This all assumes that the theory of learning stages and plateaus does not result in late bloomers.
Some people appear to expand their learning potential up to a point, plateau for a while, and then accelerate. So their learning potential expands in leaps, not continuously. These folks could reach a level of math acuity and if exposed to the best math teachers with the most oustanding techniques, they would never grow until they break that learning barrier. I will tell you that I do not know if the "education community" accepts this, but I can tell you damn sure it happens a lot. If you chop out the late bloomers, you lose a huge chunk of amazing contributors. Malcolmm On Wed, Apr 10, 2013 at 10:19 AM, Juliana Mulroy <[email protected]> wrote: > There's a difference between biologists as a cultural group 1) embracing > and celebrating the contributions of mathematics to biology, and > 2) requiring mathematics at a certain age / stage to be able to progress > in biology. The latter acts as a selective filter /barrier / turnoff that > may divert some very promising biologists into other careers -- just as > "too much like farming" initially did for you. At a critical point in your > education "farming" (and rote memorization) moved you into theoretical > physics. The imposition of a math requirement at a stage when many > students might look at math just as you did biology, perhaps because of > poor teaching that had not conveyed the excitement of the field and the > relevance and power of mathematics to many areas of biology, is more likely > to move talented students out of science altogether. > > There is a temptation to look at successful people in a field, look at > their educational backgrounds, and model curricula based on that > information. As scientists we should know better. Those who are successful > were the ones who passed through a series of filters. Do we really want a > smaller group of talented biologists? What would we lose? > > No one is saying math has no applications in biology, let alone that it > doesn't provide unique insights. (I think you describe the latter well, and > that seems more than just an application of one field onto another.) > > You conclude: > > *Yet, there can be a huge role for mathematics in biology, if only biology > would accept math.* > * > * > There's a difference between biology accepting mathematics as important, > and mandating a particular level of it, especially at a particular > stage, for all biologists if they want to learn about and contribute to > biology. Surely there is room in your current field for those who have a > non-mathematical understanding of biology. > > In fact, this Op-Ed reads like someone whose personal academic approach was > not accepted by biologists and/or funding agencies. Sort of a personal sour > grapes story: > > *I* *no longer use calculus in my studies: so few resources, so many > environmental challenges, so little time, so I've moved on to writing books > about the environmental challenges brought on by urbanization. * > > I agree that there are "so many environmental challenges," and am grateful > for every single person out there who has achieved enough environmental > /ecological literacy to be able to contribute constructively to this work. > Looking back at former students, that includes those who would have left > biology in a heartbeat if there had been a significant mathematical > requirement. Some went on to get much more than would have been required, > once they saw in grad school how useful it could be to their interests. > Others have been able to use their biological education very effectively > without getting more math. > > Julie Mulroy > > On Wednesday, April 10, 2013, Will Wilson wrote: > >> All, >> Here's my drafted op-ed in response. Thanks to whoever posted the >> initial Op-Ed! >> Cheers, >> Will Wilson >> Assoc. Prof. Biology >> Duke Univ. >> >> >> My area of science is (or, rather, was) mathematical evolutionary ecology. >> It offers an exciting blend of biological, mathematical, and computational >> challenges. As the occassional superstar biologist proclaims, people >> generally enter biology because of implicit interest of all things squirmy, >> but another factor might be the absence of mathematical demands in the >> earliest exposures when compared with subjects like physics and chemistry. >> This absence of math is a "cultural" phenomenon, however, and not because >> math has no applications to biology. It is perpetuated because the culture >> permits budding scientists to not confront and overcome their mathematical >> fears at an early age. >> >> I grew up on a farm in central Minnesota, and was the first in my extended >> family to get a doctorate. Early on I loved science, it was fun, and farm >> chores were not. I did pretty well in math and computers, and earned a >> Ph.D. in theoretical physics. I was fascinated that one could put together >> math and physical phenomena, and actually derive the numbers that came out >> of experiments. I also didn't like the memorization of biology, when the >> names of all those cell parts slipped from my brain faster than a leaky >> membrane. I grew up in an academic culture where the rough thinking was >> that if your experimental results depended on statistical interpretations, >> your math wasn't very good or the science wasn't very firm. >> >> After an extended 8-year postdoctoral re-education in Canada and >> California, I got a faculty position doing "interdisciplinary science" in a >> department of zoology, in part because interdisciplinary was popular and >> supported at the time. It was an exciting time for a young scientist >> applying mathematical and computational approaches to answer questions >> regarding the mechanisms determining the abundance and distribution of >> organisms. >> >> In theoretical biology, like all scientific fields, the focus is not on >> data. Instead, scientists are obsessed with questions. A scientist starts >> with a puzzle -- physical, biological, or sociological -- then starts >> thinking about it using one's scientific knowledge. I used math and >> computers, and in my theory work the questions concerned the following: Why >> do mutualisms between organisms persist when cheaters abound? What features >> determine spatial variation in population densities? How does smart >> foraging affect animal grouping? What role does foraging play in the >> coexistence of species? Why are some plant species hermaphroditic while >> others have two genders? Why do many hermaphroditic plant species >> self-fertilize? >> >> Sure, many biologists address these questions by going out into the field >> and doing experiments -- exactly what they love to do! To me, that's just >> too close to farming (which, as it turns out, seems quite attractive these >> days), but another approach involves sitting back with a pad of paper and >> writing down the important variables and thinking about the interactions. >> Expressing these as mathematical equations -- often sets of differential >> equations involving space, time, and life history states -- leaves a >> scientist with very challenging mathematical problems. I've used things >> from simple algebra to series manipulations to partial differential >> equations and statistical dynamics. There is no end to the mathematical >> excitement to be found in biology. >> >> The only difference between the mathematical challenges available in >> physics and biology is that most biologists never learn the mathematical >> tools because the culture of biology doesn't require it. That culture >> doesn't appear likely to change, and the last decade or so has seen a huge >> emphasis on huge amounts of genomic data that only statistical analyses can >> seemingly approach. >> >> Since about 2000, there has also been a strong emphasis on science that >> adds directly to the gross domestic product, and areas like mathematical >> evolutionary ecology involves three things the Bush Administration >> certainly did not like. Indeed, the National Science Foundation division >> that funds ecology has so little resources that grant proposals have >> rejection rates exceeding 90 percent, and a topic involving math has very >> little chance. Likewise, the discipline doesn't generate patents or >> further the sports programs that higher education now values. >> >> I no longer use calculus in my studies: so few resources, so many >> environmental challenges, so little time, so I've moved on to writing books >> about the environmental challenges brought on by urbanization. Yet, there >> can be a huge role for mathematics in biology, if only biology would accept >> math. >> >> >> -- >> http://www.biology.duke.edu/**wilson/<http://www.biology.duke.edu/wilson/> >> New Book: >> http://www.**constructedclimates.org/<http://www.constructedclimates.org/> >> -- Malcolm L. McCallum Department of Molecular Biology and Biochemistry School of Biological Sciences University of Missouri at Kansas City Managing Editor, Herpetological Conservation and Biology "Peer pressure is designed to contain anyone with a sense of drive" - Allan Nation 1880's: "There's lots of good fish in the sea" W.S. Gilbert 1990's: Many fish stocks depleted due to overfishing, habitat loss, and pollution. 2000: Marine reserves, ecosystem restoration, and pollution reduction MAY help restore populations. 2022: Soylent Green is People! 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