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- Title
OSCILLATING BETWEEN 'IS' AND 'OUGHT' IN MATHEMATICS EDUCATION RESEARCH.
- Authors
LENSING, FELIX
- Abstract
This article explores the relationship between theoretical and practical considerations in mathematics education research. It discusses the views of Johann Friedrich Herbart, who believed that pedagogy should provide educators with knowledge of the goals and means of education. However, the article raises questions about whether practical philosophy alone can determine educational goals and whether psychology adequately captures the educational process. It also highlights the importance of considering diverse perspectives in mathematics education research. The author aims to address the methodological question of how to build both theoretical and practical knowledge in the field. The text discusses the relationship between normative statements and scientificity in practical research in mathematics education. The authors argue that normative statements, which prescribe what should be done, do not deal with objective occurrences and therefore cannot be considered scientific. They propose an alternative perspective based on the work of Edmund Husserl, which suggests that normative propositions can be transformed into value propositions and then into theoretical propositions. However, they acknowledge that normative rightness is relative to a certain value stance and cannot be derived from propositions about what is. The text also discusses the question of whether a rational being can divide by zero. The author argues that the rightness of the proposition that one should not divide by zero can be justified by showing that a rational being cannot do so. However, the author also acknowledges that empirical investigations of actual human behavior show that people do perform algebraic transformations that involve concealed divisions by zero. The author concludes that while a rational being that values the ordinary laws of arithmetic cannot
- Subjects
MATHEMATICS education; EDUCATION research; SCIENCE education; MATHEMATICS teachers; APPLIED psychology
- Publication
For the Learning of Mathematics, 2024, Vol 44, Issue 1, p23
- ISSN
0228-0671
- Publication type
Article