The Illusion of Linearity: From Analysis to Improvement

Dirk de Bock, Wim van Dooren, Dirk Janssens, Lieven Verschaffel

Springer Science & Business Media, 30 sept 2007 - 184 páginas

Linear or proportional relationships are a major topic in mathematics education. However, recent research has shown that secondary school students strongly tend to apply the linear model also in situations wherein it is not applicable. This overgeneralization of linearity is sometimes referred to as the "illusion of linearity" and has a strong negative impact on students’ reasoning and problem solving skills.

"The Illusion of Linearity: From Analysis to Improvement" presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. Although the empirical study of students’ improper linear reasoning clearly constitutes a new line of research, it owes a great deal to prior work in mathematics education research community (such as the work of the scholars of the Freudenthal Institute on realistic mathematics education).

Based on both quantitative and qualitative research, "The Illusion of Linearity: From Analysis to Improvement" discusses the following issues: (1) how the illusion of linearity appears in diverse domains of mathematics and science and how it is conceptually related to other more general misconceptions identified in the research literature, (2) what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon, and (3) how the illusion of linearity can be remedied by appropriate instruction.

"The Illusion of Linearity: From Analysis to Improvement" is essential to those working in mathematics education, particularly teacher educators and curriculum research and development.

Índice

• A WIDESPREAD PHENOMENON: 1
• IN SEARCH OF EMPIRICAL EVIDENCE: 23
• A SERIES OF FOLLOWUP: 39
• AN INDEPTH INVESTIGATION: 87
• A TEACHING EXPERIMENT: 109
• STEPPING OUTSIDE THE CLASSROOM 127: 126
• PSYCHOLOGICAL AND EDUCATIONAL ANALYSIS: 143
• References: 165
• Index: 179

Pasajes populares

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Página 167 - Cooper, B. (1994). Authentic testing in mathematics? The boundary between everyday and mathematical knowledge in National Curriculum testing in English schools.

Página 174 - Niss, M. (2001). Issues and problems of research on the teaching and learning of applications and modelling. In JF Matos, W. Blum, SK Houston & SP Carreira (Eds), Modelling and mathematics education.

Página iv - Managing Editor AJ Bishop, Monash University, Melbourne, Australia Editorial Board JP Becker, Illinois, USA C.

Página 174 - R. (1997a). Every word problem has a solution : The suspension of reality and sense-making in the culture of school mathematics. Learning and Instruction, 7, 309-328.

Página 166 - In H.-W. Henn & W. Blum (Eds.), ICMI Study 14: Applications and modelling in mathematics education - Pre-conference volume (pp. 53-58). Dortmund, Germany. Cai, J., & Hwang, S. (2002). Generalized and generative thinking in US and Chinese students' mathematical problem solving and problem posing.

Página 165 - Paper presented at the 8th European Conference for Research on Learning and Instruction, Goteborg, Sweden.

Página 175 - Schwartz, DL, & Moore, JL (1998). On the role of mathematics in explaining the material world: Mental models for proportional reasoning. Cognitive Science, 22, 471-516.

Información bibliográfica

• Título: The Illusion of Linearity: From Analysis to Improvement; Mathematics Education Library; Humanities, Social Sciences and Law; Education (R0)
• Autores: Dirk de Bock, Wim van Dooren, Dirk Janssens, Lieven Verschaffel
• Edición: ilustrada
• Editor: Springer Science & Business Media, 2007
• ISBN: 0387711643, 9780387711645
• N.º de páginas: 184 páginas