The mainstream belief about the concept of visual mathematics is that it is used only for the lower-level tasks for younger students or as a runner up to open the student’s window for the advanced or abstract mathematical reasoning. It has been a popular myth that words and symbols are for serious mathematicians and pictures or visual images are for the children and layman population. Students who prefer visual thinking such as counting on fingers are labelled as babyish or those having needs for special education.
However, it is being proposed that students learn more through visual approaches with gross understanding unlike relying entirely on numerical or abstract content. Moreover, certain brain evidences are also present to help us understand the role of visualization in all levels of mathematics in bringing effective learning outcomes.
Our brain is a complex system of distributed neural networks; thereby, gaining knowledge activates or lightens up different areas and communicate with each other through synapses. Processing the mathematical information, particularly results in spreading out the brain activity across a widely distributed network including two visual pathways; the ventral and dorsal visual pathways. According to neuroimaging, our mathematical thinking grounds in visual processing when brain is working on number calculation such as 10 x 5 in the form of symbolic digits.
The dorsal visual pathway is involved in working on mathematical tasks, in particular, visual or spatial quantitative problems e.g., the concept of number line. The researchers have highlighted the utility of students grasping the numerical concept through linear visual representation. In another study on the children ages from eight to fourteen, it has been found that children develop the ventral visual pathways which make their brain more sensitive in presenting the visual numeric forms.
These two visual pathways interact through neural connections with the ongoing development of brain and increased visuo-spatial knowledge of quantities. The other major brain areas which are involve in mathematical processing are frontal regions, medial temporal lobes and the memory center; hippocampus.
One specific study on the region of brain investigates the somatosensory finger region of the brain, instrumental for the perception and representation of fingers i.e., we tend to see fingers’ representation in our brain without using them for calculation. One such example was observed in the children of age 8-13 years when they were given the complex subtraction questions. It was found that during their brain processing, the somatosensory finger region lit up, though student didn’t use finger count. The researchers also identified that this area was also involved in more complex problem solving and manipulation.
The implication of this finding was also found in the university students as this improves arithmetic knowledge, such as subtraction, counting and ordering. Among 6 years old, this finger representation unit was found to be a predictor of greater mathematical success than their achievement through cognitive processing.
“Embodied cognition” is another area of research which resonates with the evidence of important visual pathways which are connected to different neural pathways in the brain. Unlike the concept of considering mind and body as separate entities according to which mind holds all the knowledge and abstract information and body passively takes in the ideas from mind to physical environment, embodied cognition emphasizes that mathematical concepts are registered on the visual and sensory motor areas, creating memories. In addition, the researchers of embodied cognition take not of all the sensory motor behaviors which are used during mathematical processing such as posture, gesture and tools, supported by cranial evidence. It was also focused that we tend to draw symbolic sketch in air or use space when we’re explaining any idea or concept or tend to spread it out, even if it is free of any verbal input.
One such example is observed in when we tend to explain one side of the nearby desk and point it back when referring to the idea even if the desk is no more there, but we cognitively designated one. Thus, we can say that the idea of visual mathematics disagrees with the idea of mind-body dualism and considers body as an intrinsic feature of mind/cognition, proposing that perceptual and spatial area of brain are also involved in knowledge representation. For example, the knowledge of dance and sports register in the spatial and perceptual regions of brain.
Recent researches showed that teachers emphasizing on visual mathematics and use manipulative strategies encourage higher academic achievement among learners ranging from elementary school to college level. The data from the best teachers revealed that they were aware of the significance the visual representations of the concepts hold and introduce mathematical ideas through visual tools and encouraging students to use visual to think and understand mathematics.
Visual mathematics should be used in schools on a greater extent because of the increasing demands of the today’s high technology world, based largely on images, rich in content unlike those from past, entirely build on words and numbers. At organizational level, most companies have huge resources with large amounts of data which includes visualizing data patterns. There are some recommendations through which visual mathematics could be spread through teaching and parenting.
Firstly, it is important to encourage student’s visual skills to implicate mathematical concepts and perform calculations and replace the mainstream idea of memorizing mathematics and calculations is the token to academic success. Secondly, encourage them to use finger count for better mental representation. It is found that successful mathematics instills from the developed finger representations in the areas of brain to be used later in life. Lastly and most importantly, the learning and teaching of mathematics needs to be visual in approach as some scholars hypothesize that those with developed visual thinking will be at top most in class and in high-tech workplace because of the increased emergence of visual information across the domains of business, technology and sciences.
Therefore, it is the need of hour not to prioritize one learner over the other or set them limited to one type of learning style. The brain science supports the fact that mathematics engages different regions of brain and it is important for students to be well-equipped with visuals, symbols, numbers and words.