Researchers at Stanford University have released a report titled "Seeing As Understanding: The Importance of Visual Mathematics for our Brain and Learning" that aims to dispel the notion that visual math, such as pictures, finger-counting, and diagrams, are only for lower-level tasks, and that higher-level math deals exclusively in symbols, notations, and words. They present evidence to suggest that visual mathematics may help students of all levels see, understand, and extend mathematical ideas.
Generally speaking, students who prefer visual thinking are regarded as having special needs, and children grow up thinking that counting on their fingers is an immature approach to mathematics. However, several mathematics organizations such as the National Council for the Teaching of Mathematics (NCTM) and the Mathematical Association of America (MAA) have long advocated for visual representation of mathematics in the classroom. Stanford's new study reaffirms these groups' advocacy and urges the necessity of fostering visual thinking.
Scientists argue that the human brain is comprised of "distributed networks," and when humans handle knowledge, different areas of the brain are activated and communicate with one another. When we study mathematics, brain activity is distributed through many different networks, including two visual pathways. The failure to exploit these pathways through visual mathematics potentially hampers students' mathematical abilities.
Notably, researchers found that students with structural disadvantages such as low-incomes, lower-literacy rates, etc., perform just as well as their more advantaged peers after a 15-minute session with visual exercises. The researchers emphasized the importance of students learning numerical knowledge through linear representations and visuals. According to the report, the dorsal visual pathway in the brain is the core region for representing the knowledge of quantity.
Additionally, a yet-to-be published study from researchers at Stanford demonstrates that children between the ages of 8 and 14 are developing part of the ventral visual pathway, an important brain "network." This development indicates that as children learn, the visual processing parts of their brain become more interactive. If this interaction is not stimulated by visual activities, parts of children's brains will not reach their full potential.
A section of the report is devoted to exploring finger-counting. There is a specific region of the brain, the somatosensory finger area, that is dedicated to the perception and representation of fingers. Often, when doing mathematical problems, our brain's "finger-area" is stimulated whether or not we are using our fingers. The researchers urge mathematics educators to take advantage of this "finger-activity"; children who develop proficiency counting on their fingers will further brian development and promote future mathematics success. Regrettably, argue the researchers, most educators discourage finger-counting.
Despite the evidence, millions of students in the United States do not engage mathematics through visualization and representation. Most students approach it as a numeric and symbolic subject. The evidence, however, gathered by the report will help students and educators to "understand the impact of visualizing and seeing to all levels of mathematics, and suggests an urgent need for change in the ways mathematics is offered to learners."
The full report is available online.