Written By: Jerry Winn
Continuing from last month’s advocacy piece this article is about how math education can benefit significantly from being trauma-informed, as well as the ways in which our students can benefit from the new Common Core math standards. Mental functions like math happen through complex processes in the brain, and a basic understanding of these processes might help foster a deeper appreciation of the subject. Researchers in the field of cognitive neuroscience claim to have identified at least two distinct subsystems for two different kinds of math problem. Remember that being trauma-informed doesn’t mean that we need to know all or any details about someone’s experiences - only that we be committed to being compassionate, supportive, and to protecting of their dignity. After a brief summary of math and trauma in the brain, comparing two multiplication methods will hopefully help to illustrate these points.
Trauma can be thought of as a deeply disturbing or distressing event that leaves a lasting impression on the psyche, as well as on the brain itself. Because trauma doesn’t go away, it can be triggered and cause someone to experience a fight-or-flight response and relive aspects of the reaction to the toxic stress of the initial event. During a trauma reaction the right amygdala generates a fight-or-flight response, and the left brain, which is largely responsible for logical and analytical thinking, is shut off. This can become a serious obstacle in the way of a student’s education - asking someone in the midst of a trauma response to engage in left-brain thinking styles is like asking someone to reach for an object with their arms tied. Thinking that is less dependent on the left-brain may be more accessible to people with trauma.
Researchers found that there are two different subsystems in the brain that handle two different types of mathematical tasks. Both engage, in different ways, both the left and right hemispheres of the brain. Both sides of the brain operate independently and cooperate with one another. They develop relative strengths and weaknesses. The ways in which they do specialize are nuanced and complementary to one another. Even though the two hemispheres of the brain operate independently, they share information in a very efficient manner. This means that learning through one circuit is likely to be applicable within other similar circuits. One of two subsystems in the brain adapted for math is biased toward areas in the left-brain. Unfortunately previous math education methods were very focused on this type of mathematical learning, such as exact calculation and memorization of arithmetic processes.
This left-brain oriented circuit seems to be adapted for tasks like exact arithmetic calculation and memorization of facts for quick recall. It overlaps with other left-brain areas that are involved with other logical functions like grammar. The other system, however, engages both hemispheres of the brain more equally. It makes use of areas engaged with visual-spatial reasoning. It is this second circuit that had previously been neglected in math education. Common Core math methods engage this kind of reasoning head-on. In contrast to the logical, exact calculations of the left-brain system, the visual-spatial math system underlies processes of approximation. Approximation is a crucial tool in math, maybe undervalued by previous education standards. Approximation is both practical for everyday use and of theoretical importance. It’s worth noting that methods of approximation underlie much of advanced mathematics such as calculus, which is required for many STEM and business careers. Those familiar with calculus (or interested in irrational numbers such as pi) may recall that an exact answer usually doesn’t exist - only an arbitrarily close approximation based on context and modeling.
One notable way in which Common Core attempts to reconcile the divide that has grown between these two kind of reasoning is by encouraging students to explore the connections between arithmetic and geometry - something that many of us who were educated via the old methods may have never come to fully appreciate. This connections aren’t coincidence - they are due to the fact that these ways of thinking are complementary and deeply interconnected. This pair of abilities, which are distinct but interrelated, seems to align with the distinct cognitive circuits referred to by the neuroscientists. With an understanding rooted in deep connections like these, students are free to use their right-brain to aid their left-brain or vice versa. There are two ways available instead of one. Since trauma involves a lack of access to the left-brain, these visual-spatial, right-brained methods could help students circumvent the obstacle.
A good example of this approach is the new Common Core multiplication method called the ‘area model,’ or ‘box method.’ It has these names because it involves drawing a visual aid: a rectangle where the numbers to be multiplied represent the lengths of the sides. Remembering that area equals length times width, we interpret a multiplication problem as finding the area of a hypothetical rectangle. This reinforces the understanding of the connection between arithmetic and geometry, and when students are eventually taught the standard algorithms for multiplication (‘carry the 2’ etc) they are in a position to appreciate what they are doing. The area model also lends itself to approximation; whereas a problem involving decimals or fractions might be frustratingly abstract when trying to multiply out via the standard method, seeing the numbers as lengths and areas of a rectangle offers an intuitive, visual-spatial support for the abstract symbols.
Neuroscientists suggest that there are two modes of mathematics in the hardware of our brains, roughly corresponding to “left-brain, exact calculation, verbal/logical skills” and “right-brain, approximation, visual-spatial skills”. These are distinct but not mutually exclusive. They are both available to us. A deeper understanding of mathematics comes from the ability to work with both of these techniques, and to confidently apply them in creative ways. This ability is very helpful in seeking STEM or business careers. We work with a population that suffers from trauma, and so an increased emphasis on non-left brain learning can be seen as an opportunity for organizations like ours. Considering that an important step in overcoming a trauma response is reintegrating the left and right brain, exercises that involve this kind of executive function could take on a therapeutic dimension and help with social-emotional learning and executive function.