THE ROLE OF MATHEMATICS EDUCATION ADVISORS IN THE DESIGN AND IMPLEMENTATION OF SEMINARS AND WORKSHOPS: CONSULTANT, MANAGER, RESEARCHER, OR LEADER?

Stavroula Patsiomitou

Abstract


This paper describes the role of Mathematics Education Advisors in designing, organizing, and implementing professional development seminars and workshops aimed at supporting mathematics teachers’ professional development, pedagogical innovation, and instructional practices in digital learning environments. The study conceptualizes this role as extending beyond administrative responsibilities to encompass pedagogical leadership, instructional design, and the development of professional learning communities. The study is grounded in didactical and theoretical perspectives on Mathematics Education. In relation to my own contribution, my research in dynamic geometry, together with the conceptual constructs I introduced within this framework, constitutes a central theoretical foundation not only of the present study but also of the seminars and professional development activities that I organize and implement. Within this context, I present and analyse a series of professional development initiatives that integrate dynamic geometry software, digital technologies, and emerging tools such as artificial intelligence. A key dimension of my work involves the design and structure of digital learning repositories that extend classroom practice and promote the dissemination /distribution of interactive learning materials. As an illustrative example, I present my work on the systematic transformation of assessment tasks drawn from the Item Bank of Graded Difficulty (IBGD) of the Hellenic Institute of Educational Policy (IEP), in which symbolic, verbal, and mathematical representations are converted into graphical representations within the GeoGebra dynamic geometry environment, conceptualized through a “Dynamic Calculus” approach. Overall, the study concludes that seminars and workshops, when grounded in robust didactical frameworks and supported by digital technologies, can function as powerful mechanisms for pedagogical transformation, bridging educational theory, policy, and classroom practice.

Keywords


mathematics teacher education; seminars and workshops; digital environments; mathematics education advisor

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References


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Patsiomitou, S. (2009b) Learning Mathematics with The Geometer’s Sketchpad v4. Monograph. Klidarithmos Publications. Volume A. ISBN: 978-960-461-308-3) (in Greek)

Patsiomitou, S. (2009c) Learning Mathematics with The Geometer’s Sketchpad v4. Monograph. Klidarithmos Publications. Volume B. ISBN: 978-960-461-309-0) (in Greek)

Patsiomitou, S. (2009d). Cognitive and theoretical (gnostikotheoretices) links using the Geometer’s Sketchpad software’s interaction techniques. Proceedings of the 5th Pan-Hellenic ICT Conference, entitled "Exploiting Information and Communication Technologies in Didactic Practice", Greek Ministry of Education, pp. 583-591. Syros 8, 9, 10 May 2009(in Greek)

Patsiomitou, S. (2009e) Demonstration of visual proofs through decomposition and rearrangement of equivalent figures, created in a dynamic geometry software. Proceedings of the 5th Pan-Hellenic ICT Conference, entitled "Exploiting Information and Communication Technologies in Didactic Practice", Greek Ministry of Education, pp. 592-600. 8, 9, 10 May 2009 Syros. (in Greek)

Patsiomitou, S. (2009f). Tessellations, Pentominos, Structural Algebraic Units, Rep-Tiles, Tangram: A proposal for a qualitative upgrading of math curricula. In Proceedings of the 5th Pan-Hellenic ICT Conference: Exploiting Information and Communication Technologies in Didactic Practice (pp. 601–609). Syros, 8–10 May 2009. (in Greek)

Patsiomitou, S. (2009g) Students’ cognitive interactions through constructions created with the Geometer's Sketchpad v4 DG environment. Proceedings of the 1st Educational Conference entitled "Integration and Use of ICT in the Educational Process", pp. 129-134. Volos, 24-26 April. http://www.etpe.gr/custom/pdf/etpe1440.pdf (in Greek)

Patsiomitou, S. (2009h) Tessellations constructed using Geometer's Sketchpad v4 as an intuitive means for the development of students’ deductive reasoning. In Proceedings of the 1st Educational Conference: Integration and Use of ICT in the Educational Process, 1, 154–160. Volos, 24–26 April. (in Greek) https://eproceedings.epublishing.ekt.gr/index.php/cetpe/article/view/6426

Patsiomitou, S. (2010). Building LVAR (Linking Visual Active Representations) modes in a DGS environment. Electronic Journal of Mathematics and Technology (eJMT), 4(1), 1–25. https://ejmt.mathandtech.org/Contents/eJMT_v4n1p1.pdf

Patsiomitou, S. (2011a). Theoretical dragging: A non-linguistic warrant leading to dynamic propositions. 35th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3, pp. 361-368. Ankara, Turkey: PME. ISBN 978-975-429-297-8. Available at https://www.researchgate.net/publication/230648462

Patsiomitou, S. (2011b). Theoretical dragging: a non-linguistic warrant leading students to develop ‘dynamic’ propositions. 28th Panhellenic Conference of Hellenic Mathematical Society, pp.562-574, Department of Mathematics of the University of Athens. https://www.academia.edu/3544047

Patsiomitou, S. (2012a). The development of students’ geometrical thinking through transformational processes and interaction techniques in a dynamic geometry environment: Linking Visual Active Representations (PhD thesis). University of Ioannina. https://www.didaktorika.gr/eadd/handle/10442/35816 (in Greek)

Patsiomitou, S. (2012b). A Linking Visual Active Representation DHLP for student’s cognitive development. Global Journal of Computer Science and Technology, 12(6), 53–81. http://computerresearch.org/index.php/computer/article/view/479/479

Patsiomitou, S. (2012c) Didactic approaches to teaching Mathematics to students with different learning styles: Mathematics in the Real World. Self–publishing. ISBN 978-960-93-4456. (in Greek) https://www.academia.edu/2054056/ (in Greek)

Patsiomitou, S. (2012d). Building and Transforming Linking Visual Active Representations – Implementation of LVARs for the teaching of mathematics in class. Proceedings of 8th Pan-Hellenic Conference with International Participation "ICT in Education" (HCICTE, 2012), University of Thessaly http://www.etpe.gr/custom/pdf/etpe1895.pdf (in Greek)

Patsiomitou, S. (2013a) Students learning paths as ‘dynamic encephalographs’ of their cognitive development". Ιnternational journal of computers & technology [Online], 4(3) pp. 802-806 (18 April 2013) ISSN 2277-3061, https://doi.org/10.24297/ijct.v4i3.4207, http://cirworld.com/index.php/ijct/article/view/3038/pdf

Patsiomitou, S. (2013b) Instrumental decoding of students’ conceptual knowledge through the modeling of real problems in a dynamic geometry environment. EUCLID C: Scientific journal of Hellenic Mathematical Society, 79, 107–136. (in Greek)

Patsiomitou, S. (2014). Student’s learning progression through instrumental decoding of mathematical ideas. Global Journal of Computer Science and Technology, 14(1), 1–42. http://computerresearch.org/index.php/computer/article/view/41/41

Patsiomitou, S. (2015a). A Dynamic Teaching Cycle of Mathematics through Linking Visual Active Representations". Scientific Journal "ERKYNA", PanHellenic Pedagogical Society for Secondary-level Education. Vol.7, pp. 70-86. https://erkyna.gr/e_docs/periodiko/dimosieyseis/thet_epistimes/t07-05.pdf (in Greek)

Patsiomitou, S. (2015b) Gender equality in [STEM] education: Why Do Women Teach and Men Manage? Proceedings of the Panhellenic conference “The New Educator (Neos Paidagogos)”, 23-24 May, Eugenides Foundation, pp. 1267-1290(in Greek)

Patsiomitou, S. (2015c). The development of students’ competence on instrumental decoding as a non-linguistic warrant for the development of their geometric thinking. Scientific journal “The New Educator (Neos Paidagogos)”. 5th issue, pp. 29-60. (in Greek)

Patsiomitou, S. (2015d). The Open eClass platform as a means for instructional design and curriculum management. Scientific journal “The New Educator (Neos Paidagogos)”. 6th issue, pp.211-244. (The paper has been presented at the conference of "Education in the Era of ICT", 7 November 2015, Eugenides Foundation, conference proceedings: pp. 700-738) (in Greek)

Patsiomitou, S. (2016a). Synthesis, application and evaluation of a “dynamic” curriculum: Transformations of fractals objects, parametric regular polygons and number π. Linking Visual Active Representations. A keynote speech. In 3rd Panhellenic Conference of “The New Educator (Neos Paidagogos)” (pp. 3563–3602). Eugenides Foundation, 16–17 April. (in Greek)

Patsiomitou, S. (2016b). Linking Visual Active Representations: Synthesis, implementation and evaluation of a “dynamic” curriculum based on dynamic transformations of mathematical objects with the utilization of interaction techniques. The New Educator (Neos Paidagogos), 7, 315–347. (in Greek)

Patsiomitou, S. (2016c). Environment & computer environments: The role of games in the development of students’ competencies and their sense for a substantial school environment. In Proceedings of the 13th Panhellenic Conference: The Education in the era of ICT and innovation (pp. 967–994). (in Greek)

Patsiomitou, S. (2018a). A dynamic active learning trajectory for the construction of number π: Transforming mathematics education. International Journal of Education and Research, 6(8), 225–248. http://www.ijern.com/journal/2018/August-2018/18.pdf

Patsiomitou, S. (2018b). An ‘alive’ DGS tool for students’ cognitive development. International Journal of Progressive Sciences and Technologies (IJPSAT), 11(1), 35–54. http://ijpsat.ijsht-journals.org/index.php/ijpsat/article/view/636

Patsiomitou, S. (2019a). From Vecten’s Theorem to Gamow’s Problem: Building an Empirical Classification Model for Sequential Instructional Problems in Geometry. Journal of Education and Practice. 10(5), 1–23. https://doi.org/10.7176/JEP/10-5-01. https://iiste.org/Journals/index.php/JEP/article/view/46479

Patsiomitou, S. (2019b). Hybrid-dynamic objects: DGS environments and conceptual transformations. International Journal for Educational and Vocational Studies. 1(1), 31–46. pp. 31-46. DOI: https://doi.org/10.29103/ijevs.v1i1.1416. Available online at http://ojs.unimal.ac.id/index.php/ijevs

Patsiomitou, S. (2019c). A trajectory for the teaching and learning of the didactics of mathematics [using ICT]: Linking Visual Active Representations. Monograph. Global Journal Incorporated. ISBN 978-1-7340132-0-7. http://doi.org/10.34257/SPatTrajICT

Patsiomitou, S. (2020a). Didactics of Mathematics I: Linking Visual Active Representations. Monograph. Anatolikos. Athens, ISBΝ: 978-618-5136-46-8. https://www.academia.edu/42019703/ (in Greek)

Patsiomitou, S. (2020b). Didactics Instruction and Assessment of Mathematics: Learning Trajectories and Curriculum. Monograph. Anatolikos. Athens ISBΝ: 978-618-5136-49-9. https://www.academia.edu/43702210/(in Greek)

Patsiomitou, S. (2020c). Didactics and Instruction of Mathematics: From theory to action using microworlds. Monograph. Angelakis Publications. Athens. ISBN: 978-960-616-155-1. https://www.academia.edu/43795275/(in Greek)

Patsiomitou, S. (2020d). Formulation of a gender "theory" in education: established trends. Monograph. Angelakis Publications. Athens. ISBN: 978-960-616-171-1 , https://www.academia.edu/44760742/(in Greek)

Patsiomitou, S. (2021a). Dynamic Euclidean Geometry: pseudo-Toulmin modeling transformations and instrumental learning trajectories. International Institute for Science, Technology and Education (IISTE): E-Journals. Journal of Education and Practice. 12(9). pp. 80-96. https://doi.org/10.7176/JEP/12-9-09

Patsiomitou, S. (2021b). A Research Synthesis Using Instrumental Learning Trajectories: Knowing How and Knowing Why. International Institute for Science, Technology and Education (IISTE): E-Journals. Information and Knowledge Management. 11(3). https://doi.org/10.7176/IKM/11-3-02

Patsiomitou, S. (2021c). Instrumental learning trajectories: The case of GeoGebra. Athens: Angelakis Publications. ISBN 978-960-616-193. https://www.academia.edu/79248541/ (in Greek)

Patsiomitou, S. (2021d). Creativity and skills in mathematics. ISBN 978-618-00-3221-5. https://www.academia.edu/51047627/ (in Greek)

Patsiomitou, S. (2022a). Conceptual and instrumental trajectories using linking visual active representations created with the Geometer’s Sketchpad. Athens: Klidarithmos Publications. ISBN 978-960-645-302-1. (in Greek)

Patsiomitou, S. (2022b). DGS Cui-Rods: Reinventing Mathematical Concepts. GPH-International Journal of Educational Research, 5(09), 01-11. https://doi.org/10.5281/zenodo.7036045, http://www.gphjournal.org/index.php/er/article/view/693

Patsiomitou, S. (2022c). Inquiring and learning with DGS Cui-Rods: a proposal for managing the complexity of how primary-school pupils’ mathematically structure odd-even numbers". International Journal of Scientific and Management Research. Volume 5 Issue 8 August 2022, 143-163. http://doi.org/10.37502/IJSMR.2022.58.

Patsiomitou, S. (2022d). Digital-Concrete Materials: Revisiting Fröbel in Sketchpad Tasks. GPH-International Journal of Educational Research, 5(10), 01-15. https://doi.org/10.5281/zenodo.7185215

Patsiomitou, S. (2023). A dynamic multi-level curriculum based on the central idea of Linking Visual Active Representations (LVAR): Inquiring during the years 2005–2023. Angelakis Publications. (Original work published 2023 in Greek as: Δυναμικό πολυεπίπεδο πρόγραμμα σπουδών βασισμένο στην ιδέα των συνδεόμενων οπτικών ενεργών αναπαραστάσεων (ΣΟΕΑ): Ερευνητικές μελέτες από το 2005–2023. Εκδόσεις Αγγελάκη)

Patsiomitou, S. (2023a) Developing and managing knowledge through the eyes of the young learner: ‘Alive’ manipulatives before abstract notions. International Journal of Scientific and Management Research, 6(3), 18–40. http://doi.org/10.37502/IJSMR.2023.6302

Patsiomitou, S. (2023b). A brief review on my studies: Managing the complexity of using Linking Visual Active Representations (LVAR). International Journal of Scientific and Management Research, 6(5), 1–33. http://doi.org/10.37502/IJSMR.2023.6501

Patsiomitou, S. (2024a). The influence of artificial intelligence and digital media on the evaluation of school units and the enhancement of educational quality. In Proceedings of the 3rd International Conference of Educational Assessment (Vol. II, Issue 8, pp. 351–373). https://eletea.gr/el/τεύχος-8-τόμος-ιι-2024/ (In Greek)

Patsiomitou, S. (2024b). Investigating artificial intelligence technologies in generating LVAR. International Journal of Research in Education Humanities and Commerce, 5(5), 194–217. https://doi.org/10.37602/IJREHC.2024.5515

Patsiomitou, S. (2024d). Abstract, instrumental, and deductive geometric trajectories on quadrilaterals. Monograph. Angelakis Publications.ISBN: 978-960-616-370-8. https://www.academia.edu/114452254/ (in Greek)

Patsiomitou, S. (2025a). From the concept of schema to the idea of “instrumental” social schema. International Journal of Research in Education Humanities and Commerce. 6(2), 262–289. https://doi.org/10.37602/IJREHC.2025.6220

Patsiomitou, S. (2025b). A proposal for a fractal-based “Dynamic” Program: The Pythagorean Tree structure generated through instrumental schemata. International Journal of Research in Education Humanities and Commerce, 6(2), 342–388. https://doi.org/10.37602/IJREHC.2025.6327

Patsiomitou, S. (2025c). the Treasury of Atreus relieving triangle: insights form to hyperbolic geometry. International Journal of Research in Education Humanities and Commerce, 6(6), 55-76. https://doi.org/10.37602/IJREHC.2025.6605

Patsiomitou, S. (2025d). Building geometry – building relationships dynamically: Professional development material for the mathematics education advisor. Self-published. ISBN 978-618-87884-0-4

Patsiomitou, S. (2026). Reimagining sustainable school education through a fractal-based dynamic program (FDP): An experiential and interactive approach. International Journal of Research in Education Humanities and Commerce, 7(2), 285–317. https://doi.org/10.37602/IJREHC.2026.7223

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DOI: http://dx.doi.org/10.46827/ejes.v13i6.6731

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