math

Trauma Informed Math- Pt. 2

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.

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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.

Math First- AID

Written by: Jerry Winn

Starting in Fall of 2017, Chicago HOPES for Kids expanded our capacity beyond literacy to include a strong focus on mathematics in our after school program. In considering our implementation of this program, we were initially inspired by two sources: 1) the new direction of Common Core math, which puts new emphasis on a big-picture understanding of math and often associated with right-brain learning and 2) a discussion of trauma-Informed teaching practices.

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Trauma can be thought of as a deeply disturbing or distressing event, either a single event or chronic, that leaves a lasting psychological impact. It is impressed on the right-brain, which is associated with sensory input and episodic memory recall. Trauma doesn’t disappear. It can be triggered by words, facial expressions, smells, and many other experiences. This causes aspects of the toxic stress of the initial event to superimpose onto normal situations. While these symptoms may have been helpful in surviving the traumatic event,.they become maladaptive in normal situations.

People with trauma, especially children, are often not able to understand that these perceived threats are not real, and it requires leap of faith to accept this counterintuitive notion. However, there is a neurological Catch-22. A trauma-reaction involves a high level of activity in the amygdala, the part of the brain that is responsible for “fight, flight, or freeze” reactions. Due to this, the prefrontal cortex, which is responsible for analytical abstraction, becomes inactive. The ability to think in abstraction, which would be helpful for differentiating reality from the trauma reaction, becomes unavailable during the trauma response - meaning logical thought isn’t happening.

A recent brain imaging study from Stanford University discusses the neurological reaction of people with math anxiety when faced with a math problem, and it looks a lot like a trauma reaction: high activity in the amygdala and low activity in the prefrontal cortex. Interestingly, this reaction did not occur when the researchers presented both groups with spelling problems, even if they were difficult. Research has shown a close relationship between math and executive functioning that doesn’t seem as strong with other subjects, which are often more focused on memorization of content rather than performing mental tasks.

This reflects a deep learning process, unrelated to rote memorization. If students feel or experience a threat in the process of learning, their attention to the task is disrupted because they pay attention to the (real or perceived) threat. When this happens, the prefrontal cortex, where problem-solving takes place, shuts down. One way to interpret this is that some people have experienced trauma in some way associated with math, and this trauma prevents a math-anxious person from beginning to work on a problem. The children we work with tend to have a high incidence of trauma which may have been compounded by experiences at school. This could result in an even more complex negative reaction to math. Given math’s heavy engagement with executive functioning, this has the potential to become even more disadvantageous for our students.

Significantly, the Stanford researchers found that when the math-anxious person actually began to work on the problem, their neurological activity approached that of the control group  who did not have math anxiety. The important factor in this was overcoming the initial response that prevented the individual from beginning the problem. On some level, the brain anticipates similar trauma to ensue so it prevents the process from beginning. Overcoming this anxiety requires that we actively interact with our own brain.

The fact that mental activity physically changes the organization of the brain, known as neuroplasticity, is significant. The result is that new physical and mental behaviors that can become habitual through repeated engagement. This is evident in the way trauma is permanently impressed on the brain, resulting in a learned behavioral reaction, but also in the way we can overcome this trauma by learning and establishing new responses to our trauma-reactions. In fact, this is a tenet of Cognitive Behavioral Therapy - a highly flexible form of talk therapy - where people learn to change unhelpful thought patterns underlying problematic behaviors. Neuroplasticity is a double-edged sword and it is in our best interest to learn to use it with intent.

At the end of the day, our left and right brain are supposed to work together like our left and right hands. We can use right-brain thinking and understanding to get the left-brain unstuck from trauma and anxiety responses. Then, we can use left-brain analysis to reflect on what just happened and intentionally direct our capacity for re-learning. After repeating this process multiple times, the plasticity of the brain allows the new behavior to become the norm. We come to believe through experience that we can solve the problems we encounter, meeting less and less resistance as the new pathways become more established.

Math is a powerful subject, and has the potential make or break a child’s educational experience. Its engagement with executive functions in the brain can cause experiences with math to either have lifelong benefits or become traumatic and compounding. Also, considering its central importance in STEM and business fields, a student’s experience with math can be extremely empowering or disabling. A trauma-informed approach is a best practice for math education and for life in general, and the right-brained methods of Common Core math offer us a new world of opportunities for helping children with this potentially challenging subject.