Analyzed two children's use of a computer-based motion detector to make sense of symbolic expressions (Cartesian graphs). Found three themes: (1) tool perspectives, efforts to understand graphical responses to body motion; (2) fusion, emergent ways of talking and behaving that merge symbols and referents; and (3) graphical spaces, when changing…

Previous research has demonstrated that both hearing adults and hearing children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Here, the possibility is explored that the same phenomenon can be confirmed in deaf adults who have acquired a signed language as their first language. Results…

In this note we consider an experiment involving an urn and k balls with numbers 1, 2, 3, ..., k. The experiment consists of drawing n balls either with replacement or without replacement. We note some surprising results.

The main focus of this paper is on the study of students' conceptual understanding of two major concepts of Set Theory--the concepts of inclusion and belonging. To do so, we analyze two experimental classroom episodes. Our analysis rests on the theoretical idea that, from an ontogenetic viewpoint, the cognitive activity of representation of…

This article relates to an empirical study based on the use of mathematical symbolism in problem solving, twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a…

The importance of representations which are fundamental to understanding and applying mathematics, with the emphasis on the way the individuals who cannot see employ the representations is described. The teachers at Hadley school for the Blind showed the way the blind people used representations when learning mathematics with some accommodation,…

The self-worth theory of achievement motivation holds that in situations in which poor performance is likely to reveal low ability, certain students (known as self-worth protective students) intentionally withdraw effort in order to avoid the negative implications of poor performance in terms of damage to self-worth. In this study, evidence of…

Mathematics is like a language, although technically it is not a natural or informal human language, but a formal, that is, artificially constructed language. Importantly, educators use their natural everyday language to teach the formal language of mathematics. At times, however, instructors encounter problems when the technical words they use,…

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…

It is recommended that schools incorporate literacy in all aspects of the curriculum. In this way, students begin to understand that reading and writing are not just for English class--they are skills that are important for many parts of daily life. This does not mean that teachers need to take time away from their other subjects to achieve this…

This dictionary explains 225 terms used in bibliometrics, and it provides nontechnical definitions of bibliometric concepts and suggests sources where more information can be found about the defined term. Special features include sample references, cross references, variants (synonyms), and an index of names. The introduction relates the terms of…

In this paper, Piaget's theory is analyzed using Locke's philosophy. The first part, "Mental Experiences," describes the author's view (with a tentative interpretation of Piaget's position) of reflection, abstraction, re-presentation, and the use of symbols. The second part, "Piaget's Theory of Abstraction," has four sections:…

An electronics graphic symbol set for on-line construction of electrical and electronics schematic diagrams is described. Specific procedures involving off-line and on-line activities are presented for the development and entry of schematic diagrams utilizing a stored set of symbols. An example of the commands and coding required for the…

Explains that the use of symbols in some textbooks to represent both physical quantitites and numerical measures is illogical and confusing. (GA)

The development of fractional and decimal notation is outlined beginning with Egyptian hieroglyphics. (MN)