the relevant changes in Chapter 1.
Chapter 2 on number sense and the ‘number module’ has been updated to show new evidence for an abstract representation of numbers in the brain, along with new evidence on the infant brain’s number processing abilities.
In Chapter 3, I add new sections on the controversial role of fingers in the development of arithmetical competencies. There is an expanded consideration of the role of ‘domain-general’ factors such as reasoning skills, working and long-term memory, language and reading.
There are new tests of number sense and new evidence and new analyses of how core deficits in number sense interact with ‘domain-general’ cognitive and the social factors described in detail in Chapters 4 and 8. These lead to very different dyscalculic profiles, sometimes called ‘heteogeneous presentation’, despite a common core deficit.
I have extensively revised Chapter 5 on the typical development of arithmetical competence in the light of fascinating new evidence.
We now know more about how the dyscalculic brain differs from the typical brain, as I describe in Chapter 6. I also deal with claims that actually the dyscalculic brain in young learners is not systematically different from the typical brain.
Chapter 8 reiterates the original message, that should come as no surprise to any reader, that home, school and society affect a learner’s mathematical competence. But this is not to say that these factors cause dyscalculia, and so it is worth repeating that standardized tests of mathematics which are affected by these factors, don’t identify dyscalculic learners. Specific tests of number sense are needed for that.
I have stuck to the same messages in Chapter 10 on intervention, but I have added impressive new evidence from Singapore on the effectiveness of our NumberBeads game.
L. Jackson:
You write about the virtuous triangle of Recognition, Science, and Policy, needed for societal change around dyscalculia. Has there been any notable movement in these three areas between the writing of the 1st and 2nd edition of your book?
B. BUTTERWORTH:
Recognition: as I note above, there are now official definitions in two more countries since 2019. For practical recognition, teachers and educational psychologists need to be taught about dyscalculia. This rarely happens at the moment.
Policy: Chapter 11 on policy describes some of the main advances in official recognition by the governments of Scotland and the Republic of Ireland. And since the book went to press, there was a debate in the UK Parliament on dyscalculia. I am hoping that something will come of it, such as an official definition.
Science: The best new research reiterates the central theme that an inefficiency in number sense is at the root of dyscalculia. Some of this research comes from non-human animals that also possess number sense which is useful in foraging, mating, exploring, and in combat. We have a new paper which suggests that a single mutation in the genome of zebra fish makes them less good than wild type fish at choosing the larger shoal, a key ability to avoid predation.
L. Jackson:
My experience and observations resonate with your definition of what is at the core of dyscalculia. But many researchers are unable to reach a consensus on how to define and identify dyscalculia. What do you think is getting in the way?
B. BUTTERWORTH:
The main problem is that the core deficit presents in a wide variety of ways that depend on home environment, education, as well as other psychological factors, such as memory, language abilities including reading, and motivation.
All these factors affect mathematical competence, but are not causes of dyscalculia. So the variety of presentations has led some people, usually officials, policy-makers and teachers, rather than scientists, to infer that the variety of presentations means a variety of causes.
L. Jackson:
When you, Jane Emerson, and I met for lunch in London over a year ago, I asked you who was following in your footsteps to carry on this critical dyscalculia research and work. At that point there wasn’t someone specifically at the UCL. Has that changed? Are there other researchers or universities we can be following who are building on from your work and research?
B. BUTTERWORTH:
Since I retired, no-one has taken over the numerical cognition group at UCL’s Institute of Cognitive Neuroscience. Poor succession planning by me. Fortunately, there are other people working more on the educational aspects in the UCL’s Institute of Education though not on the basic science.
However, there is excellent science coming out of Italy, for example, from Marco Zorzi’s lab at the University of Padua, and Manuela Piazza’s lab at the University of Trento. There is also good new science at universities in Belgium, in Louvain and Leuven. Daniel Ansari at Western University in Canada has done pioneering work on the brains of dyscalculics, as I note in the book.
L. Jackson:
As a parent focused mainly on the “Recognition” section of the virtuous dyscalculia triangle, I work with three main groups: Parents, Educators, and Dyscalculic Adults. What is one piece of advice you would give to each of these groups, perhaps one thing they can do to help grow dyscalculia awareness?
B. BUTTERWORTH:
Parents: if your child is having difficulty with basic arithmetic, I would advise proper screening for dyscalculia by a competent qualified person. Just being bad at arithmetic is a symptom of dyscalculia, but it is also a symptom of many other causes. Maybe the student doesn’t like the teacher; if the lesson is first thing in the morning, the student could be tired or hungry; and so on. So it important to eliminate other possible reasons so as to get the appropriate support. If dyscalculia is officially recognised, then an assessment could lead to appropriate support and accommodations in, for example, timed exams.
Educators: dyscalculia is not usually part of teacher training. Where this is the case, teachers should request a CPD (continuing professional development) course in dyscalculia.
Adults: if an adult has always had difficulty with simple arithmetic or numbers more generally, they should seek professional help. However, this is rarely available since there aren’t tests standardized for adults at the moment, and there is little training for educators to support adult dyscalculics. The materials for young learners may not be suitable for adults. In my experience, just being recognised as dyscalculic rather than stupid, usually helps adults by reducing stress, and feelings of low self-worth.
Get a copy of Brian Butterworth’s second edition of Dyscalculia: From Science to Education at your local or online bookstore. This book was published by Routledge originally in 2018, 2nd edition in 2025. Other books by Butterworth include, Can Fish Count?, The Mathematical Brain, and Dyscalculia Guidance (co-authored with Dorian Yeo).