You cannot use correct mathematics to prove an incorrect statement. Or can you?
There are at least a couple of false “proofs” for stuff such as 1+1=3, which can be found simply by Googling 1+1=3.
The most famous example is too lengthy to expand upon here, but, as mathematicians are quick to point out, once you prove a false statement, you can believe anything.
The University of Southern California Brain and Creativity Institute has done some interesting work that seeks to describe the role of belief and acceptance in learning and, for that matter, in our lives.
In the institute’s unique environment, renowned neuroscientists and a new generation of brilliant psychologists and brain-imaging researchers work side-by-side with a diverse group of students and collaborate with experts from computer science, engineering, physics, education, psychiatry, philosophy and the arts to tackle a range of issues.
For example, people often discount evidence that contradicts their firmly held beliefs. However, little is known about the neural mechanisms that govern this behaviour. The institute used neuroimaging to investigate the neural systems involved in maintaining belief in the face of contradictory evidence.
Researchers found that individual differences in resistance to belief-change correlated with activity in parts of the brain such as the insular cortex and in the amygdala.
The insular cortex has increasingly become the focus of attention for its role in subjective emotional experience, which is part belief despite the evidence.
The amygdala is especially interesting when it comes to our ability to learn new things or reject them because the amygdala, brain researchers tell us, is the reason we are afraid of things outside our control. It also controls the way we react to certain stimuli, or an event that causes an emotion, which we see as potentially threatening or dangerous.
That might partly relate to why, even as adults, we are especially resistant to change when change challenges our familiar and long-accepted beliefs about politics, religion — even relationships.
One interpretation of these activations in the context of the institute’s study is that these structures are signalling threats to deeply held beliefs in the same way they might signal threats to physical safety.
And that brings us to the role of belief, acceptance and emotional safety in learning.
Every day in class, student motivation is an important concern for all teachers. Motivation, whether it is external or self-motivation, has a great deal to do with belief in and the acceptance of new information.
In fact, although there are many motivational constructs, self-efficacy is one that is key to promoting students’ engagement and learning. Self-efficacy, or self motivation — what we call being a “self starter” — is usually discussed in terms of how learners function positively in the classroom or might be inhibited by fear.
Until recently, learner anxiety and a range of so-called “academic emotions” have largely been neglected.
Now there are studies, including some by the Brain and Creativity Institute, that have identified a diversity of emotions in academic settings.
It appears that “academic emotions” are significantly related not just to students’ motivation, learning strategies, cognitive resources and self-regulation, but to academic achievement.
Since the 1980s, the amount of research on the role of classroom climate — the emotional environment supporting the learning process — has increased tremendously.
If students have certain attitudes and perceptions, they experience a mental climate conducive to learning. In general, two types of attitudes and perceptions affect learners’ mental climate: a sense of acceptance and a sense of comfort and order — safety.
Teachers can significantly influence a student’s sense of acceptance by the positive manner in which they respond to student answers: by dignifying student responses, by giving credit for the correct aspects of an incorrect response, by restating the question, by asking the question a second time, or by giving enough hints and clues so that the student will eventually determine the correct answer.
Brain research such as the studies at USC’s Brain Institute is transforming education by providing insight into why students (and adults) are able to accept new information in an environment where individuals can exercise some control and are not afraid of the risks inherent in learning — especially when it involves proving the fallacy in the 1+1=3 trick to your math teacher.
Geoff Johnson is a retired superintendent of schools.