Calculus makes its way into the news in subtle but noticeable ways; in the article, an example is provided explaining how the ozone may be healing itself because the amount of ozone damaging chemicals in the air is lowering. The article, however, appeared to confuse the idea of "amount of damaging pollutants" with "the rate that damaging pollutants are being placed into the air". The amount of pollutants are not depleting, however, the rate of increase is decreasing and leveling off, which is regardless good news, though it'd be better to hear that the ozone was actually healing itself and not taking lighter punches.
This idea of rate relates to our derivatives. The derivative, if graphed, was likely increasing rather quickly, and as it hit 1989 it began leveling out toward a slope of 1. If things keep going well this way, the graph will hopefully become concave down as the rate of pollutants produced becomes negative (i.e. pollutants being taken out of the air) and the slope takes on an increasingly negative rate until the ozone is once again completely intact.
http://www.msnbc.com/rachel-maddow/watch/flint-home-posts-highest-lead-reading-ever-672191555650
This article and many others like it detail the environmental catastrophe of Flint, Michigan, where water quality is being destroyed. In this article, lead was found to be twice the previous record found in tap water. Though there isn't a whole lot of "calculus" to this statement, there is calculus to the story; the amount of lead in water should be below a certain point (below a "carrying capacity"), the rate of change of water pollutants indicates the pollution levels of the new water source (due to the sudden increase in pollutants coinciding with fracking), and the rate of change needs to be negative in order for the water to be cleaner.
Sunday, April 24, 2016
Friday, April 15, 2016
Reflection 9
Learning is a life process that can occur through failure and success, which was described in The Practicing Mind. Failure has the ability to teach a lesson, perhaps better, than learning through success, as offered through this article. It's certainly relatable for some of our greatest life lessons; it taught us how to balance on a bike and what you shouldn't say in a relationship, and it can be applied to academic settings.
Calculus can integrate itself into this rule; through struggle we can learn in a way that'd get these lessons to stick. But, as the article mentions, the real goal is to propose a challenge that is reasonably achievable through the student's ability. The article used a bit of "clickbait" in proposing an idea that seems outlandish and leads the reader to believe that letting students learn on their own in difficulty leads to a more efficient lesson. Obviously, it ends in saying that with the ability to fail followed by success afterward, learning is perhaps more efficient, which is much more plausible.
This follows some basic ideas of learning and psychology; aversive results (failures and struggling) are avoided, and pleasurable results are seeked out (success, rewards). However, in the spirit of using science to discuss learning, it is determined that using rewards is twice as effective as resulting in a learned behavior than punishment; this is because one simply learns what to avoid and not what to seek when facing punishment. Some people fall into a cyclic-punishment where they simply are faced with so much challenge that they become frustrated, and oftentimes don't find solutions (or at least the right ones). Eventually, they just associate the whole practice of calculus with punishment-like results, and the present-day hate for math is born.
The ability to fail correctly comes with a lot of weight; it needs to be done in such a Goldilocks fashion. The challenge needs to be reasonably within the student's grasp (if they can't reach it, then it just becomes failure punishment), guidance needs to be available, and the failure shouldn't be something too devastating (because why would you try it again if there's a huge risk?). The sensitive nature of it is just why some people head down a path of hating certain subjects when at one point they were on the verge of unlocking its secrets, but due to the fault of a crappy failure setup, it went awry.
This is something I have seen in this class (as I've mentioned in other blogs) in homework problems that have kept me thinking for hours to no success, or in classes like Chemistry where equilibrium problems are now my least favorite when I used to be extremely efficient with the concept in high school.
Sometimes, I feel like this concept of letting students fail can be used as an excuse for a highly inefficient learning system at the hands of the wrong teacher where students just perish, and other times it can be orchestrated perfectly in unexpected scenarios.
Sometimes, it takes just getting back on the bike, because we know that in the end, it will be worth it. Salvaging that intrinsic worth can be what pulls us back into action when we feel that all we are capable of doing is falling off the bike.
Calculus can integrate itself into this rule; through struggle we can learn in a way that'd get these lessons to stick. But, as the article mentions, the real goal is to propose a challenge that is reasonably achievable through the student's ability. The article used a bit of "clickbait" in proposing an idea that seems outlandish and leads the reader to believe that letting students learn on their own in difficulty leads to a more efficient lesson. Obviously, it ends in saying that with the ability to fail followed by success afterward, learning is perhaps more efficient, which is much more plausible.
This follows some basic ideas of learning and psychology; aversive results (failures and struggling) are avoided, and pleasurable results are seeked out (success, rewards). However, in the spirit of using science to discuss learning, it is determined that using rewards is twice as effective as resulting in a learned behavior than punishment; this is because one simply learns what to avoid and not what to seek when facing punishment. Some people fall into a cyclic-punishment where they simply are faced with so much challenge that they become frustrated, and oftentimes don't find solutions (or at least the right ones). Eventually, they just associate the whole practice of calculus with punishment-like results, and the present-day hate for math is born.
The ability to fail correctly comes with a lot of weight; it needs to be done in such a Goldilocks fashion. The challenge needs to be reasonably within the student's grasp (if they can't reach it, then it just becomes failure punishment), guidance needs to be available, and the failure shouldn't be something too devastating (because why would you try it again if there's a huge risk?). The sensitive nature of it is just why some people head down a path of hating certain subjects when at one point they were on the verge of unlocking its secrets, but due to the fault of a crappy failure setup, it went awry.
This is something I have seen in this class (as I've mentioned in other blogs) in homework problems that have kept me thinking for hours to no success, or in classes like Chemistry where equilibrium problems are now my least favorite when I used to be extremely efficient with the concept in high school.
Sometimes, I feel like this concept of letting students fail can be used as an excuse for a highly inefficient learning system at the hands of the wrong teacher where students just perish, and other times it can be orchestrated perfectly in unexpected scenarios.
Sometimes, it takes just getting back on the bike, because we know that in the end, it will be worth it. Salvaging that intrinsic worth can be what pulls us back into action when we feel that all we are capable of doing is falling off the bike.
Sunday, April 10, 2016
Reflection 8: Demography
The Powerpoint shown was almost identical to lectures I had in Population and Community Ecology, where we discussed demographics of a population and how to calculate them, This also included discussions of growth/survivorship types and parameters that may impact a population, such as the carrying capacity or probability of surviving interactions with other individuals (assuming a sort of aggressive or predatory interaction). Some of these concepts have also been touched in Conservation Biology, Herpetology, North American Wildlife, and Intro to Wildlife Conservation.
In Calculus, we have discussed modelling functions and what goes into them, namely with the concept of population dynamics in mind. Demographics serve as model parameters that are implemented into the function, which can include things like birth rate, death rate, immigration and emigration, etc.
The idea of limits are implemented in that the population's limit is the carrying capacity, which is somewhat related to density dependence, where the density of a population can change the rates of birth/death rates, so as the number of individuals in the population approaches the limit, rates change. Logistic growth, a form of growth discussed in population ecology, was also discussed in class, which is essentially what's described above; the population approaches an upper limit, but does not surpass it. Exponential growth, another form of growth discussed in population ecology, is much simpler, in that a population grows without parameters working on it (and as such it is normally a less accurate model, since there is always a limit to growth).
In Calculus, we have discussed modelling functions and what goes into them, namely with the concept of population dynamics in mind. Demographics serve as model parameters that are implemented into the function, which can include things like birth rate, death rate, immigration and emigration, etc.
The idea of limits are implemented in that the population's limit is the carrying capacity, which is somewhat related to density dependence, where the density of a population can change the rates of birth/death rates, so as the number of individuals in the population approaches the limit, rates change. Logistic growth, a form of growth discussed in population ecology, was also discussed in class, which is essentially what's described above; the population approaches an upper limit, but does not surpass it. Exponential growth, another form of growth discussed in population ecology, is much simpler, in that a population grows without parameters working on it (and as such it is normally a less accurate model, since there is always a limit to growth).
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