Do Theories of Conceptual Change Explain the Difficulties of Enlarging the Number Concept in Mathematics Learning?

Autor/inn/en	Merenluoto, Kaarina; Lehtinen, Erno
Titel	Do Theories of Conceptual Change Explain the Difficulties of Enlarging the Number Concept in Mathematics Learning?
Quelle	(2000), (8 Seiten) PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Monographie
Schlagwörter	Calculus; Concept Formation; Foreign Countries; Higher Education; Learning Processes; Learning Theories; Mathematicians; Mathematics Education; Number Concepts; Secondary Education; Finland + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Concept learning; Begriffsbildung; Ausland; Hochschulbildung; Hochschulsystem; Hochschulwesen; Learning process; Lernprozess; Learning theory; Lerntheorie; Mathematician; Mathematiker; Mathematische Bildung; Number concept; Zahlbegriff; Sekundarbereich; Finnland
Abstract	This paper discusses the theories of conceptual change and how they explain the difficulties in mathematics learning, especially in enlarging the number concept. Two studies are presented, one of which examines the research questions: What is the role of prior knowledge in students' answers to questions about the density of rational and real numbers? and Do theories of conceptual change explain the difficulties students have in learning these concepts? Ten university professors of mathematics were interviewed about their personal learning histories as professional mathematicians, and were asked what they remembered about the initial learning of the real number concept and how they currently conceptualize the numbers system. The main result from the interviews was that most of the professors remembered that learning to understand the notion of real numbers was something unique, and it required them to move into a new kind of abstract thinking, free from the constraints of prior mathematical intuition. In the second study a number concept test was administered to 640 calculus students (aged 17-18 years) from 24 randomly selected Finnish upper secondary schools in the usual classroom conditions. The test included identification, classification, and construction problems in the domain of rational and real numbers. The role of the students' prior knowledge was then analyzed using their answers to four critical questions. Results from the second study indicate that the process of knowledge acquisition, especially in mathematics, involves restructuring as well as enriching one's prior knowledge structures, which can take place at many different levels. (Contains 30 references.) (ASK)
Erfasst von	ERIC (Education Resources Information Center), Washington, DC