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What role might images and visualizing play in the growth of mathematical understanding? Due to the many years of symbolic representation of mathematics, there is a reported reluctance by students and educators to engage visually with mathematics (Healy & Hoyles, 1996). Yet, as Zimmerman and Cunningham (1991) point out, the intuition that mathematical visualization affords is not a vague kind of intuition but is what gives depth and meaning to understanding.
December 1998 - June 2005
Rockyview School Division
- High School Mathematics teacher
Casanova's research is with individuals labelled as neurodevelopmentally disabled. He has been studying their cognitive profiles, neuroimaging studies and results of their postmortem examination. From this cumulus of work he has postulated that dyslexia and autism stand at the tail-ends of a spectrum describing different cognitive profiles. As a gr...
Early years mathematics experiences have been shown to be a significant predictor for students' school readiness and future mathematics achievement. Previous research also indicates an important connection between emotion and mathematics learning. How do students in early years education in Alberta describe their emotional relationship with mathema...
Hi David et al, I'm delighted that others are interested. When I got started thinking about the scientific evidence wrt consciousness, it was (a) taboo, and (b) interpreted in very specific ways. For example, a common euphemism was "perception" _ because that was safe. But when you compare cs vs. ucs perception (as in backward masking) you get visual cortex activation with lower amplitude and spread, as shown by Dehaene and colleagues. That tell us something new, and I believe it replicates for audition. (Systematic replications should be much more common). Another problem was circular explanation. "Conscious access" was called "awareness" or "attention to" something. But that explains nothing UNLESS you have an independent source of evidence to break the circularity. Other confusions were rife. The conscious (waking) STATE was confused with consciousness OF something. Visual imagery was not fully recognized until Steve Kosslyn, and so on. Attention was used interchangeably with consciousness. All that has cleared up now, either explicitly, or implicitly, by usage. For example, my impression is that attention is used for voluntary control of access to some conscious content. As in voluntary head movements, but not for spontaneous, unconsciously directed eye movements (most fast eye movements are that). As long as these practical usages are clear, they are good enough to avoid confusion. Recent work coming from animal and human electrophysiogy is fabulous. Buszaki's book is important reading. Invasive e-physiology has 1000x the S/N ratio as scalp recording. Both deep sleep and waking look strikingly different at that resolution. Animal researchers have known that for years, but human e-phys researchers were held back by the ethical constraints of working with humans. Penfield was right. Other methodologies are reaching that kind of spatiotemporal resolution, and have their own pros and cons, of course. Our 2013 Frontiers overview still holds water, mostly. My Scholarpedia article is still mostly up to date. But the frontier is moving fast. It's very exciting. Theorists need to integrate the wealth of evidence, clarify ambiguous usages and confusions, and so on. There are still many of them. I believe our theory writing needs much improvement, with the emphasis on INDUCTIVE thinking. (Some writers seem to think this is a form of math, but that's indefensible empirically). A recent article confused the brainstem nuclei involved with the STATE of consciousness with the mostly cortical regions that support CONTENTS of consciousness, like the ventral visual stream. There is appropriate debate about the region of visual integration (MTL or PFC? or both?). I guess I'm a "corticocentrist," but that does NOT rule out other regions, especially given the long evolutionary history of csns -- at least 200 million years for neocortex. Walter Freeman, our late friend, convinced me that paleocortex (incl hippocampus) has to be involved with gustatory-olfactory consciousness. The work on the anterior insula strongly implicates interoceptive consciousness, as in feelings of nausea. Generalization between species is now much more convincing because we have the human and macaque, plus rodent genome. The avian pallium is now considered to be much like cortex in mammals. So there is a TON of work to do. Each question deserves discussion and debate, based on the best evidence available. I HOPE YOU JOIN !!!!