In my earlier blogs, I talked about Math Anxiety, about how the brain creates a sense of Now, and various other fun issues in brain research too. Branching off of my long, professional interest in math education, I thought I would look into how ‘doing’ math actually changes your brain in many important ways, especially for children and adolescents. Brain research has come a long way in the last 15 years with the advent of fMRI and sensors that can listen-in to individual neutrons . For a detailed glimpse of modern research have a look at my reference list at the end of this blog.
Here is what we know about how math affects brain structure and maturation. My previous blog on Math Anxiety covered this topic but here are some additional points.
The Basic Anatomy of Math
First of all, let’s put to rest a popular misconception. Its a complete fallacy that we only use 10% of our brain. The misconception probably arose because glial cells that support neurons account for 90% of the cellular matter in the brain, so neurons account for 10% [9,11,10]. The truth is, by the end of each day, your brain has used nearly all of its neurons to facilitate movement, sensory processing, advanced planning, and even day-dreaming!
The architecture of our brains is controlled by about 86 million neurons and the trillions of synaptic connections between them. At the lowest level, our brains are composed of numerous modules that are specialized for specific tasks. Each has its own local knowledge system and ‘data cache’ and can act much faster than the whole-brain, which is the way evolution designed this system to help us respond quickly and not get eaten. We benefit from this ancient architecture because craftsmen, musicians and dancers cannot tell you how they perform their tasks because it is largely unconscious and controlled by specific modules. [6:p45, 198].
Before the age of 2, children use a general knowledge ‘program’ that takes up all of their working memory [2:p151] to interact with the environment. Children require more working memory to do math than adults. Number facts and basic opeations are not yet in long-term memory so they use more of their prefronal cortex (PFC) to keep math in working memory so that they can solve problems [2:p155]. But through training they develope a growing multitude of specialized modules and automatic ‘subroutines’ for specific tasks and skills. [6:p56]. Consciousness occurs when these non-communicating modules begin to share their knowledge across many communities of modules spanning the entire cerebral network. Some of these global communication pathways are highlighted by the so-called brain connectome map. This sharing of multiple representations of similar knowledge leads to problem solving and creativity which now draw inspiration from the experiences of many different modules [6:p58] spanning the entire cortex.
Development of the Brain
At birth, the average baby’s brain is about a quarter of the size of the average adult brain. Incredibly, it doubles in size in the first year. It keeps growing to about 80% of adult size by age 3 and 90% – nearly full grown – by age 5 . Over 1 million new neural connections are created every second among the synapses of the growing population of neurons and dendrites . What then ensues is a process of pruning as seldome-used connections wither and dissappear while others are strengthened .
The growing brain does not start out as a tabla rasa but through genetics and evolution there are already features in place that anticipate the growth of mathematical knowledge.
Number Line Maps
At the most elementary level, neurons already exist at birth that are active for specific numbers. These ‘number neurons’ have been found in both monkeys and in humans. In humans they are mostly found in the lateral prefrontal cortex (l-PFC) and the intraparietal sulcus (IPS). [2:p129], but also the mediotemporal lobe (MTL) [2:p98]
Our brain’s hippocampous has place and grid cells that form a direct map written on its cortex that represents the location of objects in space [7p219]. The posterior cingulate region has neurons tuned to the location of objects in the outside world, and is connected to the parahippocampal gyrus where “place cells’ are found. These neurons fire whenever an animal occupies a specific location in space like the northwest corner of your room. These place cells are so advanced that readout of individual nerve cell firings can be used to tell a researcher where the object is in the subjects visual field of view. This even works when the subject closes their eyes and imagines an animal located there. [4:p149].
A curious feature of how the young brain processes quantities is that it perceives quantities as being located on a mental number line. Called the SNARC Effect, even three-day-old infants will look-right for large quantities and look-left for smaller quantities.[2:236]. That calculation-related activity is being processed like mental movement on a number line was also tested in older subjects by studying neuron activation in the superior parietal lobule (SPL) where information is being manipulated in working memory. They found that eye motion alone predicted the answers to simple addition and subtraction problems [2:239]. So just as the brain uses an internal map in the hippocampus to locate objects in space, it also uses an internal map to locate numbers in space along a line! The number line however is not uniform.
Kindergarten students with no math knowledge see number intervals as quantities mapped out in logarithmic intervals just as many animals do, so that quantities are perceived almost the same way as light brightness or sound volume [2:87]. Large numbers with smaller intervals are crowded together in the right-hand of the mental number line while smaller numbers are more spread out in the left-side of the line.
Meanwhile, the concepts of addition and subtraction are already known to infants as young as nine months[2:196]. Thinking about quantity as symbolic numerals like 1,2,3 etc instead of dots like [.], [..], […] etc at first occupies children up to age 7 who have to use their working memory to keep track of this, but within a few years the relationship between number symbols and dots becomes automatic and unconscious [2:185]. By the way, although algebra looks like a language, algebra is not processed in the brain’s language centers [2:p222] You can think and reason logically without language. In fact, when professional mathematicians are studied and asked to solve advanced problems, their language centers are not activated. Instead, the bilateral frontal, intraparietal and ventrolateral temporal regions were active, which are connected to the regions associated with processing numbers [2:232].
Math Remodels the Brain.
For mathematicians, an interesting recycling of brain areas occurs in order to accommodate advanced mathematics. Afterall, the brain volume is fixed by the volume of the skull, so the only way that new skills are learned and mastered is by appropriating cerebral real estate from other adjacent functions. The inferior temporal gyrus (ITG) is an area where face recognition occurs. For mathematicians, part of this region is invaded by adjacent regions used in number processing [2:191], in some cases making it harder for mathematicians to recognize faces!
Admittedly, this is an extreme result of brain reorganization, but there are other examples that are more relevant to children and young adults and the answer to the question ‘Why do I need to know math?’
Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in sharing brain regions for other purposes.
Example 1: In my previous blog on Math Anxiety, I mentioned that the sub-region called the dorsolateral prefrontal cortex helps us keep relevant problem-solving information ‘fresh’ in our working memory. In math it is activated when the individual is keeping track of more than one concept at a time. As it also turns out, this region is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at having lost. It is also important in suppressing selfish behavior, fostering commitment in relationships, and most importantly inferring the intentions of others, which is called a Theory of Mind.
Example 2: The long-term effect of not continuing math education and problem-solving in adolescents has also been documented. A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16. The neurotransmitter called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later. What was found among the older adolescents was that GABA showed a marked reduction. This neurotransmitter is also correlated with brain plasticity and its ability to reconfigure itself by growing new synapses as it learns new skills or knowledge having npothing to do with math .
Example 3: The mediotemporal lobe (MTL) includes the hippocampus, amygdala and parahippocampal regions, and is crucial for episodic and spatial memory. The MTL memory function consists of distinct processes such as encoding, consolidation and retrieval, and supports many functions including emotion, affect, motivation and long-term memory. The MTL also has numerous number neurons [2:p98] and is involved in processing mathematical concepts. Activity in this region represents a short-term memory of the arithmetic rule, whereas the hippocampus may ‘do the math’ and process numbers according to the arithmetic rule at hand.”.
Example 4: Memory-based math problems stimulate a region of the brain called the dorsolateral prefrontal cortex, which has already been linked to depression and anxiety. Studies have found, for example, that higher activity in this area is associated with fewer symptoms of anxiety and depression. A well-established psychological treatment called cognitive behavioral therapy, which teaches individuals how to re-think negative situations, has also been seen to boost activity in the dorsolateral prefrontal cortex. The ability to do more complex math problems might allow you to more readily learn how to think about complex emotional situations in different ways. Greater activity in the dorsolateral prefrontal cortex was also associated with fewer depression and anxiety symptoms. The difference was especially obvious in people who had been through recent life stressors, such as failing a class. Participants with higher dorsolateral prefrontal activity were also less likely to have a mental illness diagnosis.
The bottom line for much of the research on how the brain functions with and without mathematics stimulation is that low numeracy is a bigger problem for the brain than low literacy [2:p307] It affects your economic opportunities in life, handeling personal finances, operating as a savvy consumer, and it even connects with your ability to logically process complex social situations and predict what your best course of action might be in many different circumstances.
Many of the brain regions needed for math performance are still under development between ages of 16 and 26 including most importantly the frontal cortex essential for judgment and anticipating future consequances of actions.
So when a student asks what is math good for, take a step back and walk them through the Big Picture!
Books that are definitely worth the time to read!
 The Tell-Tale Brain, V.S. Ramachandran, 2011, W.W. Norton and Co.
 A Brain for Numbers, Andreas Nieder, 2019, MIT Press
 The Consciousness Instinct, Michael Gazzangia, 2018, Farrar, Straus and Giroux
 Consciousness and the Brain, Stanislaus Dehaene, 2014, Penguin Books.
 Being You: A new science of consciousness, Anil Seth, 2021, Dutton Press
 The Prehistory of the Mind, Stevem Mithen, 1996, Thames and Hudson Publishers.
 The Idea of the Brain, Matthew Cobb, 2020, Basic Books
 The River of Consciousness, Oliver Sacks, 2017, Vintage Books
 Myth: We only use 10% of our brains. Stephen Chew ,2018, https://www.psychologicalscience.org/uncategorized/myth-we-only-use-10-of-our-brains.html
 Neurological glial cells – https://www.ncbi.nlm.nih.gov/books/NBK10869/
 Unsung brain cells play key role in neurons’ development, 2009, Bruce Goldman, https://med.stanford.edu/news/all-news/2009/09/unsung-brain-cells-play-key-role-in-neurons-development.html#:~:text=Ben%20Barres’%20research%20has%20led,90%20percent%20of%20the%20brain.
 www.sciencedaily.com/releases/2021/06/210607161149.htm and DOI:10.1073/pnas.2013155118
 Math Neurons” Fire Differently Depending On Whether You Add Or Subtract, 2022, https://www.iflscience.com/math-neurons-fire-differently-depending-on-whether-you-add-or-subtract-62658