Search results for author:"Sergei Abramovich"
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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 problemsolving context enhanced by the use of an electronic spreadsheet. It reflects the author's work with prospective K12 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 spreadsheetbased 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 Pixgraphics software for creative activities of young childrenin the context of early algebra as determined by the mathematics core curriculum of New York state. It shows how gradetwo 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...

Technology as a Context for Seconday Preteachers' Use of Algebraic Inequalities in a Capstone Course
Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2011 (Mar 07, 2011) pp. 3945–3952
This paper presents pedagogical ideas related to the use of algebraic inequalities as tools in contextoriented computing applications. Developed for and used in a capstone course, these ideas are consistent with and support recommendations for...

Spreadsheet Modelling as a Didactical Framework for InequalityBased 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 ComputerMediated 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 spreadsheetenabled pedagogy aimed at the early development of combinatorial reasoning. The setting includes manipulativecomputational 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 computermediated discourse on the Pythagorean equation in a university classroom of preservice and inservice teachers. Shows how the use of a spreadsheet as a twodimensional modeling tool enables students to conjecture the general...

Integrated spreadsheets as a paradigm of Type II technology applications in mathematics teacher education
Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2016 (Mar 21, 2016) pp. 2461–2466
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...
Topics: mathematics education, Computational Thinking, Teaching and Learning with Emerging Technologies

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 wellknown legend about young Gauss, this article demonstrates the value of...

Developing TechnologyMediated Entries into Hidden Mathematics Curriculum as a Vehicle for “Good Learning” by Elementary PreTeachers
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 twovariable inequalities can be utilized as models for the construction of geometric objects...
Topics: Instructional Design, Mathematics, Software, Preservice Teacher Education, Curriculum, Secondary Education, Programming

Toolkit Approach to Using Spreadsheets in Secondary
Sergei Abramovich; Andrew Brantlinger
Society for Information Technology & Teacher Education International Conference 1998 (1998) pp. 585–589
One of the central tenets of the current reform movement in mathematics teacher education is that the appropriate use of the tools of technology is integral to teaching and learning mathematics at all grade levels. A major force in this reform, the...

TechnologyMotivated 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,...

TechnologyEnabled 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 computerenhanced inservice training of high school mathematics teachers. Uses a computerbased graphing calculator, a dynamic geometry program, and a spreadsheet program to explore linear algebraic equations...

Technology and Hidden Curriculum in Mathematics Teacher Education
Peter Brouwer; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2003 (2003) pp. 2843–2848
Motivated by work done with preservice teachers in a problemsolving and advanced secondary mathematics courses, this paper shows how computing technologies, including a spreadsheet, Maple, and graphing software enable an informal journey into a...
Topics: Teachers, Mathematics, Curriculum, Schools

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 technologybased 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, k12, 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,...

TITE Problem Solving: Integrating Computing and Proving in Secondary Mathematics Teacher Education
Sergei Abramovich; Michael Connell
Society for Information Technology & Teacher Education International Conference 2017 (Mar 05, 2017) pp. 1894–1900
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...
Topics: mathematics education, Creativity, Technological, Pedagogical Content Knowledge (TPACK)

DEVELOPING TECHNOLOGYMEDIATED ENTRIES INTO HIDDEN MATHEMATICS CURRICULUM AS A VEHICLE FOR ‘GOOD LEARNING’ BY ELEMENTARY PRETEACHERS
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...

Burning the Candle: A Technology Immune Technology Enabled Problem within an Action on Objects Framework
Michael Connell; Sergei Abramovich
ELearn: World Conference on ELearning in Corporate, Government, Healthcare, and Higher Education 2017 (Oct 17, 2017) pp. 1724–1730
This paper illustrates how Technology Immune Technology Enabled (TITE) problems (Abramovich, 2014), in this case an exploration of correlation and regressions referred to as Burning the Candle , were incorporated into a K6 mathematics methods class ...
Topics: Instructional Design, Content Development, Implementation Examples & Issues

Digital Fabrication and Aunt Sarah: Enabling Quadratic Explorations Via Technology.
Michael Connell; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2015 (Mar 02, 2015) pp. 3583–3590
When viewed as a content area, mathematics has a split personality. To use an example from language, there are parts of mathematics that function very much like a noun (the concepts of mathematics), while others function more like a verb (procedures,...
Topics: New Possibilities with Information Technology Education, Computational Thinking, Digital Fabrication, Personality, Mathematics

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...

Spreadsheets in Education: A Peerreviewed Medium for Active Learning
Sergei Abramovich; Steve Sugden
World Conference on Educational Media and Technology 2005 (Jun 27, 2005) pp. 4542–4547
It has been more than a decade since electronic journals were first suggested as a possible means of revolutionizing traditional print. In education, the availability of teaching ideas in a refereed electronic format presents an innovation in the...

Stamping Functions: A Technology Immune Technology Enabled Problem within an Action on Objects Framework.
Michael Connell; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2017 (Mar 05, 2017) pp. 1907–1913
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 K6...
Topics: mathematics education, Teaching and Learning with Emerging Technologies

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' ProblemPosing 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

Aunt Sarah and the Farm: A guided tour of a spreadsheet exploration.
Michael Connell; Sergei Abramovich
ELearn: World Conference on ELearning in Corporate, Government, Healthcare, and Higher Education 2018 (Oct 15, 2018) pp. 1386–1393
This paper provides a guided tour illustrating how students can effectively use spreadsheets to internalize and construct meanings for quadratics. The "Aunt Sarah" activity has been used for over 20 years and has been carefully designed to allow...

Promoting Technology Uses in the Elementary Mathematics Classroom: Lessons in Pedagogy from Zoltan Dienes.
Michael Connell; Sergei Abramovich
EdMedia + Innovate Learning 2016 (Jun 28, 2016) pp. 1024–1031
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...
Topics: Instructor Training and Support, improving classroom teaching, pedagogical issues

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 problemsolving 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

Exploring Algebraic Word Problems Through Computer Based Manipulatives and Diverse Technology
Sergei Abramovich; Wanda Nabors
Society for Information Technology & Teacher Education International Conference 1996 (1996) pp. 267–271
It is generally accepted that many students have difficulties with solving word problems. MacGregor & Stacey (1993)

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 spreadsheetbased 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...

Bridging Transformational Geometry and Matrix Algebra with a SpreadsheetBased Tool Kit
Anderson Norton; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2001 (2001) pp. 1379–1384
This report presents technologyenhanced activities designed for secondary mathematics teachers within the context of matrix algebra, transformational geometry, and fractals. It concerns the ways in which a spreadsheet can be used as a tool kit...
Topics: Teachers

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 K6...

Teaching and learning mathematics in technologically intensive classrooms.
Michael Connell; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 2015 (Mar 02, 2015) pp. 2658–2663
Mathematics instruction is currently undergoing significant shifts concerning the nature of both content and the manner in which foundational understandings are to be developed. For example, the National Council of Teachers of Mathematics (NCTM),...
Topics: Classrooms, mathematics education, Mathematics, New Possibilities with Information Technology Education, Technological, Pedagogical Content Knowledge (TPACK)

Didactical Aspects of Using Technology for Problem Posing in Mathematics Teacher Education
Sergei Abramovich; Eun Kyeong Cho
Society for Information Technology & Teacher Education International Conference 2007 (Mar 26, 2007) pp. 3208–3210
This paper introduces and explores the notion of didactical coherence in technologyenhanced mathematical problem posing. The authors argue that problem posing in a technological paradigm cannot be adequately understood without attending to this...

Diophantine Equations as a Context for TechnologyEnhanced 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 nonlinear equations of this kind can be motivated by the use of technology....

Mathematics, Computers, and Young Children as a ResearchOriented 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: TechnologyMotivated Inquiry into a TwoParametric 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...

Developing Elementary Preteachers’ Problemformulating Skills in Mathematics Using Technology
Sergei Abramovich; Eun Kyeong Cho
Society for Information Technology & Teacher Education International Conference 2006 (Mar 19, 2006) pp. 4372–4377
This paper discusses the use of technology as a medium for problem formulating in elementary mathematics. It is motivated by the authors' work with elementary preservice teachers. The paper includes ideas, both practical and theoretical, related to ...
Topics: Mathematics, Teachers

New tools for new thoughts: Effects of changing the “ToolstoThink With” on the elementary mathematics methods course.
Michael L. Connell; Sergei Abramovich
Society for Information Technology & Teacher Education International Conference 1999 (1999) pp. 1052–1057
A central tenet of mathematics education reform is the integral role of technology at all grade levels. The current technological changes combined with the changes in the mathematics content and instructional method require elementary mathematics ...
Topics: Educational Technology, Computers, Mathematics, Elementary Education, Instructional Design

Preparing K12 Mathematics Teachers to Use a Spreadsheet as an Instructional Tool
Sergei Abramovich; Hollylynne Stohl Drier
Society for Information Technology & Teacher Education International Conference 1999 (1999) pp. 950–954
This paper reflects on activities to help prepare elementary and secondary mathematics teachers to use a spreadsheet as an instructional tool. Collaboration on this paper was born out of common epistemological, pedagogical, and mathematical...
Topics: Teachers, Mathematics, Collaboration

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 applicationsa 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. Technologyenabled childhood ...

Parallel Structures of ComputerAssisted 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 2ndgrade 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...