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Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 2012
This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…
Descriptors: Teaching Methods, Preservice Teacher Education, Learning Experience, Mathematics Education
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Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 2010
This classroom note shows how Fibonacci numbers with negative subscripts emerge from a problem-solving context enhanced by the use of an electronic spreadsheet. It reflects the author's work with prospective K-12 teachers in a number of mathematics content courses. (Contains 4 figures.)
Descriptors: Mathematics Education, Elementary School Mathematics, Secondary School Mathematics, Numbers
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Abramovich, Sergei; Leonov, Gennady A. – International Journal of Mathematical Education in Science and Technology, 2008
This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…
Descriptors: Mathematics Curriculum, Numbers, Educational Technology, Calculus
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Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 2005
The problem of comparison of answers in trigonometric equations arises frequently when different solution strategies are encouraged in the classroom. This paper shows how such a problem can be put in context structured by classic and contemporary perspectives on teaching problem solving, including the use of technology.
Descriptors: Teaching Methods
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Abramovich, Sergei; Brantlinger, Andrew – International Journal of Mathematical Education in Science and Technology, 2004
This paper shows how the computational and graphical capabilities of spreadsheets allow for interactive analytic and geometric constructions from numerical modelling of homogeneous Diophantine equations of the second order. Suggested activities, designed for prospective teachers of mathematics and made possible by what is referred to in the paper…
Descriptors: Mathematics Teachers, Geometric Concepts, Number Concepts, Mathematics Instruction
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Abramovich, Sergei; Strock, Tracy – International Journal of Mathematical Education in Science and Technology, 2002
The paper describes the use of a spreadsheet in a mathematics teacher education course. It shows how the tool can serve as a link between seemingly disconnected mathematical concepts. The didactical triad of using a spreadsheet as an agent, consumer, and amplifier of mathematical activities allows for an extended investigation of simple yet…
Descriptors: Preservice Teacher Education, Education Courses, Mathematical Concepts, Mathematics Instruction
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Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 1998
Argues that basic components of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet-based simulations of concrete materials. Suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for appreciation of the development of…
Descriptors: Computer Uses in Education, Educational Technology, Elementary Secondary Education, Manipulative Materials