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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012
We present background and an activity meant to show both instructors and students that mere button pushing with technology is insufficient for success, but that additional thought and preparation will permit the technology to serve as an excellent tool in the understanding and learning of mathematics. (Contains 5 figures.)
Descriptors: Educational Technology, Computer Assisted Instruction, Mathematics Instruction, Teaching Methods
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012
In this article, the author reports results in their efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in their model. They have offered the reader two sets of data and several approaches to determine the rate of sublimation of a piece of solid dry ice. They presented several models…
Descriptors: Computation, Scientific Concepts, Mathematical Models, Models
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012
We consider an oblique approach to cutting regions out of a flat rectangular sheet and folding to make a maximum volume container. We compare our approach to the traditional approach of cutting out squares at each vertex of the sheet. (Contains 4 figures.)
Descriptors: Calculus, Mathematics, Mathematics Instruction, Mathematics Education
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2012
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
Descriptors: Mathematics Instruction, Undergraduate Study, College Mathematics, Equations (Mathematics)
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2011
We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…
Descriptors: Kinetics, Chemistry, Calculus, Equations (Mathematics)
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2010
We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…
Descriptors: Mathematical Models, Calculus, Mathematics Education, Mathematics Instruction
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2009
Several activities in which population dynamics can be modelled by tossing M&M's[R] candy are presented. Physical activities involving M&M's[R] can be modelled by difference equations and several population phenomena, including death and immigration, are studied. (Contains 1 note.)
Descriptors: Equations (Mathematics), Mathematics Activities, Demonstrations (Educational), Immigration
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2008
A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…
Descriptors: Light, Calculus, Visualization, Computation
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Winkel, Brian – International Journal of Mathematical Education in Science and Technology, 2008
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Descriptors: Discovery Learning, Calculus, Mathematics Instruction, Educational Technology