Frames of Reference and Achievement in Elementary Arithmetic

  title={Frames of Reference and Achievement in Elementary Arithmetic},
  author={Eddie Gray and Demetra Pitta-Pantazi},
  journal={The Mathematics Enthusiast},
This paper considers the relationship between 8-11 years old students' numerical achievement and a possible disposition towards the construction of particular frames of reference. The paper uses the characteristics of a variety of kinds of images to focus upon frames of reference and explores a possible relationship between children's verbal descriptions of concrete and abstract nouns and the different ways they respond to aspects of elementary arithmetic. It seeks to establish whether or not… 

Figures and Tables from this paper

In this paper, we focus on the relationship between studying university mathematics and the 'thinking styles' of both undergraduate and postgraduate mathematics students. A cross- sectional


Knowledge construction and diverging thinking in elementary & advanced mathematics
This paper considers the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum and shows how students cope with the transition to advanced mathematical thinking in different ways leading once more to a diverging spectrum of success.
An analysis of diverging approaches to simple arithmetic: Preference and its consequences
Earlier research by the author indicated that many below average attainers do not remember number facts and use alternative strategies to obtain solutions to basic arithmetical problems. These
The development of arithmetic concepts and skills: Constructing adaptive expertise
This book discusses the development of Adaptive Expertise and Flexibility and neuropsychological Findings on Conceptual Knowledge of Arithmetic in children with Specific Language Impairments and young adults' strategic Choices in Simple Arithmetic.
On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking. In the study, a combined ontological-psychological outlook is applied. An analysis of
Duality, Ambiguity and Flexibility: A Proceptual View of Simple Arithmetic
In this paper we consider the duality between process and concept in mathematics, in particular using the same symbolism to represent both a process (such as the addition of two numbers 3+2) and the
Spatial ability, visual imagery, and mathematical performance
Abstract116 Foundation Year Engineering Students, at the University of Technology, Lae, Papua New Guinea, were given a battery of mathematical and spatial tests; in addition, their preferred modes of
The development of mental representations as a problem solving activity
Theories of Mathematical Learning
Contents: Preface. Part I: P. Cobb, Sociological and Anthropological Perspectives on Mathematics Learning. P. Cobb, B. Jaworski, N. Presmeg, Emergent and Sociocultural Views of Mathematical Activity.
Relational Understanding and Instrumental Understanding.
One gets faux amis between English as spoken in different parts of the world. An Englishman asking in America for a biscuit would be given what we call a scone. To get what we call a biscuit, he