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.
