Daniel Ansari, a professor of psychology and education at Western University in Ontario, says a "science of math" exists and mirrors efforts in reading research, but with important differences. The science of math draws from psychology, educational research, and cognitive neuroscience to inform teaching and assessment.
Ansari notes that both reading and math are cumulative fields where early skills predict later performance. A child who cannot link letters to sounds will struggle to read. Similarly, a child who does not understand how Arabic numerals represent quantities will struggle with calculation. However, reading has a clearer learning sequence than math. In reading, children learn sounds, map them to letters, decode, and recognize words. Math lacks such a straightforward path because it is multifaceted, with different sequences for algebra and geometry, and involves both procedural knowledge, like knowing how to add, and conceptual knowledge, like understanding that addition and subtraction are inverse operations.
On computation fluency in grades K-3, Ansari says most experts agree fluency matters, but they disagree on how to achieve it. Traditionalists emphasize the standard algorithm, while progressives argue children should learn multiple strategies and develop conceptual understanding. Ansari advocates thinking about math instruction developmentally, treating young learners as novices on a path to expertise.
For building math fact mastery, Ansari says students need to first understand arithmetic operations through grasping how numerical symbols represent quantities. They then need repeated practice solving problems, often using fingers initially. Once accuracy is high, timed activities help consolidate facts into long-term memory.
On whether math is innate or learned, Ansari states there is a genetic contribution to math ability, but "all learners are capable of learning the math they need to function in their lives."
Ansari points to Lynn Fuchs at Vanderbilt as foundational to the field. Fuchs contributed to multitiered systems of support (MTSS) used in math and reading instruction and led a 2021 Institute of Education Sciences report on helping students struggling with math. David Purpura at Purdue studied the importance of children understanding numerical symbols. Ansari recommends Stanislas Dehaene's book "The Number Sense" as a broad introduction.
Ansari observes that math education conferences feature predominantly qualitative work, while cognitive researchers use primarily empirical methods, with little cross-talk between the two approaches. He advises that the science of math should help teachers and school leaders become more effective, but teachers must determine what this means in their specific schools.