Volume 71 | Issue 4 | Year 2025 | Article Id. IJMTT-V71I4P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I4P105
Received | Revised | Accepted | Published |
---|---|---|---|
28 Feb 2025 | 30 Mar 2025 | 17 Apr 2025 | 30 Apr 2025 |
This paper presents a software application focused on the concepts of equal parts of the unit whole, improper fractions, and the ordering of rational numbers using the geometric model of the number line. The software aims to familiarize students with positive rational numbers through various activities in a dynamic multimedia environment and to help them overcome the difficulties they often encounter with fractions. This is achieved using representational tools and the 10+1 foundational mathematical elements of the applied theoretical framework "RhodeScript," on which the added value of the software is based. Findings from long-standing educational Research determined the content and activities of the software. This digital game aims to address possible gaps in existing teaching practices related to fractions, to support school textbooks and the Mathematics Curriculum, and to assist elementary and lower secondary school students in overcoming the mentioned conceptual difficulties. When implemented as supplementary material during the instruction of rational numbers, the software was found to help mitigate students' difficulties with fractional concepts.
Educational software, representational tools, positive rational numbers, 10+1 points theory (RhodeScript), primary education.
[1] E. Avgerinos, and R. Vlachou, “The Consistency Between the Concepts of Equal Parts of the Unit, Improper Fractions and Problem
Solving at Candidate Teachers of Education Departments,” Proceedings of the 30th Hellenic Conference on Mathematical Education, pp.
135-147, 2013.
[Google Scholar]
[2] Roza Vlachou, and Evgenios Avgerinos, “Current Trend and Studies on Representation of Fractions,” 7th Mediterranean Conference on
Mathematics Education, pp.135-159, 2012.
[3] E., Avgerinos, R., Vlachou, andK., Kantas, “Comparing Different Age Student Abilities on the Concept and Manipulation of Fractions,”
Research on Mathematical Education and Mathematics Applications, pp. 159-169, 2012.
[Google Scholar]
[4] E. Avgerinos, R. Vlachou, and D. Remoundou, Mathematical Tools in Education: Applied Mathematics Teaching and Practical
Application of Rhode Script Theory in the Elementary School, Rhodes, Greece: University of the Aegean, 2023.
[5] Evgenios P. Avgerinos, Roza G. Vlachou, and Dimitra I. Remoundou, “Development and Implementation of a Didactical Framework of
10+1 Elements for the Reinforcement of Students’ Mathematical Ability and Attitude Towards Mathematics: Part I,” Proceedings of
International Conference on Educational Research: Confronting Contemporary Educational Challenges through Research, pp. 17-29,
2018.
[Google Scholar]
[6] Jerome S. Bruner, The Process of Education, Cambridge, MA: Harvard University Press, 1960.
[Google Scholar]
[7] Xi Chen, and Yeping Li, “Instructional Coherence in Chinese Mathematics Classroom—A Case Study of Lessons on Fraction Division,”
International Journal of Science and Mathematics Education, vol. 8, no. 4, pp. 711-735, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[8] L. Cohen, and L. Manion, Methodology of Educational Research, Trans., Athens: Ekfrassi, 1997.
[Google Scholar]
[9] Anika Dreher, and Sebastian Kuntze, “Teachers’ Professional Knowledge and Noticing: The Case of Multiple Representations in the
Mathematics Classroom,” Educational Studies in Mathematics, vol. 88, no. 1, pp. 89-114, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Anika Dreher, Sebastian Kuntze, and Stephen Lerman, “Why Use Multiple Representations in the Mathematics Classroom? Views of
English and German Preservice Teachers,” International Journal of Science and Mathematics Education, vol. 14, no. 2, pp. 363-382,
2016.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Martha Isabel Fandiño Pinilla, “Fractions: Conceptual and Didactic Aspects,” Didactic Acta Comenius University, vol. 7, pp. 23-45, 2007.
[Google Scholar]
[12] Michael N. Fried, “Can Mathematics Education and History of Mathematics Coexist?,” Science & Education, vol. 10, no. 4, pp. 391-408,
2001.
[CrossRef] [Google Scholar] [Publisher Link]
[13] R. Gras et al., “Implicative Statistical Analysis,” Data Science, Classification, and Related Methods, pp. 412-419, 1998.
[CrossRef] [Google Scholar] [Publisher Link]
[14] R. Duval, “Registers of Semiotic Representations and Cognitive Functioning of Thought,” Annals of Didactics And Cognitive Sciences,
ULP, IREM Strasbourg. vol. 5, pp. 37-65, 1993.
[Google Scholar] [Publisher Link]
[15] R. Gras et al., “Statistical Implicative Analysis, Theory and Applications,” Studies in Computational Intelligence, Springer-Verlag, Berlin
Heidelberg Consultable, vol. 127, 2008.
[Google Scholar]
[16] Jeremy Hodgen et al., “Lower Secondary School Students' Knowledge of Fractions,” Research in Mathematics Education, vol. 12, no. 1,
pp. 75-76, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[17] Christine Howe et al., “Rational Number and Proportional Reasoning in Early Secondary School: Towards Principled Improvement in
Mathematics,” Research in Mathematics Education, vol. 17, no. 1, pp. 38-56, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[18] Uffe Thomas Jankvist, “A Categorization of the "Whys" and "Hows" of Using History in Mathematics Education,” Educational Studies
in Mathematics, vol. 71, no. 3, pp. 235-261, 2009.
[CrossRef] [Google Scholar] [Publisher Link]
[19] C. Janvier, “Problems of Representation in the Teaching and Learning of Mathematics,” American Psychological Association, pp. 27-32,
1987.
[Google Scholar] [Publisher Link]
[20] Chunlian Jiang, and Boon Liang Chua, “Strategies for Solving Three Fraction-Related Word Problems on Speed: A Comparative Study
between Chinese and Singaporean Students,” International Journal of Science and Mathematics Education, vol. 8, no. 1, pp. 73-96, 2010.
[CrossRef] [Google Scholar] [Publisher Link]
[21] Susan J. Lamon, “The Development of Unitizing: Its Role in Children’s Portioning Strategies,” Journal for Research in Mathematics
Education, vol. 27, no. 2, pp.170-193, 1996.
[CrossRef] [Google Scholar] [Publisher Link]
[22] J.J. Lo, “Conceptual Bases of Young Children’s Solution Strategies of Missingvalue Proportional Tasks,” Proceedings of the Seventeenth
International Conference of Psychology of Mathematics Education: PME XVII, Tsukuba, Japan: University of Tsukuba, pp. 162-177,
1993.
[Google Scholar]
[23] Yujing Ni, “Semantic Domains of Rational Number and the Acquisition of Number Equivalence,” Contemporary Educational Psychology,
vol. 26, no. 3, pp. 400-417, 2001.
[CrossRef] [Google Scholar] [Publisher Link]
[24] Donald M. Peck, and Stan Ley M. Jencks, “Conceptual Issues in the Teaching and Learning of Fractions,” Journal for Research in
Mathematics Education, vol. 12, no. 5, pp. 339-348, 1981.
[CrossRef] [Google Scholar] [Publisher Link]
[25] Anna Sfard, “On the Dual Nature of Mathematical Conceptions: Reflections on Processes and Objects as Different Sides of the Same
Coin,” Educational Studies in Mathematics, vol. 22, pp. 1-36, 1991.
[CrossRef] [Google Scholar] [Publisher Link]
[26] David Squires, and Anne McDougall, Choosing and Using Educational Software: A Teacher’s Guide, London: The Falmer Press, 1994.
[Google Scholar] [Publisher Link]
[27] Leen Streefland, Fractions in Realistic Mathematics Education: A Paradigm of Developmental Research, Dordrecht, Τhe Netherlands:
Kl, 1991.
[Google Scholar] [Publisher Link]
[28] Xenia Vamvakoussi, and Stella Vosniadou, “Understanding the Structure of the Set of Rational Numbers: A Conceptual Change
Approach,” Learning and Instruction, vol. 14, no. 5, pp.453-467, 2004.
[CrossRef] [Google Scholar] [Publisher Link]
[29] Roza Vlachou, and Evgenios Avgerinos, “Multiple Representatıons and Development of Students' Self-Confidence on Rational Number,”
Experiences of Teaching with Mathematics, Sciences and Technology, vol. 4, pp. 567-586, 2018.
[Google Scholar] [Publisher Link]
[30] Hajime Yoshida, and Kooji Sawano, “Overcoming Cognitive Obstacles in Learning Fractions: Equal-Partitioning and Equal-Whole,”
Japanese Psychological Research, vol. 44, no. 4, pp. 183-195, 2002.
[CrossRef] [Google Scholar] [Publisher Link]
[31] Soo Jin Lee, and Jaehong Shin, “Distributive Partitioning Operation in Mathematical Situations Involving Fractional Quantities,”
International Journal of Science and Mathematics Education, vol. 13, no. 2, pp. 329-355, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[32] Susan B. Empson, Linda Levi, and Thomas P. Carpenter, “The Algebraic Nature of Fractions: Developing Relational Thinking in
Elementary School,” Early Algebraization, pp. 409-428, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[33] Mi Yeon Lee, and Amy J. Hackenberg, “Relationships between Fractional Knowledge and Algebraic Reasoning: The Case of Willa,”
International Journal of Science and Mathematics Education, vol. 12, no. 4, pp. 975-1000, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[34] Ben Shneiderman, Jock Mackinlay, and Stuart K. Card, Readings in Information Visualization: Using Vision to Think, San Francisco:
Morgan Kaufmann Publishers, 1999.
[Google Scholar] [Publisher Link]
[35] A.A. Cuoco, and F.R. Curcio, The Roles of Representation in School Mathematics: 2001 Yearbook, Reston, VA: National Council of
Teachers of Mathematics, 2001.
[Google Scholar]
[36] Anika Dreher, and Sebastian Kuntze, “Teachers’ Professional Knowledge and Noticing: The Case of Multiple Representations in the
Mathematics Classroom,” Educational Studies in Mathematics, vol. 88, no. 1, pp. 89-114, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[37] Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, pp. 1-20, 2000.
[Publisher Link]
[38] Erik Jacobson, and Andrew Izsák, “Knowledge and Motivation as Mediators in Mathematics Teaching Practice: The Case of Drawn
Models for Fraction Arithmetic,” Journal of Mathematics Teacher Education, vol. 18, no. 5, pp. 467-488, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[39] Alice Hansen, Manolis Mavrikis, and Eirini Geraniou, “Supporting Teachers’ Technological Pedagogical Content Knowledge of Fractions
through Co-Designing a Virtual Manipulative,” Journal of Mathematics Teacher Education, vol. 19, no. 2-3, pp. 205-226, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
Roza Vlachou, "Fraction Battles: Software for Rational Numbers using Representational Tools," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 4, pp. 37-54, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I4P105