EXPLORING PRE-SERVICE MATHEMATICS TEACHERS’ UNDERSTANDINGS OF COUNTABILITY AND INFINITY IN WEBQUEST BASED LEARNING ENVIRONMENT
Abstract
Infinity concept is difficult to understand because of its nature. Even if the concept of infinity doesn’t directly take part in mathematics curriculum, it takes place on many topics such as lines, planes, sets, irrational numbers, limit, differentiation, and integration. The present study examined pre-service mathematics teachers’ understandings of infinity and countability concepts in WebQuest based learning environment. Twenty-nine pre-service teachers participated at the study. Data were collected through a questionnaire developed by the researchers and semi-structured interviews. Qualitative data were analyzed by using phenomenology research method. The findings of this study revealed that pre-service teachers generally defined infinite sets as the sets whose elements continue infinitely. They inclined to define countable sets as bounded sets, finite sets, and the sets with known elements. Whereas most of the students stated countable finite sets and countable infinite sets were existent, they also expressed uncountable finite sets and uncountable infinite sets were non-existent. They used natural numbers set as an example for the countable infinite sets. This research presented some implications for teacher education programme in the light of obtained findings.
Article visualizations:
Keywords
Full Text:
PDFReferences
Aztekin, S., Arikan, A., & Sriraman, B. (2010). The constructs of PhD Students about infinity: An application of repertory grids. The Mathematics Enthusiast, 7(1), 149-174.
Bagni, T. G. (1997). Didactics of Infinity: Euclid’s proof and Eratosthenes’ sieve prime numbers and potential infinity in high school. In B. D’Amore & A. Gagatsis (Eds.), Didactics of Mathematics Technology in Education (pp. 209-218). Erasmus ICP-96-G-2011/11, Thessaloniki.
Ball, S. J. (1990). Politics and Policy-Making in Education. London: Routledge.
Cantor, G. (1915). Contributions to the founding of the theory of transfinite numbers (P. E. B. Jourdain, Trans.). New York: Dover (Original work published 1895).
Cohen, L., Manion, L., & Morrison, K. (2007). Research methods in education (Sixth ed.). London: Routledge.
Çelik, D., & Akşan, E. (2013). Preservice mathematics teachers’ perceptions of infinity, indeterminate and undefined. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 7(1), 166-190.
Çığrık, E., & Ergül, R. (2010). The investion effect of using WebQuest on logical thinking ability in science education. Procedia Social and Behavioral Sciences, 2(2), 4918–4922.
Dede, Y., & Soybaş, D. (2011). Preservice mathematics teachers’ concept images of polynomials. Quality & Quantity, 45(2), 391-402.
Dodge, B. (1997). Some thoughts about WebQuest. Retrieved December 21, 2014 from http://webquest.sdsu.edu/about_webquests.html.
Dreyfus, T., & Tsamir, P. (2004). Ben's consolidation of knowledge structures about infinite sets. The Journal of Mathematical Behavior, 23(3), 271-300.
Dubinsky, E., Weller, K., Mcdonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An Apos-Based analysis: Part 1. Educational Studies in Mathematics, 58(3), 335-359.
Falk, R. (2010). The infinite challenge: Levels of conceiving the endlessness of numbers. Cognition and Instruction, 28(1), 1-38.
Fischbein, E. (2001). Tacit models of infinity. Educational Studies in Mathematics, 48(2), 309–329.
Fischbein, E., Tirosh, D., & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10(1), 2–40.
Fischbein, E., Tirosh, D., & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement? Educational Studies in Mathematics, 12, 491-512.
Goktepe-Yildiz, S., & Goktepe-Korpeoglu, S. (2016). A sample Webquest applicable in teaching topological concepts. International Journal of Education in Mathematics, Science and Technology, 4(2), 133-146.
Gülbahar, Y., Madran, R. O., & Kalelioglu, F. (2010). Development and evaluation of an interactive WebQuest environment: Web Macerasi. Educational Technology & Society, 13(3), 139–150.
Halat, E. (2008). Webquest-temelli matematik öğretiminin sınıf öğretmeni adaylarının geometrik düşünme düzeylerine etkisi. [The effect of Webquest-based mathematics teaching on geometric thinking levels of classroom teacher candidates]. Selçuk University Ahmet Keleşoğlu Education Faculty Journal, 25, 115-130.
Halat, E., & Peker, M. (2011). The impacts of mathematical representations developed through webquest and spreadsheet activities on the motivation of pre-service elementary school teachers. Turkish Online Journal of Educational Technology, 10(2), 259 -267.
Harel, G., Selden, A., & Selden, J. O. (2006). Advanced mathematical thinking. Handbook of research on the psychology of mathematics education: past, present and future, 147-172.
Hayes, M., & Billy, A. (2003). Web-based modules designed to address learning bottlenecks in introductory anatomy and physiology courses. Interactive Multimedia Electronic Journal of Computer-Enhanced Learning, 1(2).
Kelly, R. (2000). Working with WebQuests: Making the web accessible to students with disabilities. Teaching Exceptional Children, 32(6), 4–13.
Kolar, V. M., & Cadez, T. H. (2012). Analysis of factors influencing the understanding of the concept of infinity. Educational Studies in Mathematics, 80(3), 389-412.
Kurtuluş, A., & Kılıç, R. (2009). The effect of Webquest-aided cooperative learning method on mathematic learning. E-Journal of New World Sciences Academy Education Science, 4(1), 62-70.
Lim, S. L., & Hernandez, P. (2007). The webquest: an illustration of instructional technology implementation in MFT training. Contemporary Family Therapy, 29(3), 163-175.
Lipschutz, S. (1965). General topology. New York: McGraw-Hill.
Luis, E., Moreno, A., & Waldegg, G. (1991). The conceptual evolution of actual mathematical infinity. Educational Studies in Mathematics, 22(3), 211-231.
Mamolo, A., & Zazkis, R. (2008). Paradoxes as a window to infinity. Research in Mathematics Education, 10(2), 167-182.
Monaghan, J. (2001). Young peoples' ideas of infinity. Educational Studies in Mathematics, 48(2), 239-257.
Mura, R., & Louice, M. (1997). Is infinity ensemble of numbers? A study on teachers and prospective teachers. For the Learning of Mathematics, 17(3), 28-35.
Narli, S. (2011). Is constructivist learning environment really effective on learning and long term knowledge retention in mathematics? Example of the infinity concept. Educational Research and Reviews, 6(1), 36-49.
Narli, S., & Narli, P. (2012). Determination of primary school students’ perceptions and misconceptions of infinity using infinite number sets. Buca Eğitim Fakültesi Dergisi, 33, 122-133.
Oliver-Hoyo, M., & Allen, D. (2006). The use of triangulation methods in qualitative educational research. Journal of College Science Teaching, 35(4), 42-47.
Öksüz, C., & Uça, S. (2010). Development of a perception scale on the use of webquests. Ankara University Journal of Faculty of Educational Sciences, 43(1), 131-150
Özmantar, F. (2008). Sonsuzluk kavramı: tarihsel gelişimi, öğrenci zorlukları ve çözüm önerileri [Infinity concept: historical development, students challenges, and solution suggestions]. In M. F. Ozmantar, E. Bingolbali, & H. Akkoc (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri [Mathematical misconceptions and solution suggestions] (pp.151-180). Ankara: Pegem Akademi.
Pehkonen, E., Hannula, M. S., Maijala, H., & Soro, R. (2006). Infinity of numbers: How students understand it. International Group for the Psychology of Mathematics Education, 4, 345-352.
Rudin, W. (1976). Principles of Mathematical Analysis, New York: McGraw-Hill.
Singer, M., & Voica, C. (2008). Between perception and intuition: Learning about infinity. The Journal of Mathematical Behavior, 27(3), 188-205.
Singer, M., & Voica, C. (2003). Perception of infinity: does it really help in problem solving. In A. Rogerson (Eds.), Proceedings of the International Conference The Decidable and the Undecidable in Mathematics Education (pp. 252-256). Brno, Czech Republic: The Mathematics Education into the 21st Century Project.
Tall, D., & Bakar, M. (1992). Students’ mental prototypes for functions and graphs. International Journal of Mathematical Education in Science and Technology, 23(1), 39-50.
Tall, D., & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169.
Tirosh, D. (1991). The role of students’ intuitions of infinity in teaching the Cantorian theory. In D. Tall (Ed.), Advanced mathematical thinking (pp. 199–214). Kluwer: Dordrecht.
Tirosh, D. (1999). Finite and infinite sets: Definitions and intuitions. International Journal of Mathematical Education in Science and Technology, 30(3), 341-349.
Tirosh, D., & Tsamir, P. (1996). The role of representations in students’ intuitive thinking about infinity. International Journal of Mathematics Education in Science and Technology, 27(1), 33–40.
Tsamir, P. (1999). The transition from comparison of finite to the comparison of infinite sets: Teaching prospective teachers. Educational Studies in Mathematics, 38, 209–234.
Tsamir, P. (2001). When‘the same’ is not perceived as such: The case of infinite sets. Educational Studies in Mathematics, 48(2), 289–307.
Tsamir, P. (2002). From primary to secondary intuitions: prospective teachers’ transitory intuitions of infinity. Mediterranean Journal for Research in Mathematics Education, 1, 11–29.
Tsamir, P., & Tirosh, D. (1999). Consistency and representations: The case of actual infinity. Journal for Research in Mathematics Education, 30(2), 213–220.
Ünan, Z., & Doğan, M. (2011). Finite set and countable infinite sets and uncountable infinite sets modelling. NWSA: Education Sciences, 6(2), 1938-1950.
Vanderstoep, S. W., & Johnston, D.D. (2009). Research Methods for Everyday Life: Blending Qualitative and Quantitative Approaches. San Francisco: John Wiley & Sons.
Vinner, S., & Hershkowitz, R. (1980). Concept images and common cognitive paths in the development of some simple geometrical concepts. Proceedings of the 4th annual meeting for the Psychology of Mathematics Education (pp. 177–184). Berkeley, CA: Psychology of Mathematics Education.
Vinner, S., & Hershkowitz, R. (1980). Concepts images and common cognitive paths in the development of some simple geometrical concepts. In R. Karplus (Eds.), Proceedings of the fourth international conference for the psychology of mathematics education (pp. 177–184). Berkeley, CA: Lawrence Hall of Science, University of California.
Waldegg, G. (2005). Bolzano‘s Approach to the Paradoxes of Infinity: Implications for Teaching. Science & Education, 14(6), 559-577.
Watson, K. L. (1999). WebQuests in the middle school curriculum: Promoting technological literacy in the classroom. Meridian: A Middle school computer technologies journal, 2(2), 1-3.
Wawro, M., Sweeney, G. F., & Rabin, J. M. (2011). Subspace in linear algebra: investigating students’ concept images and interactions with the formal definition. Educational Studies in Mathematics, 78(1), 1-19.
Yang, K. H. (2014). The WebQuest model effects on mathematics curriculum learning in elementary school students. Computers & Education, 72, 158-166.
Yanik, H. B. (2014). Middle-school students’ concept images of geometric translations. The Journal of Mathematical Behavior, 36, 33-50.
Yanik, H. B., & Flores, A. (2009). Understanding rigid geometric transformations: Jeff’s learning path for translation. Journal of Mathematical Behavior, 28(1), 41–57.
Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning. The Journal of Mathematical Behavior, 29(2), 57-75.
DOI: http://dx.doi.org/10.46827/ejes.v0i0.1895
Refbacks
- There are currently no refbacks.
Copyright (c) 2018 Sevda Göktepe Yildiz, Seda Göktepe Körpeoğlu
This work is licensed under a Creative Commons Attribution 4.0 International License.
Copyright © 2015-2023. European Journal of Education Studies (ISSN 2501 - 1111) is a registered trademark of Open Access Publishing Group. All rights reserved.
This journal is a serial publication uniquely identified by an International Standard Serial Number (ISSN) serial number certificate issued by Romanian National Library (Biblioteca Nationala a Romaniei). All the research works are uniquely identified by a CrossRef DOI digital object identifier supplied by indexing and repository platforms. All authors who send their manuscripts to this journal and whose articles are published on this journal retain full copyright of their articles. All the research works published on this journal are meeting the Open Access Publishing requirements and can be freely accessed, shared, modified, distributed and used in educational, commercial and non-commercial purposes under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
