Mathematical Concepts as Emerging Tools in Computing Applications

SERGEI ABRAMOVICH

Journal of Computers in Mathematics and Science Teaching Vol. 19, No. 1 (2000) pp. 21–46

This paper deals with computational applications of number theory concepts developed from arithmetic properties of spreadsheet-based lattices. It reflects on activities explored with inservice and preservice teachers in an egalitarian, stu-dent- ...

Extending Fibonacci Numbers to Negative Subscripts through Problem Solving

Sergei Abramovich

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...

Manipulative and Numerical Spreadsheet Templates for the Study of Discrete Structures

Sergei Abramovich

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...

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

Sergei Abramovich

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...

Integrated spreadsheets as a paradigm of Type II technology applications in mathematics teacher education

Sergei Abramovich

Journal of Computers in Mathematics and Science Teaching Vol. 35, No. 4 (October 2016) pp. 301–312

The paper presents the use of spreadsheets integrated with digital tools capable of symbolic computations and graphic constructions in a master?s level capstone course for secondary mathematics teachers. Such use of spreadsheets is congruent with...

How to "Check the Result"? Discourse Revisited

Sergei Abramovich

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...

Spreadsheet Modelling as a Didactical Framework for Inequality-Based Reduction

Sergei Abramovich

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...

Cognitive Heterogeneity in Computer-Mediated Mathematical Action as a Vehicle for Concept Development

Sergei Abramovich

Journal of Computers in Mathematics and Science Teaching Vol. 22, No. 1 (2003) pp. 19–41

This article focuses on a spreadsheet-enabled pedagogy aimed at the early development of combinatorial reasoning. The setting includes manipulative-computational worksheets with enactive arithmetic tasks allowing for the variety of iconic...

Topics: Cognition

Revisiting an Ancient Problem through Contemporary Discourse

Sergei Abramovich

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...

Collateral Learning and Mathematical Education of Teachers

Sergei Abramovich

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...

Developing Technology-Mediated Entries into Hidden Mathematics Curriculum as a Vehicle for “Good Learning” by Elementary Pre-Teachers

Sergei Abramovich; Peter Brouwer

Journal of Computers in Mathematics and Science Teaching Vol. 23, No. 3 (2004) pp. 299–322

This paper suggests that knowledge of the school mathematics curriculum, as one of the key components of teachers' education, can be extended to include concepts and structures that generally belong to hidden domains of the curriculum. Motivated by...

Topics: Teachers, Elementary Education, Mathematics, Curriculum

Evolving polygons revisited: Inequalities and computer graphing

Sergei Abramovich; Peter Brouwer

Journal of Computers in Mathematics and Science Teaching Vol. 28, No. 4 (October 2009) pp. 345–358

This paper was developed with the goal of enhancing the mathematical preparation of secondary school teachers in the technological paradigm. It shows how two-variable inequalities can be utilized as models for the construction of geometric objects...

Topics: Instructional Design, Mathematics, Software, Preservice Teacher Education, Curriculum, Secondary Education, Programming

Technology-Motivated Teaching of Topics in Number Theory through a Tool Kit Approach

Sergei Abramovich; Andrew Brantlinger

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

Sergei Abramovich; Anderson Norton

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...

Promoting Technology Uses in the Elementary Mathematics Classroom: Lessons in Pedagogy from Zoltan Dienes.

Michael Connell; Sergei Abramovich

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...

Equations with Parameters: A Locus Approach

Sergei Abramovich; Anderson Norton

Journal of Computers in Mathematics and Science Teaching Vol. 25, No. 1 (January 2006) pp. 5–28

This paper introduces technology-based teaching ideas that facilitate the development of qualitative reasoning techniques in the context of quadratic equations with parameters. It reflects on activities designed for prospective secondary mathematics ...

Topics: Preservice Teachers, technology, Technology integration, Cognition, k-12, teacher education, Integration, Mathematics, Preservice Teacher Education, Professional Development, Pedagogy, problem solving, Teaching Methods, Inclusive Education

Measurement Model for Division as a Tool in Computing Applications

Sergei Abramovich; Tracy Strock

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,...

DEVELOPING TECHNOLOGY-MEDIATED ENTRIES INTO HIDDEN MATHEMATICS CURRICULUM AS A VEHICLE FOR ‘GOOD LEARNING’ BY ELEMENTARY PRE-TEACHERS

Sergei Abramovich; Peter Brouwer

Journal of Computers in Mathematics and Science Teaching

This paper suggests that knowledge of the school mathematics curriculum, as one of the key components of teachers’ education, can be extended to include concepts and structures that generally belong to hidden domains of the curriculum. Motivated by...

Promoting Technology Uses in the Elementary Mathematics Classroom: Lessons in Pedagogy from Zoltan Dienes

Michael Connell; Sergei Abramovich

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

Sergei Abramovich; Anne Pieper

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 ...

Technology as a Medium for Elementary Preteachers' Problem-Posing Experience in Mathematics

Sergei Abramovich; Eun Cho

Journal of Computers in Mathematics and Science Teaching Vol. 25, No. 4 (October 2006) pp. 309–323

This article attempts to extend current research and development activities related to the use of technology in problem posing, to early grades mathematics. It is motivated by the authors' work with elementary preservice teachers toward this goal,...

Topics: Early Childhood Education, Computers, Mathematics, Children, Standards, Preservice Teacher Education

From Measuring to Formal Demonstration Using Interactive Computational Geoboards and Recurrent Electronic Charts

Sergei Abramovich; Gary Brown

Journal of Computers in Mathematics and Science Teaching Vol. 18, No. 2 (1999) pp. 105–134

The paper shows how the joint use of dynamic geometry program and a spreadsheet may provide a computational environment for exploring geometry on plane lattices that lessens the risk of developing a false empiricist view of mathematics often...

Topics: Educational Technology, Preservice Teacher Education, Mathematics

Spreadsheets as Generators of New Meanings in Middle School Algebra

Sergei Abramovich; Wanda Nabors

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...

Computer as a medium for overcoming misconceptions in solving inequalities

Sergei Abramovich; Amos Ehrlich

Journal of Computers in Mathematics and Science Teaching Vol. 26, No. 3 (July 2007) pp. 181–196

Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching ...

Topics: Teaching Methods, Secondary Education, Preservice Teacher Education, Computers, Mathematics

Evolving polygons and spreadsheets: Connecting mathematics across grade levels in teacher education

Sergei Abramovich; Peter Brouwer

Journal of Computers in Mathematics and Science Teaching Vol. 28, No. 3 (July 2009) pp. 209–220

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to...

Topics: Curriculum, Preservice Teacher Education, Software, Instructional Design, Mathematics, Secondary Education, Programming

Problem Solving in the Digital Age: New Ideas for Secondary Mathematics Teacher Education

Sergei Abramovich; Michael Connell

Journal of Computers in Mathematics and Science Teaching Vol. 36, No. 2 (April 2017) pp. 105–116

The paper reflects on an earlier research on the use of technology in secondary mathematics teacher education through the lenses of newer digital tools (Wolfram Alpha, Maple), most recent standards for teaching mathematics, and recommendations for...

A Technology Immune Technology Enabled Problem within an Action on Objects Framework: Stamping Functions

Michael Connell; Sergei Abramovich

Journal of Computers in Mathematics and Science Teaching Vol. 36, No. 2 (April 2017) pp. 117–127

This paper illustrates how the notion of Technology Immune Technology Enabled (TITE) problems (Abramovich, 2014), in this case an exploration of variations in surface area we refer to as Stamping Functions , might be incorporated into a K-6...

Diophantine Equations as a Context for Technology-Enhanced Training in Conjecturing and Proving

Sergei Abramovich; Stephen J. Sugden

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

Sergei Abramovich; Eun Kyeong Cho

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...

Fibonacci Numbers Revisited: Technology-Motivated Inquiry into a Two-Parametric Difference Equation

Sergei Abramovich; Gennady A. Leonov

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...

Teaching Classic Probability Problems With Modern Digital Tools

Sergei Abramovich; Yakov Yu. Nikitin

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...

What Are Billy’s Chances? Computer Spreadsheet as a Learning Tool for Younger Children and Their Teachers Alike

Melody Stanton; Erin Baer; Sergei Abramovich

Journal of Computers in Mathematics and Science Teaching Vol. 21, No. 2 (2002) pp. 127–145

This article demonstrates how multiple features of a computer spreadsheet extended motivational activities with M&Ms and enhanced mathematical thinking of younger children in the context of data analysis and probability. Technology-enabled childhood ...

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

Sergei Abramovich; Jonathan Easton; Victoria O. Hayes

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...