Brain Science Tells Why Some People Excel in Math (and some don’t)

The Hippocampus has The Knowledge — image by Gemini

Is it true that “everyone can learn math to the highest levels?” If so, why do so many adult learners struggle in college algebra class? If not, why not, and what can we do about it?

A few years back, Dr. Jo Boaler of Stanford University made a bold claim. She said that everyone is capable of learning math to the highest levels (if they overcome math anxiety and embrace a growth mindset and the struggle that goes with it) [3]. This doctrine has become very popular in math education, but is it true?

The idea that anyone can learn advanced math stems from recent studies of London taxi drivers, who develop larger hippocampi — brain structures — by memorizing the city’s map. Boaler cites this as evidence that the brain can change in adulthood [3].

But becoming a London taxi is tough. Hassan Anderson, a longtime London taxi driver who writes for the SW Londoner, explains that candidates spend three to four years exploring the city on mopeds. They do not get paid while training. They memorize the city, pass many oral exams, and only one in three succeeds and earns a license [1].

London cab drivers’ hippocampi grow because this part of the brain manages memories of what we see and do [4]. However, the hippocampus does not engage in the kind of thinking we use when we solve math problems. According to research [5. 6], that job belongs to the Rostral-lateral Prefrontal Cortex, or RPFC.

The hippocampus is ancient and found in all animals with backbones [4], but the RPFC — responsible for the complex thought sequences that enable us to work with abstract concepts — exists only in primates. Brain imaging technologies show that this region is very active when a person performs a series of complex tasks composed of subtasks with no sensory cues about how to proceed, as in solving an algebra problem [5]. It develops rapidly during our teenage years and then settles down around age 20. It’s the part of the brain that lets us figure out how to do complicated tasks in a logical manner, without any outside cues or directions. It’s our brain’s Project Manager. RPFC development can vary widely among individuals within the same population, and this variation may help explain why Stage 4 thinking is not universal, yet occurs at roughly the same rate across modern and traditional cultures worldwide [11, 20]. Sure, we keep learning all our lives — but adult learning relies on the brain hardware we develop as children and teens that serves us throughout life [6].

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College is often seen as key to success, but graduation usually requires algebra — a subject that demands complex, abstract thinking. Psychologist Jean Piaget called this kind of thinking “Stage 4 Formal Operations [12, 15, 19]. Research suggests that only about 20–30% of literate adults reach this level of reasoning [6, 9, 11, 17, 19, 20]. While Piaget’s theory has been debated and updated over time, his main ideas about stages and the building of knowledge remain valid [8, 12, 15]. Recent MRI studies have even confirmed his findings regarding what Piaget referred to as Stage 4 thinking [5. 6].

What is Stage 4? It is the ability to reason deductively about abstract concepts and operations that we cannot see, hear, feel, touch, or taste. It lets us plan scientific experiments, develop abstract ideas through deductive reasoning, discern hidden patterns, and seereality as a subset of possibility [12, 15, 19].

At first, Piaget thought that all children would reach Stage 4, but now we know most people stay in what Piaget called Stage 3 Concrete Operations. At this stage, people use inductive (bottom-up) reasoning to build knowledge based on direct experience. They can do everyday math with whole numbers and decimals (OECD), but have trouble with algebra, which is the entry point to higher math [19].

Many students tell me, “I’m fine with numbers, but letters lose me.” So I use pictures, concrete examples, and real-life models to help. Still, they struggle and retake Algebra 1 many times. They celebrate when they finish their “last math class ever.” These students view algebra as a rite of passage, a hazing to prove their mettle.

This contrasts with their peers who advance to complex abstract thinking, what Piaget called Stage 4. During the teen years, some students develop deductive (top-down) reasoning. This means they can think about abstract ideas and apply these ideas to specific cases. They also become capable of metacognition, reflecting on their own thinking. As their RPFC develops, they can handle complex tasks with many steps and subtasks, even when there are no obvious clues to help them. This is how they reach Piaget’s Stage 4, Formal Operations, which is the kind of thinking needed to master algebra and beyond [5, 6, 11, 12, 17, 19].

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Research shows that students in science, technology, engineering, and math (STEM) fields need Stage 4 thinking to succeed [17, 19]. Algebra is often their first real experience with abstract thinking, and it’s a key requirement. For students who remain in Stage 3, algebra can block their progress [19]. If more people could reach Stage 4, college would be more open to everyone, the opportunities that come with a college diploma would be available to all, leading to a fairer and more thriving society.

This concern led me to investigate how adults might progress from Stage 3 to Stage 4 thinking for my master’s thesis. However, I quickly discovered that the research focused on children. With no information on how this change might happen in adults, I designed my own study. Although my results were inconclusive, my research team accepted the effort. Since then, I’ve continued my search for answers — hoping to uncover how adults might make this leap from Stage 3 to Stage 4, and how to help those who struggle with algebra along the way.

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My search took an unexpected turn when the London “Black Cab” taxi drivers hit the news. These drivers memorize the city’s complex map, and MRI scans show that their hippocampus grows as a result. This discovery challenged the previous belief that the adult brain could not produce new cells. The London taxi driver study revealed that the brain continues to generate new cells throughout life. Inspired by these findings, math educators began promoting the idea of a growth mindset, suggesting that “everyone can learn math to the highest levels.” This belief soon became a staple in our profession [3].

But there’s one catch. The hippocampus, the part of the brain that grows in London taxi drivers, does not handle complex abstract thought. Instead, its job is to manage visual/spatial and episodic memory, the type of memory required to learn the map of London. All animals with backbones have hippocampi [4]. The rostral-lateral prefrontal cortex (RPFC) is a brain region involved in higher-level abstract thought and is found only in primates. The RPFC develops rapidly during adolescence, and then seems to change little afterward [5, 6].

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Why is this so? Wouldn’t it be great if the RPFC developed completely in everyone? Wouldn’t we have a fairer and more peaceful society if everyone had Stage 4 thought? If that were so, we could identify systemic issues, grasp each other’s perspectives, and resolve our differences through reason and cooperation rather than violence. Alas, it is not so. And the fact that RPFC development varies is at the heart of understanding differences in mathematical achievement.

Think about how our ancestors lived hundreds of thousands of years ago, and how some traditional peoples in remote areas live today. We lived in small nomadic bands of hunter-gatherers, with a few skilled people who knapped flint, made weapons, used nearby herbal medicines, conducted ceremonies, and kept records. We didn’t need everyone to have all of these skills; only a few, say one in five, would have been sufficient. If everyone were a flintknapper, herbalist, or ceremonial leader, who would care for the babies and elders? Who would hunt and forage, or do any of the other routine yet vital tasks that keep life going? This could be why Stage 4 thinking occurs in about 1 in 5 people in traditional oral-based societies and about 1 in 4 in modern westernized societies. Formal education gives us a slightly higher rate, but the rate in traditional societies is nearly the same [20]. This suggests that nature has found a balance, with a small yet significant minority able to work with the invisible patterns that shape our common experiences.

In addition, Stage 4 thought is costly. Our brains, though they make up only 2% of our lean body weight, use 20% or more of our energy. The RPFC, as part of the neocortex, is especially demanding. Those with advanced abstract thinking may be more vulnerable in tough times and prone to mental health issues. These weaknesses could limit mating opportunities and threaten survival. Complex thought comes with a price [2, 14].

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So what do we do? Here are some ideas:

In college, drop the Algebra requirement for non-STEM majors. Instead, offer logic, critical thinking, and conceptual statistics — focusing on concepts rather than calculations. Conceptual statistics is accessible to Stage 3 thinkers and useful in everyday life [18].

Research shows that STEM majors who remain at Stage 3 thinking are more likely to struggle with their coursework and to drop out of college [19]. For students in this situation, meeting with a counselor can help them explore alternative paths, such as switching to a non-STEM major. Importantly, this change should be framed not as a failure but as a proactive decision to pursue a field that better matches their abilities and interests.

In K-12 education, educators should use hands-on, collaborative learning to help students build a solid knowledge base. Memorization is easier for children than for teens or adults, especially when teachers add games, music, and movement to make it enjoyable. This is related to the differing activity of the neurotransmitter GABA in children’s brains vs adult brains [rf?].

Since children begin Stage 3 thinking around age 7 and use inductive reasoning based on their observations and experiences, they can learn numeracy skills in a cyclical manner from elementary school onward. Middle schools can introduce conceptual statistics, naive set theory, and naive number theory, establishing a foundation for later development [18].

High-stakes tests like those in Common Core are often counterproductive. Instead, teachers and parents should identify students’ strengths and guide their education accordingly. Beginning in middle school, students can write about their experiences. These writings can help parents and teachers understand and shape children’s future paths. Learners who struggle with writing could track their progress through speech, art, presentations, and other means. This way, students know their strengths and goals before college, making college an intentional choice rather than a default.

Those who go to college would then have a goal of gaining a profession. Since professionals in any capacity need to think critically, non-STEM curricula should replace algebra with classes in logic, critical thinking, and conceptual statistics or statistical literacy [19]. While algebra requires S4-level thought, and most people find no use for it in everyday life, these other disciplines are useful outside the classroom and accessible to S3 thinkers. In particular, conceptual statistics focuses on the big ideas of making sense of data, while offloading the dense calculations onto technology. Understanding basic statistics enhances the critical-thinking skills necessary for their professions and everyday life [19].

Finally, we can work together to destigmatize vocational and trade education. Let’s promote these paths and make them more accessible for everyone. The USA faces a serious shortage of skilled tech workers. A person in a skilled trade often has greater job security and earns more money than someone with a college degree, allowing them to support themselves and command respect in their communities.

But why study math at all? Don’t we have calculators and computers now?

Math is important because it lets us build models that explain and predict real-world phenomena. Analogies and pictures are helpful, but only math-based models reliably map to reality. Algebra serves as the gateway to these models. That’s why people in STEM fields require algebra and beyond.

For the rest of us: if we want a fair and thriving society, we must rethink who truly needs advanced math and commit to pathways that value all forms of intelligence — not just those that show up in algebra class.

References

AI note: This essay is adapted from an academic paper I recently wrote, reworked for a general audience. I used Grammarly AI to improve this essay’s brevity and readability, but the research and ideas presented are entirely my own. If you’d like to see the full paper and annotated bibliography, they are available here (link).

References

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