The Three Worlds and Two Sides of Mathematics and a Visual Construction for a Continuous Nowhere Differentiable Function

Autor/inn/en	Oikkonen, Juha; Hannula, Jani
Titel	The Three Worlds and Two Sides of Mathematics and a Visual Construction for a Continuous Nowhere Differentiable Function
Quelle	In: LUMAT: International Journal on Math, Science and Technology Education, 10 (2022) 2, S.7-32 (26 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Zusatzinformation	ORCID (Hannula, Jani)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2323-7112
Schlagwörter	Higher Education; Teaching Methods; Mathematics Instruction; Secondary Education; Thinking Skills; Guidelines; Articulation (Education); Skill Development; Authentic Learning; Advanced Courses + Suchen Sie Ihr Suchwort? Hochschulbildung; Hochschulsystem; Hochschulwesen; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht; Sekundarbereich; Denkfähigkeit; Richtlinien; Articulation; Artikulation (Ling); Artikulation; Aussprache; Kompetenzentwicklung; Qualifikationsentwicklung; Fortgeschrittenenunterricht
Abstract	A rigorous and axiomatic-deductive approach is emphasized in teaching mathematics at university-level. Therefore, the secondary-tertiary transition includes a major change in mathematical thinking. One viewpoint to examine such elements of mathematical thinking is David Tall's framework of the three worlds of mathematics. Tall's framework describes the aspects and the development of mathematical thinking from early childhood to university-level mathematics. In this theoretical article, we further elaborate Tall's framework. First, we present a division between the subjective-social and objective sides of mathematics. Then, we combine Tall's distinction to ours and present a framework of six dimensions of mathematics. We demonstrate this framework by discussion on the definition of continuity and by presenting a visual construction of a nowhere differentiable function and analyzing the way in which this construction is communicated visually. In this connection, we discuss the importance to distinguish the subjective-social from the objective side of mathematics. We argue that the framework presented in this paper can be useful in developing mathematics teaching at all levels and can be applied in educational research to analyze mathematical communication in authentic situations. (As Provided).
Anmerkungen	LUMA Centre Finland. University of Helsinki. A.I. Virtasen aukio 1, 00014 University of Helsinki, Finland. Tel: +358-50-348-0567; e-mail: editor@lumat.fi; Web site: https://journals.helsinki.fi/lumat
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01