This research aims to explore the role of physical representations in young children's numerical learning then identify the benefits of using a graphical interface in order to understand the potential for developing interactive technologies in this domain. Three studies are reported that examined the effect of using physical representations…

This submission contains the Proceedings of the 2012 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Laval University in Québec City, Québec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study…

The universities and faculties which educate teachers of mathematics for teaching pupils/students of any age group from pre-school age to higher education carefully monitor and compare valuable results of this research, detect the areas in which the mathematical achievements of pupils should be improved at the national level and propose the ways…

Familiarity with modern methods of measurement and skill in doing quantitative thinking are essential. This text offers a "general" course intended for those who continue studies in the senior high school as well as for those who do not continue. It aims to contribute to the pupil's liberal education by preparing him to understand the…

Familiarity with modern methods of measurement and skill in doing quantitative thinking are essential. This text offers a "general" course intended for those who continue studies in the senior high school as well as for those who do not continue. It aims to contribute to the pupil's liberal education by preparing him to understand the…

This textbook is a young mathematician's guide to mathematics. The following five parts are presented: (1) Arithmetick, vulgar, and decimal, with all the useful rules; and a general method of extracting the roots of all single powers; (2) Algebra, or arithmetick in species; wherein the method of raising and resolving equations is rendered easie;…

The author cites work on visual perception which indicates that in order to study perception it is necessary to replace such classical geometrical notions as betweeness, straightness, perpendicularity, and parallelism with more general concepts. The term tolerance geometry is used for any geometry when primitive notions are obtained from the…

The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)

This paper focuses on elementary school students' use of mathematically-based (MB) and practically-based (PB) explanations. The mathematical context used in this study is multiplication. Two issues are discussed. The first issue is a comparison between MB and PB explanations used by students before they are formally introduced to multiplication in…

This paper discusses the existence of theoretical distributions subsumed within mathematical reality and it highlights several meaningful implications for psychological researchers to consider in the application of statistical procedures. It begins with a brief overview of the misinterpretation of statistical testing, followed by a discussion of…

A philosophy giving four justifications for teaching mathematics in school, based on the intrinsic qualities of mathematics (logic, language, applications, and culture). (DT)