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Research papers

Generalising calculus ideas from two dimensions to three: how multivariable calculus students think about domain and range

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Read on this site (5)

Steven R. Jones, Nicholas E. Long & Jeremy J. Becnel. (2023) Design of virtual reality modules for multivariable calculus and an examination of student noticing within them. Research in Mathematics Education 25:2, pages 219-242.
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Amy B. Ellis, Elise Lockwood, Erik Tillema & Kevin Moore. (2022) Generalization Across Multiple Mathematical Domains: Relating, Forming, and Extending. Cognition and Instruction 40:3, pages 351-384.
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Foteini Megalou. (2019) Students’ choices of definitions for the concept of limit of functions from R2 to R. International Journal of Mathematical Education in Science and Technology 50:1, pages 141-156.
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Peter Cho, Benjamin Norris & Deborah Moore-Russo. (2017) A study of common student practices for determining the domain and range of graphs. Investigations in Mathematics Learning 9:4, pages 202-219.
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Jennifer G. Cromley, Julie L. Booth, Theodore W. Wills, Briana L. Chang, Nhi Tran, Michael Madeja, Thomas F. Shipley & William Zahner. (2017) Relation of Spatial Skills to Calculus Proficiency: A Brief Report. Mathematical Thinking and Learning 19:1, pages 55-68.
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Articles from other publishers (15)

Rafael Martínez-Planell, Maria Trigueros & Vahid Borji. (2024) The role of topology in the construction of students’ optimization schema for two-variable functions. The Journal of Mathematical Behavior 73, pages 101106.
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Zackery Reed. (2022) Component-Wise Reasoning as a Mechanism of Sense-Making in Real Analysis. International Journal of Research in Undergraduate Mathematics Education 9:2, pages 217-242.
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Mustafa ÖZBEY & Şenol DOST. (2023) Concept Images of University Students for Geometric Representation of the Double Integral ConceptMatematik Öğretmeni Adaylarının Çift İntegral Kavramının Geometrik Temsiline Yönelik Kavram Görselleri. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi 17:1, pages 66-98.
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Allison Dorko. (2023) Is it a function? Generalizing from single- to multivariable settings. The Journal of Mathematical Behavior 70, pages 101036.
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Steven R. Jones. (2022) Multivariation and students’ multivariational reasoning. The Journal of Mathematical Behavior 67, pages 100991.
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Vahid Borji, Rafael Martínez-Planell & María Trigueros. (2022) Student understanding of functions of two variables: A reproducibility study. The Journal of Mathematical Behavior 66, pages 100950.
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Cheryl L. Eames, Edith Aurora Graf, Peter W. van Rijn, Greg Budzban & Tammy Voepel. (2021) The finite-to-finite strand of a learning progression for the concept of function: A research synthesis and cognitive analysis. The Journal of Mathematical Behavior 62, pages 100864.
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Rafael Martínez-Planell & Maria Trigueros. (2021) Multivariable calculus results in different countries. ZDM – Mathematics Education 53:3, pages 695-707.
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Steven R. Jones. (2020) Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding. The Journal of Mathematical Behavior 59, pages 100801.
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Rafael Martínez-Planell & María Trigueros. (2020) Students’ understanding of Riemann sums for integrals of functions of two variables. The Journal of Mathematical Behavior 59, pages 100791.
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Edgar John Sintema & José M. Marbán. (2020) Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students. International Electronic Journal of Mathematics Education 15:3, pages em0598.
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Rafael Martínez-Planell & María Trigueros. (2019) Using cycles of research in APOS: The case of functions of two variables. The Journal of Mathematical Behavior 55, pages 100687.
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Rafael Martínez-Planell, María Trigueros Gaismán & Daniel McGee. (2017) Students’ understanding of the relation between tangent plane and directional derivatives of functions of two variables. The Journal of Mathematical Behavior 46, pages 13-41.
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Steven R. Jones & Allison Dorko. (2015) Students’ understandings of multivariate integrals and how they may be generalized from single integral conceptions. The Journal of Mathematical Behavior 40, pages 154-170.
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Rafael Martínez-Planell, Maria Trigueros Gaisman & Daniel McGee. (2015) On students’ understanding of the differential calculus of functions of two variables. The Journal of Mathematical Behavior 38, pages 57-86.
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