The science of reading boom has created a groundswell of interest in whether there’s an analog for math. One of the more interesting thinkers on this count is Daniel Ansari, a professor of psychology and education at Western University in Ontario, where he directs the Numerical Cognition Laboratory. Daniel’s research focuses on how children develop mathematical and numerical skills, and he thinks there’s a lot of popular confusion regarding the “science of math.” I reached out to hear what he thinks we’re getting right and wrong. Here’s what he had to say.
—Rick
Rick: You study how young children learn math. How’d you get into that?
Daniel: It happened rather accidentally. When applying to Ph.D. programs in psychology, I came across a position that involved investigating the numerical abilities of children with Williams syndrome, a rare genetic developmental disorder. The relationship between the two sounded interesting, so I applied and was accepted.
Rick: There’s been much recent attention to the science of reading. Is there an analogous science of math?
Daniel: Yes, there is. Like the science of reading, the science of math is an effort to bring what we are learning from psychology, educational research, and cognitive neuroscience to bear on the way we teach and assess children. There is a lot of research on how children learn about numbers and math. But in my experience, too little of it reaches teacher training and professional development. Both the science of reading and the science of math are subfields under the broader umbrella of the science of learning. Certain principles—like the value of explicit instruction for novice learners and early universal screening—apply in both reading and math. But the analogy is not perfect. The learning sequence for reading is much clearer than for math.
Rick: You’ve mentioned that literacy and numeracy share some of the same building blocks. What do you have in mind?
Daniel: Think of it like the foundation of a house: A crack will compromise everything on top. The same is true in reading and math. Both are highly cumulative, and early skills strongly predict later ones. If you cannot link letters to sounds, you will struggle to become a fluent reader. Similarly, if you don’t understand how Arabic numerals represent quantities, you will struggle to acquire calculation skills.
Rick: You’ve noted that the science of reading is more straightforward than the science of math. Why is that?
Daniel: In reading, there’s a relatively well-established sequence. Children learn the sounds in our language, are taught to map them onto letters, begin decoding, and gradually learn to recognize words. Math lacks such a straightforward sequence. It is multifaceted, and the learning sequence for algebra differs from geometry. Moreover, some math knowledge is procedural, like knowing how to add, and some is conceptual, like understanding that addition and subtraction are inverse operations. The two are clearly related, but we don’t quite know which comes first or whether they develop together.
Rick: How important is it that students build fluency in computation in grades K-3?
Daniel: Most agree that fluency matters, but there are different views on how to get there. Traditionalists tend to emphasize teaching the standard algorithm, while progressives usually argue that children should be taught multiple strategies and develop their own conceptual understanding. My take is that we should think about math instruction developmentally.
Rick: OK, so what’s it mean to think about math instruction developmentally?
Daniel: It means acknowledging that young learners, as the psychologist Paul Kirschner and his colleagues argued in their famous paper, are novices on a trajectory to becoming experts. In practice, that insight should dictate the instructional approach. Take learning math facts. You wouldn’t start with speed drills. Or, for another example, consider instructional materials. Young children are easily distracted because their executive functions are still developing, so you’d choose materials that focus their attention on number rather than color or shape. Kirschner also argued that minimally guided instructional approaches—like discovery learning and problem-based instruction—are less effective for most novices because those students don’t yet have enough knowledge stored in memory, so they need external guidance.
Rick: You’ve said it’s clear that mastery of math facts frees up working memory but that it’s not clear how best to build that mastery. What’s this mean for memorization and explicit instruction?
Daniel: Building mastery begins with helping students understand arithmetic operations, and that depends on having a solid grasp of how numerical symbols represent quantities. From there, students need repeated practice solving problems. At first, they’ll use their fingers, especially for addition and subtraction. Once they’ve reached a high level of accuracy, timed activities help them consolidate their math facts into long-term memory, so they can retrieve them later when solving more advanced problems.
Rick: OK, so is math an innate talent or a learned skill?
Daniel: As with nearly all human traits, there is a genetic contribution to math ability. But I think all learners are capable of learning the math they need to function in their lives.
Rick: It can seem like the push for a science of math is a recent development. Is that fair?
Daniel: Perhaps the particular name is a recent development, but it builds on decades of empirical research on how children learn math.
Rick: Are there any foundational studies that readers should know?
Daniel: The work of the late Lynn Fuchs, who was an educational psychologist at Vanderbilt, is absolutely foundational. She contributed heavily to the development of multitiered systems of support (MTSS), which are used in both math and reading instruction. She also led a very influential 2021 report for the Institute of Education Sciences on how to assist students struggling with math. Another example would be Purdue University psychologist David Purpura’s study showing the importance of children’s understanding of numerical symbols. Finally, for a broad introduction, I recommend Stanislas Dehaene’s book, The Number Sense.
Rick: Some have suggested math education has split between those who embrace empirical methods and those with a more qualitative take. Is that your experience?
Daniel: Yes. At most of the math education conferences I’ve attended, you predominantly see qualitative work, while those of us studying the cognitive underpinnings of math use primarily empirical methods. There’s not much cross-talk, but there should be. The split seems to reflect a broader division in education research between those who see quantitative research as the primary route to practical applications and those who are more skeptical of it.
Rick: If you’ve one piece of advice when it comes to the science of math, what is it?
Daniel: The science of math is meant to help teachers and school leaders become more effective at educating students. Researchers can tell you what tends to work. But teachers are the only ones who can figure out what that means in your school.
This conversation has been edited for length and clarity.
The opinions expressed in Rick Hess Straight Up are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.