If I had to state what I think is the most important Epected Learning Outcome for students enrolled in the MS Squared program it would be-
By the time they receive their degree, a fully engaged student will be able to explain to their students, student's parents, fellow teachers, school administrators, general citizens, and the big whigs that organize education in the state of Texas why it is essential to be able to integrate mathematics and biology in middle school classroom.Why Use Math To Help Us Understand Ecology?
In a short essay entitled "Mathematics and Ecology", Louis Gross a Professor of Ecology and Evolutionary Biology and Mathematics at the University of Tennessee and Director of the National Institute for Mathematical and Biological Synthesis and The Institute for Environmental Modeling, tried to answer this question.
Mathematics, as the language of science, allows us to carefully phrase questions concerning each of the above areas of ecology. It is through mathematical descriptions of ecological systems that we abstract out the basic principles of these systems and determine the implications of these. Ecological systems are enormously complex. A major advantage of mathematical ecology is the capability to selectively ignore much of this complexity and determine whether by doing so we can still explain the major patterns of life on the planet. Thus simple population models group together all individuals of the same species and follow only the total number in the population. By ignoring the complexity of differences in physiology, size, and age between individuals, the models attempt to compare the basic dynamics obtained from the model with observations on different species. As a next step, additional complexity, associated with introducing different age classes for example, is included. How the inclusion of such additional complexity affects the predictions of the model determines whether this additional complexity is necessary to answer the biological questions you are interested in.
The above has focused on the use of mathematics to formulate basic theory in ecology. There are also many applications of mathematical and computer models to very practical questions arising from environmental problems. This includes the entire field of ecotoxicology, in which mathematical models predict the effects of environmental pollutants on populations and communities. The field of natural resource management uses models to help set harvest quotas for fish and game, based upon population models similar in form to those mentioned above. Conservation ecology uses models to help determine the relative effects of alternative recovery plans for endangered species, as well as aid in the design of nature preserves.
http://mathaware.org/mam/99/resources/mam99_matheco.html
Why Use Ecology In Math Classes?
Because I am not a math teacher my only experience in a math classroom has been as a student. Although I was undoubtedly a "science nerd" and I was pretty "good at math" I don't think that I ever really appreciated "math for math's sake" as a student (although I did think that there was something fundamentally cool about geometry).
Math is fundamentally cool. In my experience there are limited numbers of people who are inherently turned on by math. I am probably not the best person in the world to tell you how to get more students fundamentally excited about learning math. One thing that I have picked up over the years is that I am very sensitive, and students are very sensitive, to how interested a teacher/speaker appears to be about their topic. When the teacher acts as if they find a topic to be fundamentally cool, then I am more likely to pay attention and appreciate what they are saying. Thus, my suggestion to all teachers is to be excited and interested in what you are talking about and if you aren't, then fake it! In my biology classes I routinely teach topics that I find fascinating as well as those I find much less interesting (for example, the life cycle of the moss). I am always pleased when I hear students say that they are surprised that anyone "could be so excited about mosses". Don't worry if your students think that Ms. X or Mr. Y is a goofy math geek! Remember, your middle-school students are the same kids who think that Justin Bieber is cool, so why should you care what they think!?!
Math is interesting. I am always thankful that I get to teach biology rather than algebra because I get to talk about cool stuff like dolphins, canibalism, and tropical rainforests, or when all else fails, I can always bring up sex! Fortunately, a knowledgeable math teacher might be able to use a number of interesting ecological phenomena as a situation for teaching math.
Math is relevant and useful. Many students might never find math to be fun to learn, but they might want to learn more math when they realize that math is an important and relevant tool. Part of the art of being a good math teacher is to be able to choose a variety of contexts to apply mathematics because different students are going to be interested in different topics.
I have to admit that I was in the last quarter of my senior year in college before anyone ever showed me how being able to use math could help me to learn about biology (statistics and calculus to solve optimality problems). I often tell my students, and now I am telling you, if there was one thing that I could havd done differently that would have made me a better biologist it would have been to learn more math!
The mercenary approach. For many students the best way to inspire them to want to learn more about math is "greed". You can show them a result of a recent study that examined the income of students with different majors in college. It is interesting to note that two of the three highest earnings (mathematics & computers and engineering) were those that required the strongest background in math!
http://chronicle.com/article/Median-Earnings-by-Major-and/127604/
Final Thoughts
In my opinion, the second most important Expected Learning Outcome from this degree program is-
By the end of this program a fully engaged student should be able to effectively integrate appropriate mathematics into their science classroom or the appropriate science concepts into their mathematics classrooms.
Please let Brock and me know how we can help you to achieve this goal.
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