MIMICKING MATHEMATICAL MIND
Fine arts painting requires substantial skill. Some of the masterpieces we know reflect the ingenuity of the artist. Color combinations, positioning of objects, composition, the angle of light hitting objects, layers of colors, even the edge of brush strokes seem meticulously calculated. On the other hand, they mostly give the impression that all was completed in effortless action, coming from a natural well. I thoroughly believe in Ramachandra’s[1] explanation of art. He says[2] "Art is not about realism at all - it is the opposite. It involves deliberate hyperbole, exaggeration, even distortion, to create pleasing effects in the brain." It appears such a complex, unique, and rarely shared talent. Regardless, in general human beings enjoy them even if they do not understand what lies beneath it.
I saw many ordinary people make nicely done paintings. Systematically ordered movements guided lots of people to paint lovely artworks but undoubtedly they weren’t art, but rather highly qualified craft. The followers of Bob Ross or Bill Alexander ended up with delightful paintings that usually impressed others and satisfied the creators.
If this is feasible in art, I think the same can be applied in mathematics. Throughout my mathematics tutoring experiences, I have come to realize fine arts and math both can find order in a world of chaos in the brain and in the environment. For some reason, few people were born with the capacity to find eternal order, quietude and truth in the middle of chaos. This phenomenon is called talent by observers.
Language, arts, and math are byproducts of our brain. They are all abstract, so brain scientists cannot identify one specific location in the brain that drives this, such as the area of vision, or other vital capacities. We observe and internalize the world and react to it via these abstracts.
Among the three of them, the most universal one without a shadow of a doubt is mathematics. If the language of math is known by someone, compiling another unknown subject is just a matter of time. Math seems the universal language and the core abstract that the brain can gather almost automatically.
As an early childhood education professional and an admirer of arts and math I looked into children's reactions regarding how they were organizing their ‘cocoon of focus’ by using math voluntarily and naturally.
I sometimes imagine we all are ceramic clays made from different specks of dirt. The initial amount and quality of the clay will determine the final product. I imagine that a clay vessel can be formed to maximize its volume. Likewise, early childhood education can be a process of creation to maximize a child’s capacity. Thus we may mimic a natural-born mathematician’s faculties to shape a child's material – like the clay in my imagination- in other words, his/her brain.
There is a direct correlation between intelligence and mathematical comprehension. Having a quick glance at new studies about what intelligence might be, they give us a clue on what’s on the fringes of human's mental proficiency. Per a post uploaded in 2014 at the US National Library of Medicine National Institute of Health[3], there is a robust interactive link between sensory discriminations and intelligence. That means that intelligent people can naturally eliminate items not directly relevant to the core subject and can therefore focus on the essence of the matter and disconnect all other stimuli. No wonder why smart people can quickly and efficiently focus on issues!
Starting from this point, children can be helped with internalizing a clear focus faculty. Given my experience with the authentic Montessori approach, particularly sensorial exercises are ideal to involve with here. Developing focus cannot be achieved with a one-time lesson, it is an ongoing process; it cannot be taught directly - but it can be developed over time.
Sensorial exercises are ideal, because they activate one stimulus at the time, and naturally disregard all others. It’s natural guidance towards the development of focus. Beyond the sensorial exercises, children should be supported to always focus on one area, and the environment should serve them to clean up all other stimulae.
All mathematicians have an orderly mind; they eliminate irrelevant subjects, order the items of a given problem, and address the data to previously gained information, so they can reach conclusions and/or arrive at new knowledge.
Children need to be taught in an orderly manner, and repeat this with other problems, so over time it becomes a habit to approach problems in this fashion. When they eventually start doing math, they will have developed the habit to analyze the problem and to put its elements in a specific order. Instead of learning to solve a problem, they will have learned how to first of all understand the problem.
Mathematical notation is the most complex reflection of thought – mathematicians are able to directly connect these notations to a specific model and visualize what a given formula stands for. Children cannot be taught this directly, but they can be taught to make these connections initially with simpler forms of notation, such as music or languages such as Chinese – or visual arts. Early childhood educators should always be consistent, and be well prepared to help children build these connections, layer by layer, until they ultimately arrive at the mathematical mind. Mathematicians cannot be created, but we can mimic their minds…
[1] Vilayanur Subramanian Ramachandran is a neuroscientist known primarily for his work in the fields of behavioral neurology and visual psychophysics.
[2] V.J.Ramachandra (2004) A Brief Tour of Human Consciousness, PI Press Pg 43
[3] Michael D. Melnick, Bryan R. Harrison, Sohee Park, Loisa Bennetto, Duje Tadin, (2014), NCBI Resources, www.ncbi.nlm.nih.gov/pmc/articles/PMC3702042/#!po=12.5000