Search results for author:"Sergei Abramovich"
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International Journal of Mathematical Education in Science and Technology Vol. 41, No. 6 (2010) pp. 836–842
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...
International Journal of Mathematical Education in Science and Technology Vol. 29, No. 2 (1998) pp. 233–52
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...
Computers in the Schools Vol. 22, No. 3 (Jan 11, 2006) pp. 21–33
This paper describes the use of Kid Pix-graphics software for creative activities of young children--in the context of early algebra as determined by the mathematics core curriculum of New York state. It shows how grade-two appropriate pedagogy...
International Journal of Mathematical Education in Science and Technology Vol. 36, No. 4 (2005) pp. 414–423
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...
International Journal of Mathematical Education in Science and Technology Vol. 37, No. 5 (Jul 15, 2006) pp. 527–541
This paper shows how inequalities can be utilized in reducing dimensionality of problems associated with the partition of unit fractions into the sums of two, three, and four like fractions. The need for such a reduction in this context stems from...
School Science and Mathematics Vol. 99, No. 3 (1999) pp. 148–55
Presents a computer-mediated discourse on the Pythagorean equation in a university classroom of preservice and inservice teachers. Shows how the use of a spreadsheet as a two-dimensional modeling tool enables students to conjecture the general...
International Journal of Mathematical Education in Science and Technology Vol. 43, No. 3 (2012) pp. 315–336
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...
International Journal of Mathematical Education in Science and Technology Vol. 35, No. 3 (May 2004) pp. 317–333
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,...
Technology-Enabled Pedagogy as an Informal Link between Finite and Infinite Concepts in Secondary Mathematics
Mathematics Educator Vol. 10, No. 2 (2000) pp. 36–41
Reflects on activities designed for computer-enhanced in-service training of high school mathematics teachers. Uses a computer-based graphing calculator, a dynamic geometry program, and a spreadsheet program to explore linear algebraic equations...
International Journal of Mathematical Education in Science and Technology Vol. 33, No. 2 (2002) pp. 171–185
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,...
Promoting Technology Uses in the Elementary Mathematics Classroom: Lessons in Pedagogy from Zoltan Dienes
Journal of Educational Multimedia and Hypermedia Vol. 25, No. 3 (July 2016) pp. 213–227
Today technology allows for the utilization of new classes of mathematical objects which are themselves subject to new modes of student interaction. A series of notable examples may be found in the National Library of Virtual Manipulatives. These...
Fostering Recursive Thinking in Combinatorics through the Use of Manipulatives and Computing Technology
Mathematics Educator Vol. 7, No. 1 (1996) pp. 4–12
Describes the use of manipulatives for solving simple combinatorial problems which can lead to the discovery of recurrence relations for permutations and combinations. Numerical evidence and visual imagery generated by a computer spreadsheet through ...
Computers in the Schools Vol. 13, No. 1 (1997) pp. 13–25
Describes how using spreadsheets helped seventh grade algebra students develop problem-solving skills. Topics include the functional dualism of the spreadsheet as a text, uniting enactive and numeric modeling of word problems, new meanings and...
PRIMUS Vol. 18, No. 3 (May 2008) pp. 257–275
Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology....
Mathematics, Computers, and Young Children as a Research-Oriented Learning Environment for a Teacher Candidate
Asia Pacific Education Review Vol. 10, No. 2 (June 2009) pp. 247–259
The advent of computer technology in the classroom raised the issue of its appropriate use by teachers and their students alike. It has been recommended that teacher education programs provide more opportunities for teacher candidates' use of...
International Journal of Mathematical Education in Science and Technology Vol. 39, No. 6 (September 2008) pp. 749–766
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...
Computers in the Schools Vol. 34, No. 4 (2017) pp. 318–336
This article is written to share teaching ideas about using commonly available computer applications--a spreadsheet, "The Geometer's Sketchpad", and "Wolfram Alpha"--to explore three classic and historically significant problems...
Computers in the Schools Vol. 29, No. 1 (January 2009) pp. 174–190
This article was motivated by the authors' work on a project with a group of 2nd-grade students in a computer lab of a rural school in upstate New York. From this project, one goal of which was to provide a capstone experience for a teacher...