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##  Using Spreadsheets in Mathematics Education. ERIC Digest.                    

"Spreadsheets build an ideal bridge between arithmetic and algebra              and allow the student free movement between the two worlds. Students            look for patterns, construct algebraic expressions, generalize                  concepts, justify conjectures, and establish the equivalence of two             models as intrinsic and meaningful needs rather than as arbitrary               requirements posed by the teacher." (Friedlander, 1998, p.                      383) 
Electronic spreadsheets have been created and used mainly as             tools for mathematical and statistical calculations, as numerical or            textual data can be inserted into their columns and                             rows (http://wwwstaff.murdoch.edu.au/ ~kissane/spreadsheets.htm).               So, being able to manage spreadsheets has become one of the skills              sought for anybody in this technologically enhanced millennium.                 Therefore, spreadsheets have become an important part of many                   different curriculums at different levels of education. Moreover,               they have been used in education, especially mathematics education,             as a tool in helping students understand mathematical concepts such             as plotting and exploring functions and patterns, exploring                     probability and statistics, mathematical modeling, and geometric                transformations (http://www.freshpond                                           .net/treasures/math/spreadsheet/default.htm). Relationships among               different types of representations such as tables, equations and                graphs are more easily comprehendible when all representations are              visible at once and linked to each other, i.e. when one makes a                 change in one representation, corresponding changes in other                    representations are offered by the program.  Moreover, spreadsheets             allow students to focus on the mathematical reasoning by freeing                them from the burden of calculations and algebraic                              manipulations. 
Educational research supports the use of                       spreadsheets both in K-12 and teacher education and in professional             development. Abramovich and Nabors (1997) describe how using                    spreadsheets helped seventh grade algebra students develop                      problem-solving skills. Molyneux-Hodgson et. al (1999) states that              the results of their study "suggest the possibility of enhancing                students' capability to shift between a wider range of                          representations using the modeling approach embedded in computer                environments such as a spreadsheet" (p.1). Dudgale (1994) reports a             project that involved experienced K-12 teachers in mathematical                 modeling and problem solving using spreadsheets and concludes that              teachers developed models that exhibited a wide variety of                      mathematics topics and approaches in different grade                            levels. 
National Council of Teachers of Mathematics (NCTM, 2000)              suggests that "students in grades 3-5 should also become familiar               with technological tools such as dynamic geometry software and                  spreadsheets. They should learn to set up a simple spreadsheet and              use it to pose and solve problems, examine data, and investigate                patterns" (p. 207). The use of spreadsheets for higher grade levels             is also advocated by NCTM (2000): "The expanded class of functions              available to high school students for mathematical modeling should              provide them with a versatile and powerful means for analyzing and              describing their world. With utilities for symbol manipulation,                 graphing, and curve fitting and with programmable software and                  spreadsheets to represent iterative processes, students can model               and analyze a wide range of phenomena" (p. 297). NCTM published two             books on the use of spreadsheets: 
"How To Use the Spreadsheet as a            Tool in the Secondary School Mathematics Classroom." [Second                    Edition (for Windows and Macintosh Operating Systems)] by William J             Masalski. 
This book and accompanying two computer disks, one for              Windows and one for Macintosh Operating Systems, presents 30                    activities illustrating how computer spreadsheets can be used in the            secondary school mathematics classroom. 
"Spreadsheet Activities in            Middle School Mathematics" by John Russell. 
This book creates a               problem-solving environment for middle grade students using the                 computerized spreadsheet. It offers instructional ideas and                     activities on number patterns, basic arithmetic, word problems,                 percents and probability. WORLD WIDE WEB RESOURCES ON SPREADSHEETS            IN MATHEMATICS EDUCATIONSpreadsheets, Mathematics, Science, and             Statistics Education by Erich Neuwirth                                          http://sunsite.univie.ac.at/Spreadsite/spreaded.html Presents                   information about spreadsheets with an emphasis on mathematics and              statistics education. Includes spreadsheets in education;                       recommended books; papers about spreadsheets in scientific journals             and books; example spreadsheets and projects (mostly excel 5.0); and            further resources for spreadsheets in education on the                          Internet. 
Spreadsheets in the Math Class                                      http://www.math.byu.edu/~lfrancis/readings302/Spreadsheets.html#TOC             Discusses NCTM's position statements on technology, the definition              of  and benefits of using a spreadsheet, data analysis ideas from               the real world, and sample activities to introduce spreadsheets to              students. 
Spreadsheet Projects for the Middle School Math                     Curriculum http://www.parktudor.pvt.k12.in.us/Sosenke/nctm2000.htm              Lists the advantages of the spreadsheets and stages in working with             spreadsheets. Presents a seventh grade spreadsheet unit, independent            short projects, interdisciplinary projects, and references on the               use of spreadsheets in the mathematics classroom. Resources for                 Mathematics Educators: Spreadsheets in Mathematics                              http://www.freshpond.net/treasures/math/spreadsheet/default.htm                 Discusses the benefits of using spreadsheets in mathematics teaching            and some of the particular areas in which spreadsheets can be useful            in teaching and learning math. Provides a list of  web sites that               provide information on using spreadsheets in mathematics                        classrooms. 
Introduction to Math and Spreadsheets                             http://forum.swarthmore.edu/sum95/math_and/spreadsheets/intro.html              Provides a variety of math exercises utilizing                                  spreadsheets. 
Spreadsheets in Mathematics                                     http://jwilson.coe.uga.edu/Allison/Spreadsheet%20home%20page                    Discusses the reasons for using spreadsheets in math classrooms.                Provides information on  how to create a spreadsheet, enter data,               copy cells and formulas, and graph. Presents  problem sets for                  elementary, middle, and high school mathematics. 
The Use of                   Spreadsheets in Mathematics Teaching                                            http://www.geocities.com/teddy_mutadi/essay_EME717.html This essay              discusses the possible application of spreadsheets in an Indonesian             curriculum setting. It also highlights the advantages and                       disadvantages of utilizing spreadsheets in school                               mathematics. 
Spreadsheet-Based Tool Kit For Modeling Concepts In              Elementary Number Theory by Sergei Abramovich and Andrew Brantlinger            http://forum.swarthmore.edu/clime/961.html This paper presents                  pedagogical ideas concerning the use of a spreadsheet- based tool               kit for modeling several structures and concepts in elementary                  number theory such as Pythagorean triples, sums of perfect powers,              multiple representations of integers, the Euclidean algorithm, and              the Euler phi-function. REFERENCESAbramovich, S. and Nabors,              W. (1997). Spreadsheets as generators of new meanings in middle                 school algebra. "Computers in the Schools," 13(1-2),                            13-25. 
Dugdale, S. (1994). K-12 teachers' use of spreadsheet for              mathematical modeling and problem solving. "Journal of Computers in             Mathematics and Science Teaching," 13(1), 43-68. 
Friedlander,                 Alex (1998). An EXCELlent bridge to algebra. "Mathematics Teacher,"             91(50), 382-383 . 
Molyneux-Hodgson, S.; Rojano, T.; Sutherland,               R.; and Ursini, S. (1999). Mathematical modeling: The interaction of            culture and practice. "Educational Studies in Mathematics," 39(1-3),            167-183. 
National Council of Teachers of                                      Mathematics. (2000). "Principles and standards for school                       mathematics." Reston, VA: Author. 
FINDING MORE RESOURCES 
To find            more resources on this topic, search the ERIC database                          online (http://ericir.syr.edu/Eric/) and use various combinations of            the following descriptors; 
-Set 1: spreadsheets,                              tables (data) 
-Set 2: mathematics, mathematics activities,                    mathematics education, mathematics instruction, teaching                        methods 
-Set 3: elementary education, secondary education,                    elementary secondary education, postsecondary education, adult                  education 
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This digest was funded by the Office of                     Educational Research and Improvement, U.S. Department of Education,             under contract no. ED-99-CO-0024. Opinions expressed in this digest             do not necessarily reflect the positions or policies of OERI or the             U.S. Department of Education.                                                **Title:** Using Spreadsheets in Mathematics Education. ERIC Digest.                    **Document Type:** Information Analyses---ERIC Information Analysis Products (IAPs) (071); Information Analyses---ERIC Digests (Selected) in Full Text (073); **Available From:** ERIC/CSMEE, 1929 Kenny Road, Columbus, OH 43210-1080. Tel:                      800-276-0462 (Toll Free); e-mail: [email protected]; Web site:                     http://www.ericse.org.                                                       **Descriptors:**  Computer Uses in Education, Elementary Secondary Education,                    Mathematics Education,  Spreadsheets                                         **Identifiers:** ERIC Digests                                                                 
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