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International Journal of Mathematical Education in Science and Technology Volume 23, 1992 - Issue 1
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Original Articles

Students’ mental prototypes for functions and graphs

David Tall Mathematics Education Research Centre, University of Warwick, Coventry CV4 7AL, England
&
MdNor Bakar Mathematics Education Research Centre, University of Warwick, Coventry CV4 7AL, England
Pages 39-50 | Published online: 09 Jul 2006

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Hande Gülbağci Dede, Zuhal Yilmaz, Hatice Akkoç & David Tall. (2023) Enhancing pre-service mathematics teachers’ understanding of function ideas. International Journal of Mathematical Education in Science and Technology 54:10, pages 2122-2146.
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Zakieh Parhizgar, Atefe Dehbashi, Peter Liljedahl & Hassan Alamolhodaei. (2022) Exploring students’ misconceptions of the function concept through problem-posing tasks and their views thereon. International Journal of Mathematical Education in Science and Technology 53:12, pages 3261-3285.
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Amal Hussain Alajmi & Maryam Mohammed Al-Kandari. (2022) Calculus 1 college students’ concept of function. International Journal of Mathematical Education in Science and Technology 53:2, pages 251-268.
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Andrew Munns. (2017) A study of competence in mathematics and mechanics in an engineering curriculum. European Journal of Engineering Education 42:6, pages 1062-1075.
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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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Nezahat Çetin. (2009) The Ability of Students to Comprehend the Function-Derivative Relationship with Regard to Problems from Their Real Life. PRIMUS 19:3, pages 232-244.
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Frank Eade. (2003) Secondary trainee teachers' understanding of convergence and continuity. International Journal of Mathematical Education in Science and Technology 34:3, pages 371-384.
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David Tall & Mohamad Rashidi Razali. (1993) Diagnosing students’ difficulties in learning mathematics. International Journal of Mathematical Education in Science and Technology 24:2, pages 209-222.
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Articles from other publishers (24)

Omar A. Naranjo & Steven R. Jones. (2023) How Students Construct Sophisticated Differential Equations to Model Real-World Contexts. International Journal of Science and Mathematics Education.
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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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Macarena Trujillo, Lorena Atarés, María José Canet & María Asunción Pérez-Pascual. (2023) Learning Difficulties with the Concept of Function in Maths: A Literature Review. Education Sciences 13:5, pages 495.
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Ramazan EROL & Elif SAYGI. (2022) The Effect of Using Cryptology on Understanding of Function Concept. International Journal of Contemporary Educational Research 8:4, pages 80-90.
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Vasen Pillay, Jill Adler & Ulla Runesson Kempe. (2022) The sequencing and pairing of examples in the midst of sameness and difference: Opening opportunities to learn. Pythagoras 43:1.
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Ljerka Jukić Matić, Gabrijela Kehler-Poljak & Sanja Rukavina. (2022) The Influence of Curriculum on the Concept of Function: An Empirical Study of Pre-Service Teachers. European Journal of Science and Mathematics Education 10:3, pages 380-395.
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Kimberly Sirin Budak & Zeynep Akcay Ozkan. (2022) Pre-Service Teachers’ Understanding of Continuity. International Electronic Journal of Mathematics Education 17:2, pages em0674.
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Andrzej Sokolowski. 2021. Mathematical Modelling Education in East and West. Mathematical Modelling Education in East and West 433 442 .
Elif KARATAĞ ŞAHİN, Hilal GÜLKILIK & Hasan Hüseyin UĞURLU. (2020) The role of concept images in solving geometric word problems. İlköğretim Online, pages 1321-1336.
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Igor’ Kontorovich. (2018) Tacit Models that Govern Undergraduate Reasoning about Subspaces. International Journal of Research in Undergraduate Mathematics Education 4:3, pages 393-414.
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Steven R. Jones. (2017) Prototype images in mathematics education: the case of the graphical representation of the definite integral. Educational Studies in Mathematics 97:3, pages 215-234.
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Selin Urhan, Gizem Kuh, Irem Günal & Selay Arkün Kocadere. (2018) Sample Activities in Teaching Functions through ICT Support. SHS Web of Conferences 48, pages 01065.
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Sarah Bansilal, Deonarain Brijlall & Maria Trigueros. (2017) An APOS study on pre-service teachers’ understanding of injections and surjections. The Journal of Mathematical Behavior 48, pages 22-37.
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Vesife Hatisaru & Ayhan Kursat Erbas. (2015) Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes. International Journal of Science and Mathematics Education 15:4, pages 703-722.
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H. Bahadır Yanik. (2014) Middle-school students’ concept images of geometric translations. The Journal of Mathematical Behavior 36, pages 33-50.
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David Tall. 2014. How Humans Learn to Think Mathematically. How Humans Learn to Think Mathematically.
Nils Buchholtz, Frederick K. S. Leung, Lin Ding, Gabriele Kaiser, Kyungmee Park & Björn Schwarz. (2012) Future mathematics teachers’ professional knowledge of elementary mathematics from an advanced standpoint. ZDM 45:1, pages 107-120.
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Rafael Martínez-Planell & María Trigueros Gaisman. (2012) Students’ understanding of the general notion of a function of two variables. Educational Studies in Mathematics 81:3, pages 365-384.
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Filiz Tuba Dikkartin Ovez & Sevinc Mert Uyangor. (2012) Evaluation of 12th Grade of Secondary Mathematics Curriculum: Algebra Learning Domain. Procedia - Social and Behavioral Sciences 46, pages 2156-2162.
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Nils Buchholtz & Björn Schwarz. 2012. Mathematikunterricht im Kontext von Realität, Kultur und Lehrerprofessionalität. Mathematikunterricht im Kontext von Realität, Kultur und Lehrerprofessionalität 238 248 .
Rohani Ahmad Tarmizi. (2010) Visualizing Student's Difficulties in Learning Calculus. Procedia - Social and Behavioral Sciences 8, pages 377-383.
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Siti Aishah Sh Abdullah. (2010) Comprehending the Concept of Functions. Procedia - Social and Behavioral Sciences 8, pages 281-287.
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Ellen Hines. (2001) Developing the concept of linear function: one student’s experiences with dynamic physical models. The Journal of Mathematical Behavior 20:3, pages 337-361.
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M. Borovcnik & R. Peard. 1997. International Handbook of Mathematics Education. International Handbook of Mathematics Education 289 325 .

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