two perspectives on integrative learning and quantitative reasoning

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Two Perspectives on Integrative Learning and Quantitative Reasoning. Michael C. Burke College of San Mateo Innovative Pedagogy and Course Redesign IX Fairfield University June 4, 2009 AAC&U: The Essential Learning Outcomes - PowerPoint PPT Presentation


  • Two Perspectives on Integrative Learning and Quantitative ReasoningMichael C. BurkeCollege of San Mateo

    Innovative Pedagogy and Course Redesign IXFairfield UniversityJune 4, 2009

  • AAC&U: The Essential Learning Outcomes

    Knowledge of Human Cultures and the Physical and Natural World -Through study in the sciences and mathematics, social sciences, humanities, histories, languages and the arts Focused by engagement with big questions, both contemporary and enduring

    Intellectual and Practical Skills, including -Inquiry and analysis- Critical and creative thinking -Written and oral communication- Quantitative literacy -Information literacy- Teamwork and problem solving Practiced extensively, across the curriculum in the context of progressively more challenging problems, projects, and standards of performance

    Integrative Learning, including -Synthesis and advanced accomplishment across general and specialized studies Demonstrated through the application of knowledge, skills, and responsibilities to new settings and complex problems

  • Fostering students abilities to integrate learning -- across courses, over time, and between campus and community life -- is one of the most important goals and challenges of higher education. The undergraduate experience can be a fragmented landscape of general education courses, preparation to the major, co-curricular activities and the real world beyond the campus. But an emphasis on integrative learning can help undergraduates put the pieces together and develop habits of mind that prepare them to make informed judgments in the conduct of personal, professional, and civic life.

    Integrative learning comes in many varieties: connecting skills and knowledge from multiple sources and experiences; applying theory to practice in various settings; utilizing diverse and even contradictory points of view; and, understanding issues and positions contextually. Significant knowledge within individual disciplines serves as the foundation, but integrative learning goes beyond academic boundaries. Indeed, integrative experiences often occur as learners address real-world problems, unscripted and sufficiently broad to require multiple areas of knowledge and multiple modes of inquiry, offering multiple solutions and benefiting from multiple perspectives.

    a statement on integrative learningassociation of american colleges and universitiesthe carnegie foundation for the advancement of teaching

  • Quantitative literacy is more a habit of mind, an approach to problems that employs and enhances both statistics and mathematics Unlike mathematics, which is primarily about a Platonic realm of abstract structures, numeracy is often anchored in data derived from and attached to the empirical world. 1 The Quantitative Literacy Design Team

    Quantitative literacy is about challenging college-level settings in which quantitative analysis is intertwined with political, scientific, historical or artistic contexts. Here QL adds a crucial dimension of rigor and thoughtfulness to many of the issues commonly addressed in undergraduate education. QL is not a discipline but a literacy, not a set of skills but a habit of mind. 2 The Quantitative Literacy Design Team

    Richardson and McCallum argue that Quantitative literacy cannot be taught by mathematics teachers alone, not because of deficiencies in teaching but because quantitative material must be pervasive in all areas of students education . 3 For this reason the writing-across-the-curriculum model seems to offer a promising approach.

    1. In Mathematics and Democracy: The Case for Quantitative Literacy, edited by Lynn Arthur Steen. p 5.2. In Achieving Quantitative Literacy: An Urgent Challenge for Higher Education, by Lynn Arthur Steen. p 223. In Achieving Quantitative Literacy: An Urgent Challenge for Higher Education, by Lynn Arthur Steen. p 39.

  • WACPack

  • The Moose of Isle Royale

  • World Population

  • I invite you to consider the following question: What is the carrying capacity of the earth? Is it 10 billion, so that we have not yet reached it? Is it 6 billion, so that we are passing it about now? Is it 3 billion, so that we have blown past it, like the Isle Royale moose?

  • Mach Assignment

  • Mach: from the World Population Assignment You have examined data on the growth of moose and human populations by graphing them, identifying trendlines, and making projections for the future. You have given some thought to the implications of your projections. You have also read the article Optimum Human Population Size, by Gretchen C. Daily and Anne H. Ehrlich and Paul R. Ehrlich, which gives a summary of the authors opinions on the issue of world population. As good critical thinkers, you should remain open to new information as it tests the hypotheses that are forming in your mind. In this case, you should be making connections between these two sources of information, comparing your ideas with those in the reading and trying to reconcile them. In what ways are your WACPack answers consistent with the opinions in the reading? In what ways are they not? Would you change the opinions you were formulating in light on this new information or not?

    This essay should be expository, explaining for the reader the thinking processes you are going through in integrating and reconciling the information you were given. It is not meant to be an argument or persuasive piece of writing, although the thinking that you are probing and revealingthe comparing, the evaluating, and the development of new hypothesesis the basis for good argument.

  • Mach: Student Paper In the first section of the WACPack, I looked at a preserved small isolated ecosystem of Isle Island that primarily consisted of moose and wolves. The moose population was kept at approximately 1000 due to their predator, the wolf. However, in the 1980s the wolf population was hit with a fatal virus, killing off the majority of wolves. The impact on the simple ecosystem was dramatically seen throughout the years of an increase in the moose population. I was given numbers of the population size from 1980 to 1995 and was asked to plot the data. Next I was asked to predict what would happen in the years after 1995. Would the population continue to increase? Or would it decline dramatically? Initially I only took into consideration the carrying capacity of the island. I figured that the population would grow until the land was completely covered, topping at 4,200 moose in the year 2002. However, the data revealed that in the next year, 1996, the moose population actually dropped from 2,422 to 1,163 and continued to decline until about 2002 were it leveled back at 1000. This shows that the optimum population size for the land, regardless of natural predators is about 1000 moose. I feel that my predictions were too high primarily due to the fact that I did not consider the lifestyles of the moose. I found that putting a term such as quality of life on wild animals was unheard of. However, it seems that even animals maintain a certain quality of life and by doing so it affects the population trend of the species.

  • Mach: Student Paper Next, I looked at the trend of human populations versus moose populations. In the example of the Isle Island, the moose and wolves exist on a very simple ecosystem, where moose are the prey and the wolves are the predator. This I believe allowed for the natural progression of nature to keep equilibrium. I do not see this in the human population due to technological inventions and medical achievements altering the course of nature. Humans are directly altering the natural outcome of life by changing nature with things such as cloning, synthetic medications and genetically engineered foods. However, there are only a few things left that level out or acting as a predator to humans these are natural disasters, super viruses and war. I feel that these predators are the only way humans will self regulate and find equilibrium. However, I do not feel that natural disasters, super viruses, or wars are in abundance to combat the exponential growth rate of the world, especially in developed countries that have such advanced technology and weaponry to fight these natural killers.

  • Mach: Student Paper When I read the article, Tragedy of the Commons by Garrett Hardin, I was impressed by his argument against overpopulation. Hardin brings up the same issues that are addressed in the WACPack, that it is impossible to have two things at their maximum, such as population and a high quality of life. In the OHPS, it states that we cannot have a large population because the earth cannot provide enough resources to maintain a high standard of life to all. Our world now can provide a high quality of life to only a small portion of the population, primarily ones in developed countries. In addition, the small populations with the higher quality of life attribute to the majority of the waste produced on the earth. This imbalance is one of the reasons why the author of the Tragedy of the Commons believes we must address this issue now to prevent to destruction of our species.

    Throughout my journey of thought I have uncovered many revelations about the population problem our world faces. I have read three articles that confirm and contradicted some of my original beliefs. I now truly feel that our population will act as the moose population did on Isle Island and decline once we hit our maximum carrying capacity. However, the quality of life for many people will


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