A4 Refereed article in a conference publication
Revealing modes of knowing about density
Authors: González-Forte Juan Manuel, Fernández Ceneida, Vamvakoussi Xenia, Van Hoof Jo, Van Dooren Wim
Editors: Ayalon Michal, Koichu Boris, Leikin Roza, Rubel Laurie, Tabach Michal
Conference name: International Conference for the Psychology of Mathematics Education
Publisher: Psychology of Mathematics Education (PME)
Publication year: 2023
Journal: Proceedings of the PME Conference
Book title : Proceeding of the 46th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2), Haifa, Israel July 16-21, 2023 : PME-46
Journal name in source: Proceedings of the International Group for the Psychology of Mathematics Education
Series title: Proceedings of the PME Conference
First page : 395
Last page: 402
eISBN: 978-965-93112-2-4
ISSN: 0771-100X
Web address : https://www.igpme.org/wp-content/uploads/2023/08/PME-46-Vol-2-RR_A-G.pdf(external)
Rational number density has been investigated through open-ended question tasks and multiple-choice tasks or by asking to interpolate a number between two numbers. However, students’ responses to these three types of tasks were not directly compared. The objective is to look for relationships between the three types of tasks in order to identify differences regarding students’ density understanding depending on the type of knowledge elicited. Participants were 791 primary and secondary school students. Results show that most of the students believed that rational numbers are discrete. Differences between the modes of representation are also found. Finally, interpolating a number between two pseudo-consecutive ones is neither a necessary nor a sufficient condition for students to answer that there are infinitely many intermediate numbers.
