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Direct linkViviane Durand-Guerrier – ZDM: Mathematics Education, 2024
Understanding the concept of completeness for an ordered field is known to be difficult for many university mathematics students. We hypothesise that the variety of possible axioms of completeness for the set of real numbers is one of the sources of difficulties as is the lack of understanding of the "raison d'être" of these axioms. In…
Descriptors: College Mathematics, Numbers, Number Concepts, Number Systems
Karaali, Gizem; Yih, Samuel – PRIMUS, 2020
When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…
Descriptors: Mathematics Instruction, College Mathematics, Algebra, Numbers
Download full textMersin, Nazan; Karabörk, Mehmet Akif; Durmus, Soner – Malikussaleh Journal of Mathematics Learning, 2020
This study seeks to analyse the awareness of the pre-service teachers on the counting methods, systems and tools used in the prehistoric method and the Ancient period and to examine the distribution of this awareness by gender. A total of 42 sophomore-level students studying at a university in the Western Black Sea region, Turkey, participated in…
Descriptors: Preservice Teachers, Mathematics Instruction, History, Mathematics
Steinke, Dorothea A. – Journal of Adult Education, 2015
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
Descriptors: Community Colleges, Number Concepts, Number Systems, Numbers
Pinhas, Michal; Pothos, Emmanuel M.; Tzelgov, Joseph – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2013
The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…
Descriptors: Evidence, Numbers, Number Concepts, Number Systems
Rips, Lance J. – Journal of Experimental Psychology: Learning, Memory, and Cognition, 2013
When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…
Descriptors: Number Concepts, Number Systems, Numbers, Mathematics Education
