Projects
Human and Artificial Understanding in Mathematics - A comparative study of informal, but functionally valuable moves performed by mathematical agents. Vrije Universiteit Brussel
Mathematical reasoning by undergraduate mathematics students KU Leuven
This doctoral research project aims to gain insight in the level and characteristics of mathematical reasoning by undergraduate mathematics students and to find ways to improve their mathematical reasoning.
The following questions will be investigated:
· Which mathematical reasoning abilities can be identified?· What mathematical reasoning skills are eligible for inclusion in undergraduate (bachelor) ...
Explanation in mathematics. A philosophical analysis of the explanatory force of mathematical proofs and visualizations and their role in scientific explanations. Vrije Universiteit Brussel
The use of adaptive logics for the practice and the philosophy of mathematics and the use of mathematical tools for the abstract analysis of adaptive logics Ghent University
This project concerns an investigation into three aspects of the relation between mathematics and adaptive logics (AL's): it is investigated how (a) AL's can be used for the formal modeling of the mathematical practice, (b) AL's can solve problems of the foundations of mathematics, and © mathematical techniques can be used for the abstract study of AL's.
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 ...
Strategic Research Programme: Cultures of Mathematics: Logic, Philosophy and History of Mathematical Practices. Vrije Universiteit Brussel
Reverse Mathematics and Nonstandard Analysis: the actual infinite in the foundations of Mathematics Ghent University
Reverse Mathematics (RM) unveils the striking phenomenon that theorems of ordinary Mathematics fall in only five equivalence classes, although there are infinitely many nonequivalent classes in Logic. My project analyzes RM where equality = is replaced with $\approx$, equality up to infinitesimals from Nonstandard Analysis. There are applications in Physics and the Philosophy of Science.
Effects of school, class/teacher, and student characteristics on attitude toward mathematics and mathematics achievement of boys and girls in Ugandan secondary schools KU Leuven
Mathematics learning performance and mathematics learning difficulties in China Ghent University
This research focuses on the development of a mathematics performance test for Chinese Primary schools. A calibrated instrument will be developed. In relation to the testing information about pupil variables will be gathered (math anxiety, attitudes and motivation). These are considered as potential secondary causes for learning difficulties. At the instructional level information about teaching strategies and methods used is gathered. ...