If the principles of languages are applied to the learning of arithmetic, it appears that elementary grade pupils are being introduced to mathematical symbols at too early an age. (MP)

Misconceptions and abuses of manipulative aids for teaching mathematics are discussed, as well as suggestions for their more effective use. (JMF)

Argues that the correct use of positive and negative signs in textbooks is often ignored and that this misuse might be because the authors are unaware of some basic rules. (DDR)

Analyzes visual and symbolic strategies developed by students to express generalizations of number patterns and connections between them. Compares approaches adopted by students working through parallel task sequences which integrate different computer tools in different ways. Makes suggestions as to how students might be encouraged to exploit…

This paper examines the effect of applying symbolic computation and graphics to enhance students' ability to move from a visual interpretation of mathematical concepts to formal reasoning. The mathematics topics involved, Approximation and Interpolation, were taught according to their historical development, and the students tried to follow the…

The importance of visual representation, usually a geometric figure presented in words and in mathematical symbols that is frequently found on high-stakes standardized tests is evaluated. The study shows that mathematics teachers can help prepare students to solve mathematical problems containing a figure not drawn to scale by looking for and…

The author advocates for writing as an essential communication skill for learning mathematics. Mathematical diary writing is cited as a good way for students to privately represent their thinking through pictures, language, or symbols, and also as a channel for children to communicate with themselves and with their teachers. Cited research…

Problems in mathematics instruction in Thailand that are related to language include the simultaneous use of both traditional Thai numerals and Hindu-Arabic numerals, misunderstanding of mathematics problems for cultural reasons, and/or difficulty in understanding problem context. Research has shown that elementary and secondary school children…

This research addressed itself to the development of a novel teaching-learning scheme for non-trivial, first-degree equations in one unknown, based on an analysis of the notions and misconceptions of junior high students. The approach was tried in a "teaching experiment" involving six case studies of students of various abilities in…

This report contains recommendations on chemical nomenclature, guidance on symbols, and terminology and units for physiochemical quantities. This report, intended to provide guidance to science teachers, consists of eleven sections: (1) general introduction; (2) introduction to symbols, terminology, and units for physiochemical quantities; (3)…

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)

Many elementary and junior high school students do not become proficient with common and decimal fractions because they have established few connections between the form they learn in the classroom and understandings they already have. (Author/GC)

The National Committee on Mathematical Requirements was organized in the late summer of 1916 under the auspices of the Mathematical Association of America for the purpose of giving national expression to the movement for reform in the teaching of mathematics, which had gained considerable headway in various parts of the country, but which lacked…

Describes how 2 10-year olds developed drawings and numeral systems to symbolize their mental operations while dividing unit bars into thirds and fourths using TIMA: Bars, a computer microworld, as a medium for enacting mathematical actions. The symbolic nature of their partitioning operations was crucial in establishing more conventional…