Sergei Abramovich

Revealing hidden mathematics curriculum to pre-teachers using technology: the case of partitions

Motivated by work done with pre-teachers of mathematics in a problem-solving course, this paper shows how computing technologies, including a spreadsheet and Maple, facilitate an informal journey into a hidden aspect of the formal content of the pre-college curriculum dealing with the arithmetic of partitions. By using three problems from different grade levels within a state curriculum as an example, the paper suggests that a deeper perspective on seemingly disconnected problem-solving contexts may serve as a powerful didactical tool in helping teachers to appreciate mathematics and its pedagogy as an integrated whole. The connection of the hidden aspect of the curriculum to the concept of mathematical play is also explored.

Spreadsheet-Enhanced Problem Solving in Context as Modeling

This paper is prompted by a recent call by the International Commission on Mathematical Instruction (ICMI) for the study of mathematical modeling as technology-enhanced didactic inquiry into relations between mathematics and the real world. It reflects on activities designed for a teacher education course that focuses on the computer spreadsheet as a tool for concept development through situated mathematical problem solving. Modeling activities described in this paper support the epistemological position regarding the interplay that exists between the development of mathematical concepts and available methods of calculation. The spreadsheet used is Microsoftr °Excel 2001.

Manipulative and numerical spreadsheet templates for the study of discrete structures

The paper shows that basic concepts of discrete mathematics can be introduced to students through gradual elaboration of experiences with iconic spreadsheet‐based simulations of concrete materials. It suggests that the study of homogeneous and heterogeneous patterns of manipulative spreadsheet templates allows for the appreciation of the development of knowledge about discrete structures and offers a vision of mathematics as a human activity.

Spreadsheet Modelling as a Didactical Framework for Inequality-Based Reduction

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 using a spreadsheet as a modelling tool. Activities described in this paper are grounded in standards for teaching and recommendations for teachers in North America. They are designed for prospective teachers of secondary mathematics.

Measurement model for division as a tool in computing applications

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 intriguing properties of whole numbers. The authors argue that revisiting elementary content in a technological context enables pre-service teachers to appreciate the role that conceptual knowledge can play in the development of a spreadsheet-enabled pedagogy.

Technology for deciding the convergence of series

The use of technology to motivate the study of calculus is very popular in todays undergraduate mathematics classroom. This article presents some new ways of using a spreadsheet in teaching foundations of the theory of infinite series. The approach is based on a spreadsheets ability to model inequalities of the Bolzano‐Cauchy type and provides students with a kind of visual imagery of the process of convergence (divergence). The main concern of the work is the issue of a computer visualization and exploration that lead to a conjecture. For treating slowly converging series the method of dynamic visualization is proposed which illustrates the usefulness of a spreadsheet in rather delicate explorations. It is shown that a computer laboratory equipped with spreadsheets can be a good teaching environment to help students develop the basic concepts of infinite

Applications of Spreadsheets in Education : The Amazing Power of a Simple Tool

This e-book is devoted to the use of spreadsheets in the service of education in a broad spectrum of disciplines: science, mathematics, engineering, business, and general education. The effort is aimed at collecting the works of prominent researchers and educators that make use of spreadsheets as a means to communicate concepts with high educational value. The e-book brings some of the most recent applications of spreadsheets in education and research to the fore. To offer the reader a broad overview of the diversity of applications, carefully chosen articles from engineering (power systems and control), mathematics (calculus, differential equations, and probability), science (physics and chemistry), and education are provided. Some of these applications make use of Visual Basic for Applications (VBA), a versatile computer language that further expands the functionality of spreadsheets. The material included in this e-book should inspire readers to devise their own applications and enhance their teaching and/or learning experience.

Parallel Structures of Computer-Assisted Signature Pedagogy: The Case of Integrated Spreadsheets.

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 candidate in teaching application-oriented mathematics with technology, the ideas about parallel structures of two universes—the teachers and the students’—that echo Shulmans structures of signature pedagogy have been developed. In the article the authors introduce the notion of computer-assisted signature pedagogy and explore its features through the combined lens of teaching and learning using the concept of Type I/Type II technology integration.

Early Algebra with Graphics Software as a Type II Application of Technology

Abstract This paper describes the use of Kid Pixgraphics 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 makes it possible to bring about a qualitative change in the learning process of those commonly struggling with mathematics by substituting computer-mediated tasks for algebraic tasks. The pedagogy is analyzed along the lines of Vygotskys theory of using tools and signs in the internalization of higher psychological functions.

Spreadsheets in teaching and learning topics in calculus

The use of spreadsheets in introducing students to the concept of a limit of a sequence is demonstrated and the possible computer‐based scenario as the enhancement of the teaching/learning process of calculus is exemplified. It is shown how the spreadsheets operational capability assists visualizing the Bolzano‐Cauchy principle of convergence and leads eventually to the possibility of employing computer technology in deciding the convergence of positive series.