The Brain Image from Brain Facts: A Primer of the Brain and the Nervous Sysem, p Society for Neuroscience th Street, NW, Suite 1010 Washington, DC USA
Image from Brain Facts: A Primer of the Brain and the Nervous Sysem, p Society for Neuroscience th Street, NW, Suite 1010 Washington, DC USA The Neuron
“Any nervous system, whether it belongs to a human or a leech, consists primarily of a packed bundle of cables. Each neuron has an axon, a long cable that conveys information through waves of depolarization called action potentials. Each neuron also possesses a bushy arborization of dendrites that receive the signals coming from other nerve cells. When an action potential reaches a synapse – the contact zone between one neuron’s axon terminal and another’s dendrite – neurotransmitter molecules are released from the nerve terminal, and tie on to other specialized molecules, called receptors, inserted within the dendritic membrane. This causes the receptors to alter their shape. They switch to an ‘open’ configuration in which a channel opens through the cell membrane, letting ions flow into the cell. Very schematically, this is how a nerve impulse crosses the barrier of the cellular membrane and is transmitted from one neuron to the next. Since ions carry an electric charge, their movement across the cellular membrane and within the dendritic tree produces a very small amount of current. Each neuron thus behaves as a tiny electric generator.” (Dehaene, 2011, The Number Sense, How the Mind Creates Mathematics, p.205)
“[Consider]... a baby becoming aware of light coming from a window. First, the baby perceives a distinct line of contrast at the edges of the window (notice the what and where in window edge) in her room. Later, the edges that enclose the window define a new object, the window itself. Even later, the spatial location of the window (it is in the wall separating inside from outside) leads the child to understand the window better; it lets light into the house. The child learns to move things closer to the window to see them better. Later, the child may realize that seeing things better reveals physical relationships better, and from there it is a small step to the metaphor of casting light on ideas or shining light on a subject so we can understand it better and become enlightened. Even later, in college perhaps, the young adult may encounter the term enlightenment, and connect his or her original insight with understanding a historical period in philosophy. As adults, we become aware of more complex ideas, identify new categories, and see new relationships throughout a lifetime of personal growth and development, as we construct our own ‘enlightenment’ of life.“ Zull, James E., (2011). From Brain to Mind, Using Neuroscience to Guide Change in Education (p. 91)
Neurons that fire together, wire together.
There is evidence that sleep allows for restructuring of neuronal networks (new memory representations) for more efficiency. Sleep’s neuronal restructuring facilitates insight, recognition of patterns, shortcuts, and hidden rules.
Your students are not going to grasp the profound aspects of your lectures and assignments until they have had time to Sleep on it!
Image from Zull, James E., (2011). From Brain to Mind, Using Neuroscience to Guide Change in Education (p. 86) S sensory function area of cortex M motor function area of cortex I integrative function area of cortex
Arithmetic’s “Triple Code” Quantity Code, Intraparietal Cortex, L/R Hemispheres – numeracy; number comparison; proximity judgment; approximation; quantity manipulations such as subtraction Arabic Code, Visual Cortex, L/R Hemispheres – Arabic reading and writing; multidigit calculations Verbal Code, Temporal Lobe, L Hemisphere – Spoken comprehension and production; Rote memorization such as multiplication tables Modified from Dehaene, Ch. 9, The Calculation Brain, in Mind, Brain, & Education, Neuroscience Implications for the Classroom, D. A. Sousa, Editor, 2010
From Dehaene, 2011, The Number Sense, How the Mind Creates Mathematics, p. 180
From Dehaene, 2011, The Number Sense, How the Mind Creates athematics, p. 180
Calculation Prefrontal Cortex – Central resource that cannot be shared with other tasks Effortful Process, Deep Focus Strategy Choice Working Memory – retrieval from “triple code” areas; back associative (integrative cortex)
Hand your students a simple calculator.
“I would contend that the most effective way of brining neuroscience into the classroom is to provide teachers with access to knowledge that neuroscientific studies are yielding. This knowledge will inform teachers’ conceptualization of the learning... And therefore their pedagogical approaches.” From Ansari, Ch. 10, The Computing Brain, in Mind, Brain, & Education, Neuroscience Implications for the Classroom, D. A. Sousa, Editor, 2010
Animals and Numeracy Babies and Numeracy
Students need to know their brains were born with a sense of number. Indeed even animal brains, (rats, dogs, birds, etc.) are wired for a sense of number.
If human brains are biological predisposed to have a sense of number, what causes math anxiety? Why do so many become uncomfortable with numbers and their manipulation?
Home Address: Charlie David lives on George Avenue. Charlie George lives on Albert Zoe Avenue. George Ernie lives on Albert Bruno Avenue. Professional Address: Charlie David works on Albert Bruno Avenue. Charlie George works on Bruno Albert Avenue. George Ernie works on Charlie Ernie Avenue. Dehaene, 2011, p. 113
Hand your students a calculator!
Associate (integrate) difficult concepts with concepts already known and understood by the students. Dehaene calls this “mental modeling.” For example, the adult number line, negative numbers, and overdrawing a checking account.
Different types of math, different neuronal networks.
It does not follow that a student who performs poorly at arithmetic will also perform poorly at algebra.
Math Geniuses and Prodigies Idiot Savants – often autistic; large memory storage; isolation allows focus Great Calculators – numbers have personalities; extraordinary devotion of time All have passion for the subject. French naturalist Buffon, “genius is but a greater aptitude for patience.”
Neuroscientists now think that the time and effort one dedicates to a domain modulates the extent of its representation in the cortex. Students need to understand that “giftedness” is a function of effort. This is particularly true in mathematics where students believe only certain people are born with mathematical ability.
The integration of the front cortex “involves the intentional combination of separate networks of neurons to solve problems.” (Zull, 2011, p. 92) Working memory resides in the frontal cortex, and, in general, we can hold and manipulate no more than seven elements at a time.
Working memory is the primary machinery for planning and problem solving. “Remembered” stimuli in working memory can disappear immediately if there is interference from secondary stimuli.
Educators often overload working memory in their hurry to “cover” material. This can be avoided by ▪ Focusing on how much is understood, rather than how much is “covered.” (CATs, clicker technology and related i-phone apps) Incorporation of repetition and summaries. Decrease the length of classes, increase the frequency with which they meet, e.g. 40 minute classes that meet each workday instead of 90 minute classes that meet twice a week.
The Reward Circuit : Perception of possible reward → Dopamine driven, reward seeking (sensory/postsensory back cortex) behavior (nucleus accumbens-front cortex) ↓ blocking Analysis of perception-memory (back association cortex) ↑ ↓ ↑ Warning of negative outcome or suppression (amygdala) → ↑
Reduce threat/fear responses by encouraging a mistake-rich environment. When frustrated or overwhelmed, tell students to take a break and visualize success, or any past success.
“ My collaborators and I have elaborated a theory we call ‘global neuronal workspace.’ We propose that consciousness is global information broadcasting within the cortex: it arises from a neuronal network whose raison d’etre is the massive sharing of pertinent information throughout the brain. The philosopher Daniel Dennett aptly calls this idea ‘fame in the brain.’... Thus, consciousness has a precise role to play in the computational economy of the brain – it selects, amplifies, and propagates relevant thoughts. ” From Dehaene, 2014, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts.
“ What circuit is responsible for this broadcasting function of consciousness? We believe that a special set of neurons diffuses conscious messages throughout the brain: giant cells whose long axons crisscross the cortex, interconnecting it into a integrated whole... When enough brain regions agree about the importance of incoming sensory information, they synchronize into a large-scale state of global communication. A broad network ignites into a burst of high-level activation – and the nature of this ignition explains our empirical signatures of consciousness.” From Dehaene, 2014, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts.
“ Although unconscious processing can be deep, conscious access adds an additional layer of functionality. The broadcasting function of consciousness allows us to perform uniquely powerful operations. The global neuronal workspace opens up an internal space for thought experiments, purely mental operations that can be detached from the external world. Thanks to it, we can keep important data in mind for an arbitrarily long duration. We can pass it on to any other arbitrary mental process...” From Dehaene, 2014, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts.
“Even complex operations linking perception to action can unfold covertly, demonstrating how frequently we rely on an unconscious ‘automatic pilot.’ Oblivious to this boiling hodgepodge of unconscious processes, we constantly overestimate the power of our consciousness in making decisions – but in truth, our capacity for conscious control is limited.” From Dehaene, 2014, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts.
Much of your unconscious brain activity is like a council of statisticians using Bayesian statistics to analyze incoming stimuli and work on a variety of problems.
Nearly all the brain’s regions can participate in both conscious and unconscious thought.
“Our unconscious perception uses incoming sense data to compute the probability that colors, shapes, animals or people are present in our surroundings. Our consciousness, on the other hand, offers only a glimpse of the probabilistic universe – what statisticians call a ‘sample’ from this unconscious distribution. It cuts through all ambiguities and achieves a simplified view, a summary of the best current interpretation of the world, which can then be passed on to our decision–making system.” From Dehaene, 2014, Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts.
Subliminal priming experiments, confirmed with observed MRI observations that indicated the number sense regions were activated, indicate unconscious extraction of a number’s meaning.
“Freud was right: consciousness is overrated. Consider the simple truism: we are conscious only of our conscious thoughts. Because our unconscious operations elude us, we constantly overestimate the role that consciousness plays in our physical and mental lives.” Dahaene, 2014 There is mounting evidence that many of the mental activities that we consider hallmarks of conscious thought are really occurring on an unconscious level, to include mathematics.
There is now strong Evidence that Hadamard (1945) is correct in his identification of the stages of mathematical discoveries: Initiation – conscious exploration of a problem; launches the unconscious mind on a quest Incubation – unconscious; mind vaguely preoccupied with the problem but shows no conscious sign of working hard on it Illumination – conscious; solution miraculously appears in consciousness Verification – conscious; slow and effortful
The Mystery of the Chicken Sexers and the Plane Spotters Eagleman (2011). Incognito: The Secret Lives of the Brain, pp
Explicit, Conscious Learning High energy burn High Focus Brain is cued to work on task or problem Neuronal networks begin to be formed Practice Re-cues brain Relevant neuronal networks are strengthen Implicit Learning Low energy, efficient burn Learning is burned into the brains circuits and is now “hard-wired” Tasks now reside in subconscious and can be done “without thinking”
Bransford, J., Donovan, S., & Pellegrino, J. (Eds.) (2000). How people learn: Brain, mind, experience and school. Washington, DC: National Academy Press. (Available for free download at Campbell, J. I. D., editor (2004). The handbook of mathematical cognition. New York: Psychology Press Dehaene, S. (2014). Consciousness and the brain: Deciphering how the brain codes our thoughts. New York: Penguine Group (USA) LLC. Dehaene, S. (2011). Reading in the brain. New York: Oxford University Press, Inc. Dehaene, S. (2011). The number sense, how the mind creates mathematics. New York: Oxford University Press, Inc. Eagleman, D. (2011). Incognito: The secret lives of the brain. New York: Vintage Books
Hadamard, J. (1945). An essay on the psychology of invention in the mathematical field. New York : Princeton University Press Sousa, D. A., editor (2010). Mind, brain, and education: Neuroscience implications for the classroom. Bloomington, IN: Solution Tree Press Society for Neuroscience (2008) Brain facts: A primer of the brain and the nervous system. Washington, DC, Sousa, D. A. (2011). How the brain learns, 4 th ed. Thousand Oaks, CA: Corwin, A SAGE Company Zull, J. E. (2011). From brain to mind: Using neuroscience to guide change in education. Sterling, VA: Stylus Publishing, LLC.