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Circle’s Ontology Extended: Circumference and Surface Area of a Circle

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 916))

Abstract

In this paper, we present how the use of ontologies and modern information technology tools helped students to connect geometrical meanings with mathematical concepts, based on the properties of circles and regular polygons ontologies, aiming to find the circumference and the surface area of a circle. In order to evaluate this concept, an experiment was set up in a junior high school classroom. The ontology, via abstract and combined thinking, helped the students to have a better understanding of the geometrical meanings and their dynamic interconnections.

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References

  1. diSessa, A., Hoyles, C., Noss, R. (eds.): Computers and Exploratory Learning. Springer, Berlin (1995)

    Google Scholar 

  2. Sutherland, R., Balacheff, N.: Didactical complexity of computational environments for the learning of mathematics. Int. J. Comput. Math. Learn. 4, 1–26 (1999)

    Article  Google Scholar 

  3. Hoyles, C.: From describing to designing mathematical activity: the next step in developing the social approach to research in Mathematics education. Educ. Stud. Math. 46, 273–286 (2001)

    Article  Google Scholar 

  4. Nardi, B. (ed.): Context and Consciousness: Activity Theory and Human Computer Interaction. MIT Press (1996)

    Google Scholar 

  5. Hoyles, C., Noss, R.: A pedagogy for mathematical microworlds. Educ. Stud. Math. 23, 31–57 (1992)

    Article  Google Scholar 

  6. GEOGEBRA. http://www.geogebra.org/

  7. SCRATCH. https://scratch.mit.edu/

  8. Tzoumpa, D., Karvounidis Th., Douligeris, C.: Towards an ontology approach in teaching geometry. In: Proceedings of ICL 2016 19th International Conference on Interactive Collaborative Learning 45th IGIP International Conference on Engineering Pedagogy. 21–23 September 2016, Belfast, UK (2016)

    Google Scholar 

  9. Bloom, B.S., Englehart, M.D., Furst, E.J., Hill, W.H., Krathwohl, D.R.: The Taxonomy of educational objectives, handbook I: The Cognitive domain. David McKay Co., Inc, New York (1956)

    Google Scholar 

  10. Anderson, L.W., Krathwohl, D.R., et al. (eds.): A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom’s Taxonomy of Educational Objectives. Allyn & Bacon, Boston, MA (2001). (Pearson Education Group)

    Google Scholar 

  11. Tzoumpa, D., Karvounidis, Th., Douligeris, C.: Extending the application of ontologies in the teaching of geometry: the right triangle in the circley. In: Proceedings of EDUCON 2017, 25 – 28 April 2017, Athens, Greece (2017)

    Google Scholar 

  12. OntoMathPro Ontology: A Linked Data Hub for Mathematics (2014) Knowledge Engineering and the Semantic Web - 5th International Conference. https://arxiv.org/pdf/1407.4833

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Acknowledgment

The work presented in this paper has been partially funded by National Matching Funds 2016–2017 of the Greek Government, and more specifically by the General Secretariat for Research and Technology (GSRT), related to EU project Medusa.

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Correspondence to Dimitra Tzoumpa , Theodoros Karvounidis or Christos Douligeris .

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Tzoumpa, D., Karvounidis, T., Douligeris, C. (2020). Circle’s Ontology Extended: Circumference and Surface Area of a Circle. In: Auer, M., Tsiatsos, T. (eds) The Challenges of the Digital Transformation in Education. ICL 2018. Advances in Intelligent Systems and Computing, vol 916. Springer, Cham. https://doi.org/10.1007/978-3-030-11932-4_12

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