by Judy Willis M.D., M.Ed., radteach.com
“Algebra is a way of arranging knowns and unknowns in equations so that the unknowns are made knowable. The three fundamentals involved…are commutation, distribution, and association. Once a student grasps the ideas embodied by these three fundamentals, he is in a position to recognize wherein ‘new’ equations to be solved are not new at all. Whether the student knows the formal names of these operations is less important for transfer than whether they are able to use them.”
Jerome Bruner’s The Process of Education, Harvard University Press. 1977
Long-Term Memory Building and Maintaining
Grasping the structure of a subject is understanding and holding it in a relevant memory category. This becomes a neural network that be used for transfer, where it can link with other networks for application beyond the original learning situation.
Constructing neural networks is achieved not by rote memorization, but by mental manipulation where new input and prior knowledge are related meaningfully. Concept knowledge in math is the authentic way of achieving long-term memory and is best achieved by learning how things are related.
Repetitive stimulation of the neuronal circuits holding the information is necessary for the memory to be maintained and even for the neuronal connections to remain in place and not be pruned. The mental manipulation and active processing of learned information through the executive functions especially in the prefrontal cortex stimulates memory circuits. It is these networks, activated during mental manipulation of the new information through prioritizing, comparing/contrasting (similarities/differences), deduction (constructing new knowledge from existing information), and induction that stimulation of the memory storage areas increase the strength of the neural networks through additional dendrite sprouts, more synapses, and thicker myelin around axons that speeds transmission between neurons.
Practice really does make permanent–as long as the practice involves active mental manipulation, construction of new ideas, and truly using the new information in different ways that it was originally learned.
To be clear, mental manipulation is not what happens when students passively repeat procedures over and over on worksheets. For example when students review learned material by solving well designed word or story problems, they are making judgements about what question is being asked, analyzing the data provided to determine what is needed to reach a solution and what is extraneous, and considering the procedures the know to see which might be useful.
To carry out these executive functions there is information exchange from the executive function networks to the areas of stored memory in categories deemed relative to the problem.
These stored memories are found throughout the various lobes of the brain depending on the different sensory modalities that carried the input into the brain. If the knowledge was acquired through multisensory learning and review, there is activation in the visual, tactile, auditory, and kinesthetic input receptor cortexes when the problem is considered.
Similarly, when learning is reviewed by authentic incorporation in new learning, the storage circuits are reactivated. For example, each time a long division problem is done correctly there is practice of subtraction and multiplication.
The Brain Likes Practice
When learning is examined through follow-up lessons using open-ended discussions, students are encouraged to seek multiple approaches to solving problems and to verbalize and communicate with classmates.
This also provides opportunities for more student engagement. When classmates add new approaches to the problem solving, the other students extend their established, stored memory patterns and categories to incorporate the new insights.
It is not only neuroimaging evidence of multicentric brain cortex activation (metabolism) during problem-solving, but also of activation of emotional networks throughout the limbic system that can be stimulated by problem solving.
These areas that are important in memory consolidation and retrieval such as the amygdala, hippocampus, and basal ganglion can be “exercised” and receive increased blood flow and neuronal network fortification when the stored information is associated with positive emotional experiences.
These are the activities described earlier as having a beneficial influence on the amygdala and dopamine release related to pleasure and enjoyment influence on memory when these activities are incorporated in the teaching or review.
Through practice, these are the powerful lessons you create to incorporate personal interest, prior knowledge, global real world connections, surprising discrepant experiences, and the intrinsic reward of achieving challenges the students feel are significant.
Stigler, J. & Hiebert, J. (2004). Improving mathematics teaching. Educational Leadership, 61(5), 12-17; this article was excerpted from a full article that was first published in STEM Magazine; image attribution flickr user flickeringbrad