Publications
Chosen filters:
Chosen filters:
On the complexity of mathematical problems : Medvedev degrees and reverse mathematics Ghent University
We investigate the complexity of mathematical problems from two perspectives: Medvedev degrees and reverse mathematics. In the Medvedev degrees, we calculate the complexity of its first-order theory, and we also calculate the complexities of the first-order theories of several related structures. We characterize the join-irreducible Medvedev degrees and deduce several consequences for the interpretation of propositional logic in the Medvedev ...
New Perspectives on Mathematical Practices. Essays in Philosophy and History of Mathematics Vrije Universiteit Brussel
This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics. It contains a well-balanced mixture of contributions by internationally extablished experts, such as Jeremy Gray and Jens Hoyrup; upcoming scholars, such as Erich Reck and Dirk Schlimm; and young, promising researchers at the beginning of their careers. The book is situated within a relatively new and broadly ...
Defining modern mathematics: Willy Servais (1913-1979) and mathematical curriculum reform in Belgium KU Leuven
The New Math reform which swept Europe in the 1960’s was in a significant way influenced by the Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques. Since its foundation in 1952 the CIEAEM held annual meetings where mathematicians, logicians and psychologists discussed the direction of the modernization process. Several Belgian mathematicians played a prominent role in the CIEAEM, in particular Willy ...
Naturalism in the Philosophy of Mathematics: On Mathematical Explanations of Empirical Phenomena KU Leuven
This research is concerned with a current debate on naturalism in the philosophy of mathematics. Discussing key notions like truth, (logical) necessity, and justification to approach the topic, an investigation into the different positions within this debate will be carried out. These will subsequently be contrasted with other schools of thought, such as nominalism and platonism. The dialectics of the debate between these different schools of ...
The early roots of the European Modern Mathematics Movement: How a model for the science of mathematics became a model for mathematics education KU Leuven
The cradle of modern mathematics in Europe is likely to be traced to the founding meeting of the International Commission for the Study and Improvement of Mathematics Teaching in 1952 in La Rochette par Melun (France). The organizer of that meeting, Caleb Gattegno, had chosen Mathematical and Mental Structures as a theme and succeeded in bringing together several “big names” from the fields of psychology, epistemology, and mathematics, ...
Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure KU Leuven
BACKGROUND: The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. AIM: This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. SAMPLE: Data ...
Purifying applied mathematics and applying pure mathematics Vrije Universiteit Brussel
In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a ...