There is a common belief in education – that visual mathematics is for lower level work, and for struggling or younger students, and that students should only work visually as a prelude to more advanced or abstract mathematics. As Thomas West, author, states, there is a centuries-old belief that words and mathematical symbols are “for serious professionals – whereas pictures and diagrams” are “for the lay public and children”. This idea is an example of a damaging myth in education, and this paper will present compelling brain evidence to help dispel the myth. We will also provide examples of ways that visual mathematics may be integrated into curriculum materials and teaching ideas across grades K-16. The provision of ways to see, understand and extend mathematical ideas has been under developed or missed in most curriculum and standards, that continue to present mathematics as an almost entirely numerical and abstract subject. Yet when students learn through visual approaches, mathematics changes for them, and they are given access to deep and new understandings. The brain evidence we will share, helps us understand the impact of visualizing and seeing, to all levels of mathematics, and suggests an urgent need for change in the ways mathematics is offered to learners.
Read also: Perceiving fingers in single-digit arithmetic problems
Why Kids Should Use Their Fingers in Math Class
Does finger training increase young children’s numerical performance?
Posted in Brains, Education, Learning, Maths, Student, Visual
Tagged brain, education, learning, maths, student, Visual
When Albert Einstein died in 1955, his brain was removed, weighed and measured, preserved in formalin, photographed, and sectioned for microscopic study. Although we often think of technologic breakthroughs as coming from corporations or industry sectors, ideas come from individual brains. Human brain tissue is the source of the invention, conceptualization, and implementation of new technologies. Einstein was the preeminent genius of his era and one of the greatest scientists of all time, on par with Leonardo Da Vinci and Isaac Newton (whose brains were not preserved). What can we learn from the anatomy of Einstein’s brain that might lead to the creation of more new ideas and advanced technologies? In 1955, the neurosciences were in their infancy. In 1949 Moniz was awarded the Nobel Prize for the frontal lobotomy in which white matter connections of the brain are severed with an “ice pick” instrument, a procedure now considered barbaric by modern medicine.
Neuroscience has advanced by leaps and bounds since then, and recent insights have been made on the uniqueness of Albert Einstein’s brain.
This paper begins with a historical review of the mutual influence of physics and psychology, from Freud’s invention of psychic energy inspired by von Boltzmann’ thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing toward foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making.
Scholars in the area of Evolutionary Sociology and Biosociology explicitly seek to examine the interplay of social and environmental factors with evolved biological factors and its implications for social behavior. It is a broad area covering a wide array of research topics and methodologies. Neuro sociologists in the area describe the neural circuitry underlying social processes, such as empathy, understanding, and the social creation of the self and self-identity. Other researchers examine the effects of our evolutionary history on emotional processes that influence social behaviors and the implications for humans of comparative primatology. There are researchers examining the role of stress hormones on life course events and the effects of other hormonal levels (e.g., testosterone) on social behaviors as well as the reciprocal effect of social situations on hormonal states. Other researchers examine the correlation between genes and social behaviors and how environments influence gene expression (epigenetics). Researchers using the techniques of behavioral genetics apportion the percentage of variation in social behaviors that can be attributed to genetic factors. Some bio sociologists examine how aspects of human appearance including voice, body, and face influence social interactions. Others test hypotheses drawn from evolutionary biology on aggregate social outcomes.
Posted in Biosociology, Evolution, Evolutionary sociology, Genes, Hormones, Sociobiology, Sociology
Tagged Biosociology, evolution, Evolutionary sociology, genes, Hormones, Sociobiology, Sociology
I get a lot of email asking me for advice on paper publishing. There’s no way I can make time to read all these drafts, let alone comment on them. But simple silence leaves me feeling guilty for contributing to the exclusivity myth of academia, the fable of the privileged elitists who smugly grin behind the locked doors of the ivory tower. It’s a myth I don’t want to contribute to. And so, as a sequel to my earlier post on “How to write your first scientific paper”, here is how to avoid roadblocks on the highway to publication.
There are many types of scientific articles: comments, notes, proceedings, reviews, books and book chapters, for just to mention the most common ones. They all have their place and use, but in most of the sciences it is the research article that matters most. It’s what we all want, to get our work out there in a respected journal, and it’s what I will focus on.
The main proposition of this paper is that science communication necessarily involves and includes cultural orientations. There is a substantial body of work showing that cultural differences in values and epistemological frameworks are paralleled with cultural differences reflected in artifacts and public representations. One dimension of cultural difference is the psychological distance between humans and the rest of nature. Another is perspective taking and attention to context and relationships. As an example of distance, most (Western) images of ecosystems do not include human beings, and European American discourse tends to position human beings as being apart from nature. Native American discourse, in contrast, tends to describe humans beings as a part of nature. We trace the correspondences between cultural properties of media, focusing on children’s books, and cultural differences in biological cognition. Finally, implications for both science communication and science education are outlined.
Posted in Communication, Cultural context, Culture, Science, Science communication, Science education
Tagged communication, cultural context, culture, science, Science communication, Science education
The hypothesized role of rapid eye movement (REM) sleep, which is rich in dreams, in the formation of new associations, has remained anecdotal. We examined the role of REM on creative problem solving, with the Remote Associates Test (RAT). Using a nap paradigm, we manipulated various conditions of prior exposure to elements of a creative problem. Compared with quiet rest and non-REM sleep, REM enhanced the formation of associative networks and the integration of unassociated information. Furthermore, these REM sleep benefits were not the result of an improved memory for the primed items. This study shows that compared with quiet rest and non-REM sleep, REM enhances the integration of unassociated information for creative problem solving, a process, we hypothesize, that is facilitated by cholinergic and noradrenergic neuromodulation during REM sleep.
Posted in Brain networks, Creative problem solving, Creativity, Dreams, Humans, Memory, Sleep
Tagged brain networks, Creative problem solving, creativity, Dreams, human, memory, sleep
To be rational is to be able to reason. Thirty years ago psychologists believed that human reasoning depended on formal rules of inference akin to those of a logical calculus. This hypothesis ran into difficulties, which led to an alternative view: reasoning depends on envisaging the possibilities consistent with the starting point—a perception of the world, a set of assertions, a memory, or some mixture of them. We construct mental models of each distinct possibility and derive a conclusion from them. The theory predicts systematic errors in our reasoning, and the evidence corroborates this prediction. Yet, our ability to use counter examples to refute invalid inferences provides a foundation for rationality. On this account, reasoning is a simulation of the world fleshed out with our knowledge, not a formal rearrangement of the logical skeletons of sentences.
Posted in Abduction, Deduction, Induction, Logic, Rationality, Reason, Reasoning
Tagged Abduction, Deduction, Induction, Logic, Rationality, reason, Reasoning
Memory illusions and distortions have long been of interest to psychology researchers studying memory, but neuropsychologists and neuroscientists have paid relatively little attention to them. This article attempts to lay the foundation for a cognitive neuroscience analysis of memory illusions and distortions by reviewing relevant evidence from a patient with a right frontal lobe lesion, patients with amnesia produced by damage to the medial temporal lobes, normal aging, and healthy young volunteers studied with functional neuroimaging techniques. Particular attention is paid to the contrasting roles of prefrontal cortex and medial temporal lobe structures in accurate and illusory remembering. Converging evidence suggests that the study of illusory memories can provide a useful tool for delineating the brain processes and systems involved in constructive aspects of remembering.
Springing from memory and imagination, mind wandering is a mental state occupying as much as half of our waking life, involving a shift of attention away from the external environment and toward task-unrelated concerns. Although mind wandering may play an important role in planning and creativity, it is also widely associated with negative mood and degraded performance on measures of vigilance, working memory, fluid intelligence, and reading comprehension. The intrinsically subjective and spontaneous nature of mind wandering has made it difficult to investigate with direct experimental manipulations. Researchers have used various approaches to do so indirectly, by altering related factors such as mood, motivation, the amount of time spent on a task, or cognitive load. However, these factors may influence various cognitive processes besides mind wandering. Moreover, these approaches do not directly implicate underlying neural mechanisms of mind wandering. In contrast, Axelrod et al. demonstrate that mind wandering can be increased by direct experimental manipulation of brain activity using transcranial direct current stimulation (tDCS) to the prefrontal cortex (PFC). The article by Axelrod et al. thus marks a new era for research into mind wandering and previews some of the insights that continued methodological advances will likely make possible.