Number System Conversions in Spreadsheets for vocational school students: A Case Study from Instrumental Genesis

Abdullah Ozkale, Emel Ozdemir Erdogan

Abstract


Theoretical frameworks for mathematics teaching and learning technology-supported provide a systematic structure in examining the contribution of the tool to conceptual development. This study examines the processes for the use of spreadsheets and the mathematical development of the participants in the tasks for performing the conversions between number systems using the instrumental genesis approach, which deals with transforming a tool into an instrument that will contribute to the conceptual development. In the study, the screen images of the worksheets of the participants, who are at the Department of Computer Technologies Program in a vocational school in Turkey, are analyzed together with the observation notes and evaluation scales prepared based on the outcomes. In the study, while the efforts of the participants to transform the spreadsheet into an instrument are observed, it is seen that their habits of paper-and-pencil experiences and misconceptions lead to an obstacle to transferring their operations to the spreadsheet and hesitations. However, their developments in instrumentalization processes are reflected by the following: they use subjective usage schemes, realize the advantages of spreadsheet functions and features, and create dynamic worksheets through dragging and cell addresses. Nevertheless, it can be stated that the reflections of instrumentalization progress on the instrumentation processes for conceptual development are limited.


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Abramovich S, Grinshpan A-Z & Milligan D-L (2019) Teaching mathematics through concept motivation and action learning. Education Research International, 2019. https://doi.org/10.1155/2019/3745406

Ainley J, Bills L & Wilson K (2005) Designing spreadsheet-based tasks for purposeful algebra. International Journal of Computers for Mathematical Learning, 10(3), 191-215. https://doi.org/10.1007/s10758-005-8420-9

Artigue M (2002) Learning mathematics in a CAS environment: The genesis of a reflection about instrumentation and the dialectics between technical and conceptual work. International Journal of Computers for Mathematical Learning, 7, 245–274. https://doi.org/10.1023A:1022103903080

Baker J-E & Sugden S (2015) 101 Applications for a Binary Table and a Spreadsheet, Spreadsheets in Education, 8(2), 6. https://sie.scholasticahq.com/article/4631-101-applications-for-a-binary-table-and-a-spreadsheet

Bakos, S. (2022). Mathematics, TouchTimes and the Primary School Teacher: Generating Opportunities for Transitions Across and Beyond. Digital Experiences in Mathematics Education, 1-26. https://link.springer.com/content/pdf/10.1007/s40751-022-00109-y.pdf

Balacheff N & Kaput J-J (1996) Computer-based learning environments in mathematics. In A.J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde, (Eds.), International Handbook of Mathematics Education (pp. 429–501). Dordrecht: Kluwer. https://hal.archives-ouvertes.fr/hal-01775249/file/1996%20Balacheff%20%26%20Kaput.pdf

Beigie D (2017) Solving optimization problems with spreadsheets. The Mathematics Teacher, 111(1), 26-33. https://doi.org/10.5951/mathteacher.111.1.0026

Bozkurt G & Uygan C (2020) Lesson hiccups during the development of teaching schemes: a novice technology-using mathematics teacher’s professional instrumental genesis of dynamic geometry. ZDM, 52(7), 1349-1363. https://doi.org/10.1007/s11858-020-01184-4

Caglayan, G. (2017). Almost Every Term of a Sequence from a Multi-Representational Pedagogical Context: Making Sense of Convergence via Spreadsheets. Digital Experiences in Mathematics Education, 3(1), 1-8. https://link.springer.com/content/pdf/10.1007/s40751-016-0027-3.pdf

Castle L (2021) Developing Non-Calculus Service Courses That Showcase the Applicability of Mathematics. In Improving Applied Mathematics Education (pp. 51-64). Springer International Publishing. https://doi.org/10.1007/978-3-030-61717-2_4

Corbin J-M & Strauss A (1990) Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative sociology, 13(1), 3-21. https://link.springer.com/content/pdf/10.1007%252FBF00988593.pdf

Drier H-S (2001) Teaching and learning mathematics with interactive spreadsheets. School science and mathematics, 101(4), 170-179.

Drijvers P, Godino J-D, Font V & Trouche L (2013) One episode, two lenses. Educational Studies in Mathematics, 82(1), 23-49. https://doi.org/10.1007/s10649-012-9416-8

Drijvers P, Doorman M, Boon P, Reed H, & Gravemeijer K (2010) The teacher and the tool; instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213–234. https://doi.org/10.1007/s10649-010-9254-5

Drijvers P & Trouche L (2008) From artifacts to instruments: A theoretical framework behind the orchestra metaphor. In G. W. Blume & M. K. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 2. Cases and perspectives (pp. 363-392). Charlotte, NC: Information Age. https://www.didaktik.mathematik.uni-wuerzburg.de/edumatics/de/mod4/ media/reading/DrijversTrouche2008-0576924161/DrijversTrouche2008.doc

Goos M, Soury-Lavergne S, Assude T, Brown J, Kong C-M, Glover D, ... & Sinclair M (2009) Teachers and teaching: Theoretical perspectives and issues concerning classroom implementation. In Mathematics education and technology-rethinking the terrain (pp. 311-328). Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0146-0_14

Gueudet G & Trouche L (2011) Mathematics teacher education advanced methods: an example in dynamic geometry. ZDM, 43(3), 399-411. https://doi.org/10.1007/s11858-011-0313-x

Haspekian, M. (2014). Teachers’ instrumental geneses when integrating spreadsheet software. In A.Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on technology focused professional development (pp. 241–275). Springer.

Haspekian M (2005) An “instrumental approach” to study the integration of a computer tool into mathematics teaching: The case of spreadsheets. International journal of computers for mathematical learning, 10(2), 109-141. https://doi.org/10.1007/s10758-005-0395-z

Hoyles C & Lagrange J-B (Eds) (2010) Mathematics education and technology –Rethinking the Terrain. The 17th ICMI Study. New York: Springer. https://doi.org/10.1007/978-1-4419-0146-0

Jalbert T & Jalbert M (2019) A Comparison of Financial Calculators. Journal of Financial Education, 45(1), 58-71. https://www.jstor.org/stable/26918024

Marley-Payne J & Dituri P (2019) Spreadsheets as an Effective Use of Technology in Mathematics Education. Spreadsheets in Education, 10138. https://ficycle.org/wpcontent/uploads/2021/12/ Spreadsheets-merged.pdf

Mays T (2015) Using spreadsheets to develop applied skills in a business math course: Student feedback and perceived learning, Spreadsheets in Education, 8(3), 1. https://sie.scholasticahq.com/article/4642-using-spreadsheets-to-develop-applied-skills-in-a-business-math-course-student-feedback-and-perceived-learning

Melkonian V (2019) On Binary Representation of Integers, Primus, 29:5, 474-486. https://doi.org/10.1080/10511970.2018.1489923

Miles R (2021) An alternative route to the Mandelbrot set: connecting idiosyncratic digital representations for undergraduates. Teaching Mathematics and its Applications: An International Journal of the IMA, 40(1), 72-82. http://shura.shu.ac.uk/26290/1/Alternative_routes_to_the_Mandelbrot_set.pdf

National Council of Teachers of Mathematics (NCTM) (2015) Strategic Use of Technology in Teaching and Learning Mathematics. Reston, VA. Retrieved from https://www.nctm.org/uploadedFiles/Standards_and_Positions/Position_Statements/Strategic%20Use%20of%20Technology%20July%202015.pdf

Ozdemir E-O & Turan P (2014) The Primary School Students’ Pattern Seeking Process in the Spreadsheet Environment. Education and Science, 39(173). http://egitimvebilim.ted.org.tr/index.php/EB/article/view/2653/707

Sanford J (2018) Introducing computational thinking through spreadsheets. In Computational Thinking in the STEM Disciplines (pp. 99-124). Springer, Cham. https://doi.org/10.1007/978-3-319-93566-9_6

Stewart I (2009) Professor Stewart's cabinet of mathematical curiosities. Basic Books.

Sutherland R (2007) A dramatic shift of attention: From arithmetic to algebraic thinking. Algebra in the early grades. In Kaput, J., (Ed.) Employing Children’s Natural Powers to Build Algebraic Reasoning in the Content of Elementary Mathematics. Mahwah, Lawrence Erlbaum Associates.

Trouche L (2004) Managing The Complexity Of Human/Machine Interaction In Computerized Learning Environment: Guiding Students’ Command Process Through Instrumental Orchestrations. International Journal of Computers For Mathematical Learning, 9(3), 281-307. https://doi.org/10.1007/s10758-004-3468-5

van Dijke-Droogers, M Drijvers P & Bakker A (2021) Statistical modeling processes through the lens of instrumental genesis. Educational Studies in Mathematics, 107(2), 235-260. https://doi.org/10.1007/s10649-020-10023-y




DOI: https://doi.org/10.51383/ijonmes.2023.297

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