Researchers Daniel Durstewitz, Nicole M. Vittoz, Stan B. Floresco, Jeremy K. Seamans (the latter from my old alma mater, the University of British Columbia) discovered that
"when rats were required to deduce a new rule through trial and error, the entire prefrontal cortex neural network [emphasis mine] would abruptly shift to a new pattern of activity, rather than gradually as one might expect. Further, they found the shift in neural activity occurred one or two trials after the rats exhibited the correct behaviour for the task." (Ashman)It turns out that when we have to abandon old, less advanageous, rules and develop new strategies to cope with changing situations, the change in neural activity is not gradual and incremental and does not occur in isolated regions of the brain. Collecting new evidence through trial and error and formulating a better procedure requires that "virtually all the cells in the prefrontal cortex contribute to encoding all the elements in each task." The entire network then puts "together arbitrary types of information in novel ways" (Floresco quoted in Ashman).
"The rats tried different things, then hit on the correct strategy, realized it was correct, and then encoded the new rule all at once within the prefrontal cortex" (Seamans quoted in Ashman).Interestingly, the prefrontal cortex not only governs problem-solving and complex thought, but it's also in charge of emotion. It plays an important role in executive functions such as mediating conflicting thoughts, making choices between right and wrong or good and bad, predicting future events, and governing social control through the suppression of emotions. To my way of thinking this may explain why unlearning an old ineffective process and adopting a new one -- even with the promise that it will be more successful -- can be such a difficult process. It requires a huge amount of brain power plus a willingness to suspend disbelief in one's ability to conquer learning monsters and old beahviours long enough to change not only one's procedural understanding but all the emotional baggage that goes along with previous failure or ways of handling problems.
I think back to many of my former 'remedial' math students who still had not mastered such skills as fractions by the age 15 or more. In adolescents and adult learners the neural networks which encode the unsuccessful procedure have been strengthened during many hours of incorrect rehearsal over several years. These students also have to deal with a high level of emotional distress which we know blocks learning. In addition, " the same ensemble of prefrontal cortex neurons encodes two different rules through unique activity states or patterns" (Ashaman) which means the old learning and the new use the same neural real estate.
Unlearning and relearning requires that students be willing to attempt enough trials to 'get' the new process without even really registering any discernable brain activity which could reinforce their willingness to proceed. The light of the new learning doesn't turn up gradually like a rheostat. The switch is just off until it's flipped on. The realization that they've finally 'got it' and the encoding in the brain occur at the same time. They aren't going to feel like they are learning until they've let go of the old procedure and wholly accepted the new one.
What then can teachers do to help such students replace ineffective math learning with reliable methods? I think helping them understand just why they are finding the task so difficult can help. We should also clue in their parents and enlist their support when the going gets tough. We have to refrain from making promises we can't keep because they will be depending on their trust relationship with us to get them through moments of great self-doubt. If we say they are going to master an old skill, we have to to ensure that actually occurs. Finally we have to understand that presenting new information in an old way is not going to make the learning process or emotional self-governance easier. Giving students a new vivid learning experience to compete with the old pathway will mean they'll have distinct alternatives in their minds when confronted with new problems. I think as well, periodic review accompanied with a verbal rehearsal of the new process and discussion of how it differs from the old one can strengthen the new pattern and reinforce just how far the students have come from 'the old days'.
It's a big job to light up someone's entire prefrontal cerebral cortex in a new way. Success for the learner means making a global change in knowledge, emotional response, and self-image as a learner of math. The students and their teacher must share the belief that past failure need not predict future success, and the math classroom has to become a possibility space for all learners.
Ashman, Melissa (May, 2010). Brains Research Centre: Uncovering the science behind the "a-ha" moment. In Vancouver Coastal Health Research Institute News & Information.
Ehrenberg, Rachel (June, 2010). Eureka, brain makes real mental leaps. In Science News.
(May, 2010) Eureka! Natural Evidence for Sudden Insight. In Science Daily.