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TRANSFORMATION OF MATHEMATICAL KNOWLEDGE FOR TEACHING NON-EUCLIDEAN GEOMETRY CONCEPT THROUGH E-LEARNING BASED ON THE THEORY OF DIDACTIC SITUATIONS USING A MULTIPHASE MIXED METHOD

Jurnal Ilmiah Ilmu Terapan Universitas Jambi · Vol. 9 No. 2 (2025) · pp. 578–597

DOI
10.22437/jiituj.v9i2.42976
ISSN
2580-2259, 2580-2240
Published
2025-04-18
Publisher
LPPM Universitas Jambi
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

The understanding of non-Euclidean geometry is essential for mathematics teachers as it can broaden the spatial perspective and enhance logical and abstract thinking. However, many teachers face challenges in teaching this concept because it conflicts with the long-established intuitive understanding of Euclidean geometry. An innovative technology-based method is then required to make non-Euclidean geometry learning more effective. Therefore, this research aimed to explore how mathematical knowledge related to non-Euclidean geometry could be transformed and enhanced through e-learning based on the Theory of Didactic Situations (TDS). A multiphase mixed method (MMM) was used to achieve this objective. Approximately 20 mathematics teachers, including 6 males and 14 females, were selected as the participants. Data were collected using content development guidelines, observation sheets, interviews, and tests, as well as analyzed qualitatively and quantitatively. The results showed that e-learning based on TDS effectively improved teachers' understanding of non-Euclidean geometry. In addition, this method enhanced teachers' engagement and encouraged independent exploration during the learning process. There were still challenges in understanding hyperbolic, spherical, and elliptic geometry due to a limited understanding of non-Euclidean axiomatic systems. Conceptual and procedural errors were commonly traced back to the limitations of visualizing non-Euclidean spaces. To address such issues, a more interactive method, combining visual simulation and problem-based learning, was recommended to improve non-Euclidean geometry literacy among teachers and students.

Keywords

Collaboration network of the authors

29 authors · 75 co-authorship links · 33 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Indonesia Open University
  • Hasanuddin University
  • Universidad de la Costa
  • Universidad Autónoma de Guerrero
  • University of Timor
  • Universiti Teknologi MARA
  • Universitas Nahdlatul Wathan Mataram
  • Other organisations
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Muh PauzanUniversitas Wiralodra2
Ardi Dwi SusandiIndonesia Open University2
Muhamad Galang IsnawanUniversitas Nahdlatul Wathan Mataram2
Yumiati YumiatiIndonesia Open University1
Aloisius Loka SonUniversity of Timor1
Camilo Andrés Rodríguez-NietoUniversidad de la Costa1
Javier García‐GarcíaUniversidad Autónoma de Guerrero1
Ucu RahayuIndonesia Open University1
Dyah Aniza KismiatiIndonesia Open University1
Yos SudarsoIndonesia Open University1
Rafidah Abd KarimUniversiti Teknologi MARA1
Sarip HidayatAffiliation unknown1
St. Aisjah FarhumHasanuddin University1
Muhammad Banda SelamatHasanuddin University1
Mukti ZainuddinHasanuddin University1
Safruddin SafruddinHasanuddin University1
Alfa NelwanHasanuddin University1
Alfa F. P. NelwanAffiliation unknown1
MUHAMMAD FARHAN KURNIAHasanuddin University1
Angelina Siswaty Br HombingAffiliation unknown1
Jarnawi A DahlanAffiliation unknown1
Erlina ayu SusilowatiAffiliation unknown1
Yumiati YumiatiAffiliation unknown1
Ebenezer BonyahAffiliation unknown1
Saleh HajiUniversity of Bengkulu1
SUDIRMAN SUDIRMANState University of Malang1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://online-journal.unja.ac.id/index.php/JIITUJ/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">TRANSFORMATION OF MATHEMATICAL KNOWLEDGE FOR TEACHING NON-EUCLIDEAN GEOMETRY CONCEPT THROUGH E-LEARNING BASED ON THE THEORY OF DIDACTIC SITUATIONS USING A MULTIPHASE MIXED METHOD</dc:title>
	<dc:creator xml:lang="en">Noviyanti, Mery</dc:creator>
	<dc:creator xml:lang="en">Sudirman, Sudirman</dc:creator>
	<dc:creator xml:lang="en">Rodríguez-Nieto, Camilo Andrés</dc:creator>
	<dc:subject xml:lang="en">E-learning</dc:subject>
	<dc:subject xml:lang="en">Mathematical knowledge for teaching</dc:subject>
	<dc:subject xml:lang="en">Multiphase mixed method</dc:subject>
	<dc:subject xml:lang="en">Non-Euclidean geometry</dc:subject>
	<dc:subject xml:lang="en">Theory of didactic situations</dc:subject>
	<dc:description xml:lang="en">The understanding of non-Euclidean geometry is essential for mathematics teachers as it can broaden the spatial perspective and enhance logical and abstract thinking. However, many teachers face challenges in teaching this concept because it conflicts with the long-established intuitive understanding of Euclidean geometry. An innovative technology-based method is then required to make non-Euclidean geometry learning more effective. Therefore, this research aimed to explore how mathematical knowledge related to non-Euclidean geometry could be transformed and enhanced through e-learning based on the Theory of Didactic Situations (TDS). A multiphase mixed method (MMM) was used to achieve this objective. Approximately 20 mathematics teachers, including 6 males and 14 females, were selected as the participants. Data were collected using content development guidelines, observation sheets, interviews, and tests, as well as analyzed qualitatively and quantitatively. The results showed that e-learning based on TDS effectively improved teachers' understanding of non-Euclidean geometry. In addition, this method enhanced teachers' engagement and encouraged independent exploration during the learning process. There were still challenges in understanding hyperbolic, spherical, and elliptic geometry due to a limited understanding of non-Euclidean axiomatic systems. Conceptual and procedural errors were commonly traced back to the limitations of visualizing non-Euclidean spaces. To address such issues, a more interactive method, combining visual simulation and problem-based learning, was recommended to improve non-Euclidean geometry literacy among teachers and students.</dc:description>
	<dc:publisher xml:lang="en">LPPM Universitas Jambi</dc:publisher>
	<dc:date>2025-04-18</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://online-journal.unja.ac.id/JIITUJ/article/view/42976</dc:identifier>
	<dc:identifier>10.22437/jiituj.v9i2.42976</dc:identifier>
	<dc:source xml:lang="en">Jurnal Ilmiah Ilmu Terapan Universitas Jambi; Vol. 9 No. 2 (2025): Volume 9, Nomor 2, June 2025; 578-597</dc:source>
	<dc:source>2580-2259</dc:source>
	<dc:source>2580-2240</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://online-journal.unja.ac.id/JIITUJ/article/view/42976/22255</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2025 Mery Noviyanti, Sudirman Sudirman, Camilo Andrés Rodríguez-Nieto</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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