Why some people are good at math while others struggle

Dr. Daniel Hajovsky, associate professor in the Department of Educational Psychology at Texas A&M University, studies human intelligence and the cognitive processes that affect learning. In a study published in the Journal of Intelligence, Hajovsky and his co-authors examined the relationship between cognitive abilities and mathematics skills. The findings point to fluid reasoning and comprehension knowledge as two of the most consistent cognitive predictors of math skills.

To better understand which processes are most closely tied to math ability, the researchers compared findings across a broad range of cognitive and academic assessments.

In psychology, a test battery is a set of tests that measures cognitive or behavioral abilities. For example, the Wechsler cognitive test is one test battery commonly used to evaluate children’s intellectual abilities. Hajovsky said the research is unique because it brings together 122 distinct test batteries in a single analysis, allowing researchers to examine relationships between a wide range of cognitive abilities and math skills, including math knowledge, calculation, problem solving and fluency.

The researchers found one cognitive skill that strongly influences math skills is comprehension knowledge, which represents language, vocabulary and the ability to engage in verbal reasoning, Hajovsky said.

“If someone wants to go to law school, they’ll take the law school admission test. Part of that test requires strong reading comprehension skills and bringing in your own background knowledge or schemas of understanding to make sense of the new information you’re learning. That’s comprehension knowledge,” he said. “It’s important for reading, it’s important for writing and we see now it’s important for mathematics.”

The second key cognitive skill is fluid reasoning, or the ability to engage in deductive or inductive reasoning.

“The example I like to use to explain fluid reasoning is, ‘How well can a student learn a game when there are no prior rules or background knowledge required for it?’” Hajovsky said. “When you’re reasoning internally, you’re still using verbal knowledge and information, but fluid reasoning helps you figure out which information is relevant and what’s irrelevant.”

But being good at math isn’t simply a matter of having strong general cognitive abilities. Foundational math skills mattered, too.

“We found in our study that number sense, which is this general understanding of math and how numbers are related to each other, was just as important and a strong foundation for later math skills,” he said. “Cognitive abilities are important for learning and academic outcomes, but it’s not what fully makes up someone’s math ability.”

Hajovsky said these skills develop constantly, both inside and outside the math classroom, and can continue to be developed through time and effort.

“One of the most robust, consistent findings within psychology is something called the positive manifold. Performance on one mental task is positively correlated on a different mental task,” he said. “For example, how well someone can manipulate visual puzzles and mentally turn them is positively correlated with someone’s vocabulary development. They’re both tapping into this mental engine that drives performance on these unique cognitive tasks.”

Because math classes constantly build on previous topics, early intervention is crucial to avoid ongoing struggles. By understanding which skills support classroom success, Hajovsky said he wants to promote new screening approaches that provide targeted support.

“Instead of looking at a student’s scores, we can pay attention to the pattern of errors they make so we can pinpoint where the greatest learning needs exist,” he said. “In other words, using error analysis to distinguish if math challenges stem from conceptual difficulties like language, reasoning or efficiency issues and adjusting instruction accordingly. This strategy could be helpful in improving math outcomes for all students.”