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Original Articles

The Effects of Different Problem Presentations and Formulations on the Illusion of Linearity in Secondary School Students

Pages 65-89 | Published online: 18 Nov 2009

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Read on this site (6)

Brian Greer. (2010) Overview of the Papers: Why is Linear Thinking so Dominant?. Mathematical Thinking and Learning 12:1, pages 109-115.
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Cristina B. Esteley, Mónica E. Villarreal & Humberto R. Alagia. (2010) The Overgeneralization of Linear Models among University Students' Mathematical Productions: A Long-Term Study. Mathematical Thinking and Learning 12:1, pages 86-108.
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Vesna Vlahović-Štetić, Nina Pavlin-Bernardić & Miroslav Rajter. (2010) Illusion of Linearity in Geometry: Effect in Multiple-Choice Problems. Mathematical Thinking and Learning 12:1, pages 54-67.
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Modestina Modestou, Iliada Elia, Athanasios Gagatsis & Giorgos Spanoudis. (2008) Behind the scenes of pseudo-proportionality. International Journal of Mathematical Education in Science and Technology 39:3, pages 313-324.
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Modestina Modestou & Athanasios Gagatsis. (2007) Students' Improper Proportional Reasoning: A result of the epistemological obstacle of “linearity”. Educational Psychology 27:1, pages 75-92.
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Wim Van Dooren, Dirk De Bock, An Hessels, Dirk Janssens & Lieven Verschaffel. (2005) Not Everything Is Proportional: Effects of Age and Problem Type on Propensities for Overgeneralization. Cognition and Instruction 23:1, pages 57-86.
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Articles from other publishers (22)

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Tobias Rolfes. (2021) Interpretation of Quantities Displayed in Pictorial Charts. Frontiers in Psychology 12.
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Janina Krawitz & Stanislaw Schukajlow. (2020) When Can Making a Drawing Hinder Problem Solving? Effect of the Drawing Strategy on Linear Overgeneralizations and Problem Solving. Frontiers in Psychology 11.
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Ronghuan Jiang, Xiaodong Li, Ping Xu & Tingting Mao. (2020) Why students are biased by heuristics: Examining the role of inhibitory control, conflict detection, and working memory in the case of overusing proportionality. Cognitive Development 53, pages 100850.
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Rukiye Ayan & Mine Isiksal Bostan. (2016) Middle School Students’ Reasoning in Nonlinear Proportional Problems in Geometry. International Journal of Science and Mathematics Education 16:3, pages 503-518.
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Catherine Thevenot. 2017. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts. Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts 47 66 .
Tine Degrande, Lieven Verschaffel & Wim Van Dooren. 2016. Posing and Solving Mathematical Problems. Posing and Solving Mathematical Problems 209 229 .
Dirk De Bock, Daam Van Reeth, Janne Minne & Wim Van Dooren. (2014) Students’ overreliance on linearity in economic thinking: An exploratory study at the tertiary level. International Review of Economics Education 16, pages 111-121.
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Miranda Rioux & Audrey Ann Couture. (2014) Dual-process theory et résolution de problèmes additifs de comparaison par des étudiants universitaires. Éducation et francophonie 42:2, pages 120-137.
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Modestina Modestou & Athanasios Gagatsis. (2013) A didactical situation for the enhancement of meta-analogical awareness. The Journal of Mathematical Behavior 32:2, pages 160-172.
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Mieke De Cock. (2012) Representation use and strategy choice in physics problem solving. Physical Review Special Topics - Physics Education Research 8:2.
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Yuhui Ma, Kai Tan, Limin Shao & Xiaojing Shang. (2011) Constructing the representation model of arithmetic word problems for intelligent tutoring system. Constructing the representation model of arithmetic word problems for intelligent tutoring system.
Dirk De Bock, Wim Van Dooren & Lieven Verschaffel. (2010) Students’ Overuse of Linearity: An Exploration in Physics. Research in Science Education 41:3, pages 389-412.
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Yuhui Ma & Ying Zhou. (2010) The method of semantic analysis for arithmetic word problems. The method of semantic analysis for arithmetic word problems.
Ma Yuhui, Zhou Ying, Cui Guangzuo, Ren Yun & Huang Ronghuai. (2010) Frame-Based Calculus of Solving Arithmetic Multi-Step Addition and Subtraction Word Problems. Frame-Based Calculus of Solving Arithmetic Multi-Step Addition and Subtraction Word Problems.
Mirjam Ebersbach, Wim Van Dooren, Wim Van den Noortgate & Wilma C.M. Resing. (2008) Understanding linear and exponential growth: Searching for the roots in 6- to 9-year-olds. Cognitive Development 23:2, pages 237-257.
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John K. Lannin, David D. Barker & Brian E. Townsend. (2007) How students view the general nature of their errors. Educational Studies in Mathematics 66:1, pages 43-59.
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Dirk De Bock, Wim Van Dooren & Dirk Janssens. 2007. Modelling and Applications in Mathematics Education. Modelling and Applications in Mathematics Education 241 248 .
Stephen K. Reed. (2005) From Research to Practice and Back: The Animation Tutor Project. Educational Psychology Review 17:1, pages 55-82.
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Wim Van Dooren, Dirk De Bock, An Hessels, Dirk Janssens & Lieven Verschaffel. (2004) Remedying secondary school students’ illusion of linearity: a teaching experiment aiming at conceptual change. Learning and Instruction 14:5, pages 485-501.
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Alexander Jordan, Michael Kleine, Alexander Wynands & Lothar Flade. 2004. Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland. Mathematische Kompetenzen von Schülerinnen und Schülern in Deutschland 159 173 .
D. De Bock, L. Verschaffel, D. Janssens, W. Van Dooren & K. Claes. (2003) Do realistic contexts and graphical representations always have a beneficial impact on students’ performance? Negative evidence from a study on modelling non-linear geometry problems. Learning and Instruction 13:4, pages 441-463.
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