Contextualized mathematics Web resources Contextualized Teaching & Learning: A Faculty Primer "is directed to faculty with little specific knowledge about contextualized learning—particularly related to basic skills. It includes four key components including a case statement and a review of the literature. This first section communicates the requirements for success in the 21st century, the skills gap and the role of the community college in addressing this issue. It defines CTL and the various ways it is implemented and identifies and connects learning theories that support and inform the practice of CTL. Finally, it summarizes what we know about the impact of CTL on student outcomes." "The case statement and literature review set the stage for two additional sections of the primer. Featuring promising CTL instructional practices collected through faculty interviews, these promising practices provide an instructor’s perspective on course/program design, target population and recruitment, assessment of student readiness, pedagogy, outcomes and role of institutions and partners. Practices represent a range of settings including academic, occupational and workforce development programs as well as a continuum of models from stand-alone courses to bridge and academy models." "The final section offers recommendations and considerations for a range of stakeholders interested in supporting faculty to take a “next step” with contextualized teaching and learning. Stakeholders include academic, occupational and student services faculty, program directors, deans, college presidents, policy makers and funders." Opening statement from this summary: Contextualized Teaching and Learning Primer Project Contextualizing Basic Skills into CTE Curriculum -- Merced College "Evidence is mounting that shows just how well students benefit if their basic skills needs are addressed in the context of their career path. Contextualized instruction (also known as contextual teaching and learning, functional context learning, customized instruction, experiential learning, active learning, real-world education, and learner-centered instruction), is based on developing new skills, knowledge, abilities, and attitudes in students by presenting subject matter in meaningful and relevant contexts: contexts of previous experience, real-life, or the workplace. New skills are then applied in these relatable contexts. Key words that describe this method are applied, relatable, relevant, and authentic." Beyond the Usual Formulas: Bringing Context to Math Education -- UC Santa Barbara Journal articles Bottge, Brian A. "Effects of Contextualized Math Instruction on Problem Solving of Average and Below-Average Achieving Students." Journal of Special Education, vol. 33 (2), summer 1991, p. 81-91.Focuses on middle school students but the basic issues might be interesting. Nicol, Cynthia. Where's the Math? Prospective Teachers Visit the Workplace. Educational Studies in Mathematics, 2002, vol. 50 (3), p. 289-309. Parr, B. A. and Edwards, M. C. "Effects of a Math-Enhanced Curriculum and Instructional Approach on the Mathematics Achievement of Agricultural Power and Technology Students: An Experimental Study." Journal of Agricultural Education vol. 85 (3), 2006. Reports Cobourne, Marvett (2004) Analyzing the NCTM Standards: Looking at Arguments by the Mathematicians versus the Mathematics Educators. Masters, Department of Mathematical Sciences, Central Connecticut State University. Available fulltext. Looks as though this gives a background understanding of the discussion about contextualization vs. more theoretical approaches. See also the Hyman Bass quotation, below. Books Research and Practice of Active Learning in Engineering Education by Erik De Graaf, Gillian Saunders-Smits, and Michael Nieweg. Amsterdam: Amsterdam University Press, 2005. The whole book can be read on Google books <http://books.google.com> Here's a direct link to it. There are a series of "using math to..." books. Aimed for middle schoolers, but you might get ideas from them.?
For others, go to http://worldcat.org and search for "using math to". Parts of some of these books are available to read on Google Books, e.g., Using Math To Design a Roller Coaster. Let us know if you want us to borrow any of these books -- or any other books -- for you on interlibrary loan. Quotations Hyman Bass (University of Michigan, School of Education) studies and writes about mathematics teaching in the pre-college years, but has said this about contextualized mathematics teaching: "Mathematics instruction should be contextualized and avoid the abstraction associated with the traditional curriculum." This common refrain of current reforms is more complex than most of its advocates appreciate. One argument, which goes back to Dewey and others, is that learning best starts with experience, to provide both meaning and motivation for the more general and structured ideas that will follow. Dewey's idea differs in two respects from the above recommentation. First, it does not eschew abstraction. Second, it speaks of the experience of the learner, not of the eventual context of application of the ideas, which may be highly specialized and much later in adulter in adult experience, still remote from the learner's. Another argument is that mathematics is best learned in the comples contexts in which it is most significantly used. This idea has a certain appeal, provided that it is kept in balance. Authentic contexts are complex and idiosyncratic. Which contexts should one choose for a curriculum? Their very complexity often buries the mathematical ideas in other features, so that, while the mathematical effects might be appreciated, there is limited opportunity to learn the underlying mathematical principles. So the main danger here is the impulse to convert a major part of the curriculum to this form of instruction. The resulting loss of learning of general (abstract) principles then may, if neglected, deprive the learner of the foundation necessary for recognizing how the same mathematics witnessed in one context in fact applies to many others. Quoted in Lynn Arthur Steen's Achieving Quantitative Literacy: An Urgent Challenge for Higher Education. American Mathematical Association of America, 2004. Portions of the book are available at Google Books <http://books.google.com>. It looks as tho the original is posted at the Mathematical Association of America Web site -- see point no. 2 in this by Hyman Bass. Other "Get Real!" Assessing for Quantitative Literacy, by Grant Wiggins, posted at the Mathematical Association of America Web site. First published in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, Editors, Princeton, NJ: National Council on Education and the Disciplines, 2003, pp. 121-143.
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