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...

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...

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...

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...

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,...

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,...

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...

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...

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...

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...

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...

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...

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- ...

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...

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

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

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

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...

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

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...

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 ...

Technology as a Context for Seconday Pre-teachers' 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 context-oriented computing applications. Developed for and used in a capstone course, these ideas are consistent with and support recommendations for...

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

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 pre-service teachers in a problem-solving 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

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)

Burning the Candle: A Technology Immune Technology Enabled Problem within an Action on Objects Framework

Michael Connell; Sergei Abramovich

E-Learn: World Conference on E-Learning 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 K-6 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

Spreadsheets in Education: A Peer-reviewed 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 K-6...

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 ...

Aunt Sarah and the Farm: A guided tour of a spreadsheet exploration.

Michael Connell; Sergei Abramovich

E-Learn: World Conference on E-Learning 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...

Topics: (2017) Implementation Examples & Issues

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

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)

Bridging Transformational Geometry and Matrix Algebra with a Spreadsheet-Based Tool Kit

Anderson Norton; Sergei Abramovich

Society for Information Technology & Teacher Education International Conference 2001 (2001) pp. 1379–1384

This report presents technology-enhanced 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

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 technology-enhanced mathematical problem posing. The authors argue that problem posing in a technological paradigm cannot be adequately understood without attending to this...

Developing Elementary Pre-teachers’ Problem-formulating 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 pre-service teachers. The paper includes ideas, both practical and theoretical, related to ...

Topics: Mathematics, Teachers

New tools for new thoughts: Effects of changing the “Tools-to-Think- 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 K-12 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

Professional Development School as a Venue for Integrating Technology in Teacher Education

Sergei Abramovich; Eun Kyeong Cho; Cara Dodge Coffin

Society for Information Technology & Teacher Education International Conference 2007 (Mar 26, 2007) pp. 3211–3215

This presentation reports the results of a faculty-student partnership in the framework of Professional Development School. It reflects on a collaborative effort of two faculty members and a teacher candidate enrolled in a graduate program in...

Spreadsheets: A New Form of Educational Software for School Mathematics?

Sergei Abramovich; Hollylynne Stohl Drier; Sharon Dugdale; Simon Mochon; Erich Neuwirth; John Woodward

International Conference on Mathematics / Science Education and Technology 1999 (1999) pp. 390–395

It has been a worldwide concern that novice mathematics teachers are not well prepared to use technology in the classroom. The lack of such preparation may be due, in part, to a gap between technology offered by schools of education and what the...

Topics: Mathematics, Educational Technology, Teachers, Schools

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...

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...