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International Journal of Mathematical Education in Science and Technology Volume 40, 2009 - Issue 7: The Seventh Southern Hemisphere Conference on Undergraduate Mathematics and Statistics Teaching and Learning, Gordon's Bay, South Africa, 29 November–4 December 2009
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Original Articles

A framework for mathematical thinking: the case of linear algebra

Sepideh Stewart Department of Mathematics, Mathematics Education Unit, The University of Auckland, PB 92019, Auckland, New ZealandCorrespondence[email protected]
&
Michael O.J. Thomas Department of Mathematics, Mathematics Education Unit, The University of Auckland, PB 92019, Auckland, New Zealand
Pages 951-961 | Received 16 Jul 2009, Published online: 16 Sep 2009

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Vahid Borji & Hassan Alamolhodaei. (2022) Complexities in university students’ understanding of parametric equations and curves. International Journal of Mathematical Education in Science and Technology 53:4, pages 890-908.
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Vahid Borji, Hedyeh Erfani & Vicenç Font. (2020) A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates. International Journal of Mathematical Education in Science and Technology 51:3, pages 405-423.
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John Hannah, Sepideh Stewart & Mike Thomas. (2013) Emphasizing language and visualization in teaching linear algebra. International Journal of Mathematical Education in Science and Technology 44:4, pages 475-489.
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Megan Wawro, Chris Rasmussen, Michelle Zandieh, George Franklin Sweeney & Christine Larson. (2012) An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence. PRIMUS 22:8, pages 577-599.
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Judy Paterson & Jamie Sneddon. (2011) Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course. International Journal of Mathematical Education in Science and Technology 42:7, pages 879-889.
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E. Ertekin, S. Solak & E. Yazici. (2010) The effects of formalism on teacher trainees’ algebraic and geometric interpretation of the notions of linear dependency/independency. International Journal of Mathematical Education in Science and Technology 41:8, pages 1015-1035.
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Maryam Taghizadeh Bilondi & Farzad Radmehr. Students’ mathematical thinking of the tree concept: an integration of APOS with Tall’s three worlds of mathematics. Research in Mathematics Education 0:0, pages 1-22.
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Farzad Radmehr. Learning Eigenvalues and Eigenvectors with Online YouTube Resources: A Journey in the Embodied, Proceptual-symbolic, and Formal Worlds of Mathematics. PRIMUS 0:0, pages 1-20.
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Articles from other publishers (21)

Saba Gerami, Eric Khiu, Vilma Mesa & Thomas Judson. (2024) Conceptions of span in linear algebra: from textbook examples to student responses. Educational Studies in Mathematics.
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Armando Cuevas-Vallejo, José Orozco-Santiago & Sofía Paz-Rodríguez. (2023) A learning trajectory for university students regarding the concept of vector. The Journal of Mathematical Behavior 70, pages 101044.
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Dhanya Surith. (2022) Understanding students’ transition in mathematical thinking in algebra: The three worlds of mathematics. Understanding students’ transition in mathematical thinking in algebra: The three worlds of mathematics.
Ann Sophie Stuhlmann. (2021) Interactionist perspective on negotiation processes of students’ different understandings during small group work on linear algebra. The Journal of Mathematical Behavior 64, pages 100911.
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Gurwinder Singh, Neha Tuli & Archana Mantri. (2021) Issues and Challenges in Learning Foundation Linear Algebra Course with Technology: A Literature Review. Issues and Challenges in Learning Foundation Linear Algebra Course with Technology: A Literature Review.
Michelle Zandieh & Christine Andrews-Larson. (2019) Symbolizing while solving linear systems. ZDM 51:7, pages 1183-1197.
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Gulden Karakok. (2019) Making connections among representations of eigenvector: what sort of a beast is it?. ZDM 51:7, pages 1141-1152.
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Guershon Harel. (2018) Varieties in the use of geometry in the teaching of linear algebra. ZDM 51:7, pages 1031-1042.
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Ricardo Gonçalves & Cecília Costa. 2019. Multimodal Narratives in Research and Teaching Practices. Multimodal Narratives in Research and Teaching Practices 305 323 .
Khalid Bouhjar, Christine Andrews-Larson, Muhammad Haider & Michelle Zandieh. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 193 216 .
Lillias H.N. Mutambara & Sarah Bansilal. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 147 173 .
Sepideh Stewart. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 51 67 .
Hamide Dogan. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 219 239 .
Barbara Jaworski, Angeliki Mali & Georgia Petropoulou. (2016) Critical Theorising from Studies of Undergraduate Mathematics Teaching for Students’ Meaning Making in Mathematics. International Journal of Research in Undergraduate Mathematics Education 3:1, pages 168-197.
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Sepideh Stewart. 2017. And the Rest is Just Algebra. And the Rest is Just Algebra 219 233 .
John Hannah, Sepideh Stewart & Michael Thomas. (2016) Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking. Teaching Mathematics and its Applications, pages hrw001.
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Utkun Aydın & Behiye Ubuz. (2014) THE THINKING-ABOUT-DERIVATIVE TEST FOR UNDERGRADUATE STUDENTS: DEVELOPMENT AND VALIDATION. International Journal of Science and Mathematics Education 13:6, pages 1279-1303.
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Ye Yoon Hong & Michael O. J. Thomas. (2014) Graphical construction of a local perspective on differentiation and integration. Mathematics Education Research Journal 27:2, pages 183-200.
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Chris Rasmussen, Megan Wawro & Michelle Zandieh. (2014) Examining individual and collective level mathematical progress. Educational Studies in Mathematics 88:2, pages 259-281.
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Mike O. J. Thomas, Iole de Freitas Druck, Danielle Huillet, Mi-Kyung Ju, Elena Nardi, Chris Rasmussen & Jinxing Xie. 2015. The Proceedings of the 12th International Congress on Mathematical Education. The Proceedings of the 12th International Congress on Mathematical Education 265 284 .
Natalie E. Selinski, Chris Rasmussen, Megan Wawro & Michelle Zandieh. (2014) A Method for Using Adjacency Matrices to Analyze the Connections Students Make Within and Between Concepts: The Case of Linear Algebra. Journal for Research in Mathematics Education 45:5, pages 550-583.
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