By the end of primary school, children are expected to acquire a range of mathematical skills that progressively develop. This study aimed to gain insight into how a large number of numerical and geometrical measures are grouped and whether the structures shift or remain invariant along child's development based on the data obtained from a sample…

How do children construct a concept of natural numbers? Past research addressing this question has mainly focused on understanding how children come to acquire the cardinality principle. However, at that point children already understand the first number words and have a rudimentary natural number concept in place. The question therefore remains;…

Numbers are represented as ordered magnitudes along a spatially oriented number line. While culture and formal education modulate the direction of this number-space mapping, it is a matter of debate whether its emergence is entirely driven by cultural experience. By registering 8-9-month-old infants' eye movements, this study shows that numerical…

The ability to connect numbers and magnitudes is an important prerequisite for math learning, here referred to as number-magnitude skills. It has been proposed that working memory plays an important role in constructing these connections. The aim of the current study was to examine if working memory accounts for constructing these connections by…

Background: Evidence exists that there are two main underlying cognitive factors in mathematical difficulties: working memory and number sense. It is suggested that real math difficulties appear when both working memory and number sense are weak, here referred to as the double deficit (DD) hypothesis. Aims: The aim of this study was to test the DD…

How is number-concept acquisition related to overall language development? Experiments 1 and 2 measured number-word knowledge and general vocabulary in a total of 59 children, ages 30-60 months. A strong correlation was found between number-word knowledge and vocabulary, independent of the child's age, contrary to previous results (D. Ansari et…

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

External number representations are commonly used throughout the first years of instruction. The twenty-frame is a grid that contains two rows of 10 dots each, and within each row, dots are organized in two groups of five. The assumption is that children can make use of these structures for enumerating the dots, rather than relying on one-by-one…

Small numbers are spontaneously associated with left space and larger numbers with right space (the SNARC effect), for example when classifying numbers by parity. This effect is often attributed to reading habits but a causal link has so far never been documented. We report that bilingual Russian-Hebrew readers show a SNARC effect after reading…

Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human…

The enumeration of small numbers of objects (approximately 4) proceeds rapidly, accurately, and with little effort via a process termed subitization. Four experiments examined whether it was possible to subitize the number of features rather than objects present in a display. Overall, the findings showed that when features are presented randomly…

This document, the first of three volumes, reports on the 15th annual conference of the International Group for the Psychology of Mathematics Education (PME) held in Italy 1991. Plenary addresses and speakers are: "Social Interaction and Mathematical Knowledge" (B. M. Bartolini); "Meaning: Image Schemata and Protocols" (W.…

Research reports from the annual conference of the International Group for the Psychology of Mathematics Education include: "A Comparison of Children's Learning in Two Interactive Computer Environments" (Edwards); "On Building a Self-Confidence in Mathematics" (Eisenberg); "Classroom Discourse and Mathematics…

The Proceedings of PME-XVII has been published in three volumes because of the large number of papers presented at the conference. Volume I contains a brief Plenary Panel report, 4 full-scale Plenary Addresses, the brief reports of 10 Working Groups and 4 Discussion Groups, and a total of 23 Research Reports grouped under 4 themes. Volume II…