Abstract
This study aims to
examine the extent to which the mobile application of Desmos graphing
calculator supports undergraduate students’ learning of exponential and
logarithmic functions at the Middle School Mathematics Education Program in
Faculty of Education. More specifically, the study investigates the
undergraduate students’ views about and actions in utilizing Desmos while
learning exponential and logarithmic functions. Convenience and purposive
sampling methods were used to conduct this study. Seventeen freshmen
were participated to the study within the context of Fundamentals of
Mathematics course where the exponential and logarithmic functions were
introduced to the undergraduates and in which one of the researchers was the
instructor. Following the qualitative research principles, case study design
was conducted to collect data from observation and documental sources. The data
come from the observations of students' in-class activities, classroom
discussions, researchers’ field notes, and reflection papers over a 3-week
period that was scheduled to teach the concept of exponential and logarithmic
functions. The content analyses of the data reveal that undergraduate students
find Desmos graphing calculator beneficial by highlighting its affordances such
as i) compensating the lack of procedural knowledge, ii) providing
opportunities for exploration, and iii) enhancing engagement with the tasks.
Thus, the study shows that Desmos is a multipurpose learning source for
learning exponential and logarithmic functions. Finally, the study discusses
the role of Desmos on learning functions and provides implications for its use
in undergraduate mathematics courses.
Keywords
Educational technology Desmos graphing calculator exponential function logarithmic function undergraduate students
References
- Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramlarin künyesi. Ankara: Gazi Kitabevi.
- Aslan-Tutak, F. (2013). Tarihi ve Uygulama Alanları ile Logaritma Fonksiyonu. In İsmail Özgür Zembat, Mehmet Fatih Özmantar, Erhan Bingölbali, Hakan Şandır, Ali Delice. (Eds.), Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (p. 399-414). Ankara: Pegem Akademi.
- Ball, D., L. (2000). Bridging practices intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241 – 247.
- Beigie, D. (2014). The algebra artist. Mathematics Teacher, 108(4), 258-265.
- Bourassa, M. (2014). Technology corner - Desmos activities. Ontario Mathematics Gazette, 52(4), 8-10.
- Caniglia, J., Borgerding, L. & Meadows, M. (2017). Strengthening oral language skills in mathematics for english language learners through Desmos technology. International Journal of Emerging Technologies in Learning (iJET), 12(5), 189-194.
- Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction, 28(2), 113–145. https://doi.org/10.1080/07370001003676587.
- Çetin, Y. (2004). Teaching logarithm by guided discovery learning and real life applications. Unpublished master's Thesis). Ankara, TR: Middle East Technical University.
- Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. 4th edition.
- Desmos (2017). Desmos user guide: variables and sliders. Retrieved online from https://desmos.s3.amazonaws.com/Desmos_User_Guide.pdf in 14.08.2017.
- Desmos (2015). About us section. Retrieved 9 September, 2017, from https://www.desmos.com/about
- Ebert, D. (2015). Graphing projects with Desmos. Mathematics Teacher, 108(5), 388-391.
- Edwards, C. M. (2015). Free online resources not to miss for teaching middle school mathematics. Iowa Council of Teachers of Mathematics Journal, 41(Winter 2014-15), 46-51.
- Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5) 433-463.
- Gramble, M. (2005). Sharing teaching ideas: Teaching logarithms day one. Mathematics Teacher, 99(1), 66.
- Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Hoang, B. T. V, & Caverly, D. C. (2013). Techtalk : Mobile apps and college mathematics. Journal of Developmental Education, 37(2), 30-31.
- Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students’ understanding of function. Journal for Research in Mathematics Education, 30(2), 220.
- Hurwitz, M. (1999). We have liftoff! Introducing the logarithmic function. Mathematics Teacher, 92(4), 344–345.
- Karadeniz, I., & Thompson, D. R. (2017). Precalculus teachers’ perspectives on using graphing calculators: an example from one curriculum. International Journal of Mathematical Education in Science and Technology, 1-14. http://dx.doi.org/10.1080/0020739X.2017.1334968
- Kenney, R., & Kastberg, S. (2013). Links in learning logarithms. Australian Senior Mathematics Journal 27(1), 12 - 20. King, A. (2017). Using Desmos to draw in mathematics. Australian Mathematics Teacher, 73(2), 33 - 37.
- Liang, S. (2016). Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator. International Journal of Research in Education and Science, 2(1), 35-48.
- Mcculloch, A. W., Kenney, R. H., & Keene, K. A. (2012). My Answers Don’t Match ! Using the Graphing Calculator to Check. Mathematics Teacher, 105(6), 464-468.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
- Oates, G., Sheryn, L., & Thomas, M. (2014). Technology-active student engagement in an undergraduate mathematics course. Proceeding of PME 38 and PME-NA 36, 4, 329-336.
- Rösken, B., & Rolka, K. (2007). Integrating intuition: The role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, 3, 181-204.
- Shulman, L. (1986). Those who understand knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
- Smith, K. B., & Shotsberger, P. G. (1997). Assessing the use of graphing calculators in college algebra: Reflecting on dimensions of teaching and learning. School Science and Mathematics, 97(7), 368-376.
- Tall, D., & Vinner, S. (1981). Concept images and concept definitions in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/bf00305619
- Thomas, R. (2015, August). ‘‘A graphing approach to algebra using Desmos’‘. Presented at 27th International Conference on Technology in Collegiate Mathematics, edited by Przemyslaw Bogacki, Las Vegas, Nevada.
- Ural, A. (2006). Fonksiyon öğreniminde kavramsal zorluklar [Conceptual obstacles concerning the learning of the function]. Ege Eğitim Dergisi, 7(2), 75–94.
- Venturini, M. (2015). How teachers think about the role of digital technologies in student assessment in mathematics (Doctoral Dissertation). Bologna, IT: Simon Fraser University. Retrieved from http://summit.sfu.ca/item/15703.
- Vinner S. (1991) The role of definitions in the teaching and learning of mathematics. In: D. Tall (Ed.) Advanced Mathematical Thinking. (pp. 65-81). Boston: Academic Publishers.
- Weber, K. (2002a). Developing students' understanding of exponents and logarithms. Proceedings of the 24th Annual Meeting of the North American Chapter of Μathematics Εducation (Vols. 1–4). Retrieved from http://eric.ed.gov/ERICDocs/data/ericdocs2/content_storage_01/0000000b/80/27/e8/b5.pdf
- Weber, K. (2002b). Students’ understanding of exponential and logarithmic functions. Proceedings from the 2nd International Conference on the Teaching of Mathematics. Retrieved from http://www.eric.ed.gov/PDFS/ED477690.pdf
- Williams, H. R. A. (2011). A conceptual framework for student understanding of logarithms (Unpublished master's thesis). Provo, UT: Brigham Young University. Retrieved from http://scholarsarchive.byu.edu/etd/3123.
- Yin, R. K. (2013). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage. Zazkis, R., & Chernoff, E. J. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195–208.
- Zheng, T. (1998, August). Impacts of using calculators in learning mathematics. In The 3 rd Asian Technology Conference on Mathematics (ATCM’98).
- Zucker, A., Kay, R., & Staudt, C. (2014). Helping students make sense of graphs: an experimental trial of SmartGraphs software. Journal of Science Education and Technology, 23(3), 441-457.
Abstract
References
- Argün, Z., Arıkan, A., Bulut, S., & Halıcıoğlu, S. (2014). Temel matematik kavramlarin künyesi. Ankara: Gazi Kitabevi.
- Aslan-Tutak, F. (2013). Tarihi ve Uygulama Alanları ile Logaritma Fonksiyonu. In İsmail Özgür Zembat, Mehmet Fatih Özmantar, Erhan Bingölbali, Hakan Şandır, Ali Delice. (Eds.), Tanımları ve Tarihsel Gelişimleriyle Matematiksel Kavramlar (p. 399-414). Ankara: Pegem Akademi.
- Ball, D., L. (2000). Bridging practices intertwining content and pedagogy in teaching and learning to teach. Journal of Teacher Education, 51(3), 241 – 247.
- Beigie, D. (2014). The algebra artist. Mathematics Teacher, 108(4), 258-265.
- Bourassa, M. (2014). Technology corner - Desmos activities. Ontario Mathematics Gazette, 52(4), 8-10.
- Caniglia, J., Borgerding, L. & Meadows, M. (2017). Strengthening oral language skills in mathematics for english language learners through Desmos technology. International Journal of Emerging Technologies in Learning (iJET), 12(5), 189-194.
- Carlson, M., Oehrtman, M., & Engelke, N. (2010). The precalculus concept assessment: A tool for assessing students’ reasoning abilities and understandings. Cognition and Instruction, 28(2), 113–145. https://doi.org/10.1080/07370001003676587.
- Çetin, Y. (2004). Teaching logarithm by guided discovery learning and real life applications. Unpublished master's Thesis). Ankara, TR: Middle East Technical University.
- Creswell, J. W. (2013). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. 4th edition.
- Desmos (2017). Desmos user guide: variables and sliders. Retrieved online from https://desmos.s3.amazonaws.com/Desmos_User_Guide.pdf in 14.08.2017.
- Desmos (2015). About us section. Retrieved 9 September, 2017, from https://www.desmos.com/about
- Ebert, D. (2015). Graphing projects with Desmos. Mathematics Teacher, 108(5), 388-391.
- Edwards, C. M. (2015). Free online resources not to miss for teaching middle school mathematics. Iowa Council of Teachers of Mathematics Journal, 41(Winter 2014-15), 46-51.
- Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34(5) 433-463.
- Gramble, M. (2005). Sharing teaching ideas: Teaching logarithms day one. Mathematics Teacher, 99(1), 66.
- Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Lawrence Erlbaum Associates.
- Hoang, B. T. V, & Caverly, D. C. (2013). Techtalk : Mobile apps and college mathematics. Journal of Developmental Education, 37(2), 30-31.
- Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students’ understanding of function. Journal for Research in Mathematics Education, 30(2), 220.
- Hurwitz, M. (1999). We have liftoff! Introducing the logarithmic function. Mathematics Teacher, 92(4), 344–345.
- Karadeniz, I., & Thompson, D. R. (2017). Precalculus teachers’ perspectives on using graphing calculators: an example from one curriculum. International Journal of Mathematical Education in Science and Technology, 1-14. http://dx.doi.org/10.1080/0020739X.2017.1334968
- Kenney, R., & Kastberg, S. (2013). Links in learning logarithms. Australian Senior Mathematics Journal 27(1), 12 - 20. King, A. (2017). Using Desmos to draw in mathematics. Australian Mathematics Teacher, 73(2), 33 - 37.
- Liang, S. (2016). Teaching the concept of limit by using conceptual conflict strategy and Desmos graphing calculator. International Journal of Research in Education and Science, 2(1), 35-48.
- Mcculloch, A. W., Kenney, R. H., & Keene, K. A. (2012). My Answers Don’t Match ! Using the Graphing Calculator to Check. Mathematics Teacher, 105(6), 464-468.
- National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
- Oates, G., Sheryn, L., & Thomas, M. (2014). Technology-active student engagement in an undergraduate mathematics course. Proceeding of PME 38 and PME-NA 36, 4, 329-336.
- Rösken, B., & Rolka, K. (2007). Integrating intuition: The role of concept image and concept definition for students’ learning of integral calculus. The Montana Mathematics Enthusiast, 3, 181-204.
- Shulman, L. (1986). Those who understand knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
- Smith, K. B., & Shotsberger, P. G. (1997). Assessing the use of graphing calculators in college algebra: Reflecting on dimensions of teaching and learning. School Science and Mathematics, 97(7), 368-376.
- Tall, D., & Vinner, S. (1981). Concept images and concept definitions in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151–169. https://doi.org/10.1007/bf00305619
- Thomas, R. (2015, August). ‘‘A graphing approach to algebra using Desmos’‘. Presented at 27th International Conference on Technology in Collegiate Mathematics, edited by Przemyslaw Bogacki, Las Vegas, Nevada.
- Ural, A. (2006). Fonksiyon öğreniminde kavramsal zorluklar [Conceptual obstacles concerning the learning of the function]. Ege Eğitim Dergisi, 7(2), 75–94.
- Venturini, M. (2015). How teachers think about the role of digital technologies in student assessment in mathematics (Doctoral Dissertation). Bologna, IT: Simon Fraser University. Retrieved from http://summit.sfu.ca/item/15703.
- Vinner S. (1991) The role of definitions in the teaching and learning of mathematics. In: D. Tall (Ed.) Advanced Mathematical Thinking. (pp. 65-81). Boston: Academic Publishers.
- Weber, K. (2002a). Developing students' understanding of exponents and logarithms. Proceedings of the 24th Annual Meeting of the North American Chapter of Μathematics Εducation (Vols. 1–4). Retrieved from http://eric.ed.gov/ERICDocs/data/ericdocs2/content_storage_01/0000000b/80/27/e8/b5.pdf
- Weber, K. (2002b). Students’ understanding of exponential and logarithmic functions. Proceedings from the 2nd International Conference on the Teaching of Mathematics. Retrieved from http://www.eric.ed.gov/PDFS/ED477690.pdf
- Williams, H. R. A. (2011). A conceptual framework for student understanding of logarithms (Unpublished master's thesis). Provo, UT: Brigham Young University. Retrieved from http://scholarsarchive.byu.edu/etd/3123.
- Yin, R. K. (2013). Case study research: Design and methods (4th ed.). Thousand Oaks, CA: Sage. Zazkis, R., & Chernoff, E. J. (2008). What makes a counterexample exemplary? Educational Studies in Mathematics, 68(3), 195–208.
- Zheng, T. (1998, August). Impacts of using calculators in learning mathematics. In The 3 rd Asian Technology Conference on Mathematics (ATCM’98).
- Zucker, A., Kay, R., & Staudt, C. (2014). Helping students make sense of graphs: an experimental trial of SmartGraphs software. Journal of Science Education and Technology, 23(3), 441-457.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | December 31, 2017 |
| Submission Date | December 8, 2017 |
| Published in Issue | Year 2017Volume: 2 Issue: 2 |
Dear Colleagues,
We are very pleased to announce that the latest issue of IHEAD (Vol. 9- Iss. 1) has been released. We kindly want to express our speacial thanks to the editorial board members, reviewers, and authors for their invaluable contribution to this issue. Also, we are delighted to announce that the next issue (Vol. 9- Iss. 2) of the IHEAD will be available online in December, 2024. As of January, 2024, IHEAD has been accepting submissions in English along with Turkish. Handling your papers within the scope education for the next issue will be a great pleasure for us. Many thanks in advance for your contributions.
Editorial Board
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