Skip to main content

Digital Technology in Higher Education: Identification of Surfaces in Space Generated by Functions of Two Variables

  • Conference paper
  • First Online:
Perspectives and Trends in Education and Technology (ICITED 2023)

Abstract

This forms part of a research project to characterize the mathematical work performed by higher education students in developing a didactic sequence, through digital technology, in which they mobilize the concept of surfaces in space. One task proposed in the didactic sequence is presented that is constituted by a GeoGebra applet that allows the graphic representation of different surfaces to be obtained, including planes, cylinders, and quadrics (elliptic and hyperbolic paraboloids) from the manipulation of the parameters of a real function of two variables. The expected results of the task are analyzed in the context of theory of the Mathematical Working Space (MWS) to demonstrate how the use of a digital artifact promotes the execution of semiotic, instrumental, and discursive processes that are present in the student’s mathematical work.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Chapman, T., Sholukha, V., Semal, P., Louryan, S., Rooze, M., Van Sint Jan, S.: Femoral curvature variability in modern humans using three-dimensional quadric surface fitting. Surg. Radiol. Anat. 37, 1169–1177 (2015). https://doi.org/10.1007/s00276-015-1495-7

  2. Guillén, D.A., Puga, K.L., Puga, M.E.: Design of a playful environment for the manipulation of mathematical objects in 3D. AMUITEM ELECTRONIC MAGAZINE. Vol. VI, No. 1. Periodical Publication of the Mexican Association of Researchers of the Use of Technology in Mathematics Education. ISSN: 2395–955X. Mexico (2018). http://funes.uniandes.edu.co/20387/1/Guillen2018Dise%C3%B1o.pdf

  3. Hoyos-Salcedo, E.A., Acosta-Minoli, C.A., Aristizábal-Zapata, J.H., Mesa-Mazo, M.J., Trujillo-Salazar, C.A., Rincón-Penagos, J.A., … Jaime-Pastor, A.: Influence of educational software in the consolidation of the learning of quadric surfaces. Tecne, Epis-teme and Didaxis: TED 49, 123–142 (2021). https://doi.org/10.17227/ted.num49-9574

  4. Kuzniak, A., Richard, P.: Mathematical workspaces. Points of view and perspectives. Relime 17(4), 9–10 (2014). https://doi.org/10.12802/relime.13.1741a

  5. Kuzniak, A., Nechache, A.: A methodology to analyze the personal work of students in the theory of mathematical workspaces. In: Montoya, E. (Presidency) Space for Mathematical Work. Symposium held at the Sixth MWS International Symposium, Valparaíso, Chile (2018)

    Google Scholar 

  6. Kuzniak, A.: The theory of mathematical working spaces—theoretical characteristics. In: Kuzniak, A., Montoya-Delgadillo, E., Richard, P.R. (eds.) Mathematical Work in Educational Context. Mathematics Education in the Digital Era, vol. 18. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-90850-8_1

  7. Larson, R., Hostetler, R., Edwards, B.: Calculus with Analytic Geometry, 8a edn. Brooks Cole, USA (2005)

    Google Scholar 

  8. Nuñez, M.A., Buill, F., Regot, J., De Mesa, A.: Reverse engineering in small size models. VIII International Geomatic Week. Text en actes de congrés presented at the VIII Semana Geomática Internacional, Barcelona (2009). http://hdl.handle.net/2117/6214

  9. Salazar, J.V.F., Gaona, J., Richard, P.: Mathematical Work in the Digital Age. Variety of Tools and the Role of Geneses. En Mathematical Work in Educational Context, pp. 165–209. Springer (2022). https://doi.org/10.1007/978-3-030-90850-8_8

  10. Vara, T.N.P., Salazar, J.V.F., Vivas-Pachas, J.L.: Study of the visual variables of the elliptic paraboloid and their representations through digital technology. In: Mesquita, A., Abreu, A., Carvalho, J.V., de Mello, C.H.P. (eds.) Perspectives and Trends in Education and Technology. Smart Innovation, Systems and Technologies, vol. 320. Springer, Singapore (2023). https://doi.org/10.1007/978-981-19-6585-2_7e

Download references

Acknowledgements

We thank the Universidad de Lima, the San Ignacio de Loyola University (USIL) and the Pontificia Universidad Católica del Perú (PUCP) for their contributions to the study which allowed us to write this paper. Likewise, we appreciate the collaboration of the San Ignacio de Loyola University for the English translation of this research.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jorge Luis Vivas-Pachas .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Vivas-Pachas, J.L., Trujillo, E.C.J., Salazar, J.V.F., Saravia-Molina, N. (2023). Digital Technology in Higher Education: Identification of Surfaces in Space Generated by Functions of Two Variables. In: Mesquita, A., Abreu, A., Carvalho, J.V., Santana, C., de Mello, C.H.P. (eds) Perspectives and Trends in Education and Technology. ICITED 2023. Smart Innovation, Systems and Technologies, vol 366. Springer, Singapore. https://doi.org/10.1007/978-981-99-5414-8_53

Download citation

Publish with us

Policies and ethics