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PRIMUS
Problems, Resources, and Issues in Mathematics Undergraduate Studies
Volume 22, 2012 - Issue 8
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Original Articles

An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

Pages 577-599 | Published online: 10 Dec 2012

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Saba Gerami, Vilma Mesa, Lynn Chamberlain & Carlos Quiroz. (2023) The role of textbooks for supporting instruction with inquiry: the case of Active Calculus. International Journal of Mathematical Education in Science and Technology 0:0, pages 1-22.
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Johanna Rämö, Juulia Lahdenperä & Jokke Häsä. (2021) The Extreme Apprenticeship Method. PRIMUS 31:10, pages 1106-1120.
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Osama Swidan. (2020) A learning trajectory for the fundamental theorem of calculus using digital tools. International Journal of Mathematical Education in Science and Technology 51:4, pages 542-562.
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Daniel L. Reinholz. (2018) Large Lecture Halls: Whiteboards, Not Bored Students. PRIMUS 28:7, pages 670-682.
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George Kuster, Estrella Johnson, Karen Keene & Christine Andrews-Larson. (2018) Inquiry-Oriented Instruction: A Conceptualization of the Instructional Principles. PRIMUS 28:1, pages 13-30.
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Christine Andrews-Larson, Megan Wawro & Michelle Zandieh. (2017) A hypothetical learning trajectory for conceptualizing matrices as linear transformations. International Journal of Mathematical Education in Science and Technology 48:6, pages 809-829.
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Michelle Zandieh, Megan Wawro & Chris Rasmussen. (2017) An Example of Inquiry in Linear Algebra: The Roles of Symbolizing and Brokering. PRIMUS 27:1, pages 96-124.
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Dov Zazkis. (2016) On Transitions Between Representations: The Role of Contextual Reasoning in Calculus Problem Solving. Canadian Journal of Science, Mathematics and Technology Education 16:4, pages 374-388.
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Articles from other publishers (42)

Jessi Lajos. (2023) An updated conceptualization of the intuition construct for mathematics education research. The Journal of Mathematical Behavior 71, pages 101080.
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Joaquin Marc Veith, Meeri-Liisa Beste, Marco Kindervater, Michel Krause, Michael Straulino, Franziska Greinert & Philipp Bitzenbauer. (2023) Mathematics education research on algebra over the last two decades: quo vadis?. Frontiers in Education 8.
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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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Mollee Shultz, Eleanor Close, Jayson Nissen & Ben Van Dusen. (2023) Enacting Culturally Relevant Pedagogy when “Mathematics Has No Color”: Epistemological Contradictions. International Journal of Research in Undergraduate Mathematics Education.
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Kathleen Melhuish, Paul C. Dawkins, Kristen Lew & Sharon K. Strickland. (2022) Lessons Learned About Incorporating High-Leverage Teaching Practices in the Undergraduate Proof Classroom to Promote Authentic and Equitable Participation. International Journal of Research in Undergraduate Mathematics Education.
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Anthony Cronin & Sepideh Stewart. (2022) Analysis of tutors’ responses to students’ queries in a second linear algebra course at a mathematics support center. The Journal of Mathematical Behavior 67, pages 100987.
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Benjamin P. Schermerhorn, Giaco Corsiglia, Homeyra Sadaghiani, Gina Passante & Steven Pollock. (2022) From Cartesian coordinates to Hilbert space: Supporting student understanding of basis in quantum mechanics. Physical Review Physics Education Research 18:1.
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Melih Turgut, Jessica Lynn Smith & Christine Andrews-Larson. (2022) Symbolizing lines and planes as linear combinations in a dynamic geometry environment. The Journal of Mathematical Behavior 66, pages 100948.
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Mollee C. Shultz. (2022) The Rationality of Undergraduate Mathematics Instructors: The Choice to Use Inquiry-Oriented Instructional Practices. Journal for Research in Mathematics Education 53:3, pages 227-246.
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Keith A. Nabb. 2022. Global Perspectives and Practices for Reform-Based Mathematics Teaching. Global Perspectives and Practices for Reform-Based Mathematics Teaching 293 322 .
Johanna Rämö, Jokke Häsä & Tarja Tuononen. 2022. Practice-Oriented Research in Tertiary Mathematics Education. Practice-Oriented Research in Tertiary Mathematics Education 449 467 .
Vilma Mesa. 2022. Practice-Oriented Research in Tertiary Mathematics Education. Practice-Oriented Research in Tertiary Mathematics Education 265 288 .
Khalid Bouhjar, Christine Andrews-Larson & Muhammad Qadeer Haider. (2021) An analytical comparison of students’ reasoning in the context of Inquiry-Oriented Instruction: The case of span and linear independence. The Journal of Mathematical Behavior 64, pages 100908.
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Matthew Mauntel, Benjamin Levine, David Plaxco & Michelle Zandieh. (2021) The Characterization and Evolution of Strategies About Vector Equations in the Game Vector Unknown. Digital Experiences in Mathematics Education 7:3, pages 453-476.
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Elise Lockwood & Knut Mørken. (2021) A Call for Research that Explores Relationships between Computing and Mathematical Thinking and Activity in RUME. International Journal of Research in Undergraduate Mathematics Education 7:3, pages 404-416.
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Guillermo Ramírez-Montes, Ana Henriques & Susana Carreira. (2021) Undergraduate Students’ Learning of Linear Algebra Through Mathematical Modelling Routes. Canadian Journal of Science, Mathematics and Technology Education 21:2, pages 357-377.
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Matthew Voigt, Helge Fredriksen & Chris Rasmussen. (2020) Leveraging the design heuristics of realistic mathematics education and culturally responsive pedagogy to create a richer flipped classroom calculus curriculum. ZDM 52:5, pages 1051-1062.
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Rogier Bos, Michiel Doorman & Margherita Piroi. (2020) Emergent models in a reinvention activity for learning the slope of a curve. The Journal of Mathematical Behavior 59, pages 100773.
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Vilma Mesa, Mollee Shultz & Ashley Jackson. (2019) Moving Away from Lecture in Undergraduate Mathematics: Managing Tensions within a Coordinated Inquiry-Based Linear Algebra Course. International Journal of Research in Undergraduate Mathematics Education 6:2, pages 245-278.
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Lars Siemer, Ingolf Schäfer, Jens D. M. Rademacher & Marc Keßeböhmer. 2020. Forschendes Lernen als Studiengangsprofil. Forschendes Lernen als Studiengangsprofil 91 106 .
Maria Trigueros & Megan Wawro. 2020. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 474 478 .
Sepideh Stewart, Christine Andrews-Larson & Michelle Zandieh. (2019) Linear algebra teaching and learning: themes from recent research and evolving research priorities. ZDM 51:7, pages 1017-1030.
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Sepideh Stewart, Jonathan Troup & David Plaxco. (2019) Reflection on teaching linear algebra: examining one instructor’s movements between the three worlds of mathematical thinking. ZDM 51:7, pages 1253-1266.
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María Trigueros. (2019) The development of a linear algebra schema: learning as result of the use of a cognitive theory and models. ZDM 51:7, pages 1055-1068.
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Spencer Payton. (2019) Fostering mathematical connections in introductory linear algebra through adapted inquiry. ZDM 51:7, pages 1239-1252.
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Andrea Cárcamo, Claudio Fuentealba & Diego Garzón. (2019) Local Instruction Theories at the University Level: An Example in a Linear Algebra Course. EURASIA Journal of Mathematics, Science and Technology Education 15:12.
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Daniel L. Reinholz, Kenneth Bradfield & Naneh Apkarian. (2019) Using Analytics to Support Instructor Reflection on Student Participation in a Discourse-Focused Undergraduate Mathematics Classroom. International Journal of Research in Undergraduate Mathematics Education 5:1, pages 56-74.
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Maria Trigueros & Megan Wawro. 2019. Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education 1 5 .
Günhan Caglayan. (2018) Coordinating analytic and visual approaches: Math majors’ understanding of orthogonal Hermite polynomials in the inner product space in a technology-assisted learning environment . The Journal of Mathematical Behavior 52, pages 37-60.
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Günhan Caglayan. (2018) Coordinating representation registers: linear algebra students' understanding of orthogonal Legendre polynomials in the inner product space. Annales de didactique et de sciences cognitives:23, pages 137-178.
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David Plaxco, Michelle Zandieh & Megan Wawro. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 175 192 .
María Trigueros. 2018. Challenges and Strategies in Teaching Linear Algebra. Challenges and Strategies in Teaching Linear Algebra 29 50 .
John Hannah. 2017. And the Rest is Just Algebra. And the Rest is Just Algebra 205 217 .
Ivonne Sandoval & Edgar Possani. (2016) An analysis of different representations for vectors and planes in ℝ 3 $\mathbb {R}^{3}$. Educational Studies in Mathematics 92:1, pages 109-127.
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Spencer Bagley & Jeffrey M. Rabin. (2015) Students’ Use of Computational Thinking in Linear Algebra. International Journal of Research in Undergraduate Mathematics Education 2:1, pages 83-104.
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Megan Wawro. (2015) Reasoning About Solutions in Linear Algebra: the Case of Abraham and the Invertible Matrix Theorem. International Journal of Research in Undergraduate Mathematics Education 1:3, pages 315-338.
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David Plaxco & Megan Wawro. (2015) Analyzing student understanding in linear algebra through mathematical activity. The Journal of Mathematical Behavior 38, pages 87-100.
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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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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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Megan Wawro. (2014) Student reasoning about the invertible matrix theorem in linear algebra. ZDM 46:3, pages 389-406.
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Sean P. Larsen. (2013) A local instructional theory for the guided reinvention of the group and isomorphism concepts. The Journal of Mathematical Behavior 32:4, pages 712-725.
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Sean Larsen & Elise Lockwood. (2013) A local instructional theory for the guided reinvention of the quotient group concept. The Journal of Mathematical Behavior 32:4, pages 726-742.
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