In the present article, we argue that the conceptual change approach to learning can apply in the case of mathematics, taking into consideration the particular nature of mathematical knowledge and the neurobiological bases of mathematical cognition. In the empirical study that is reported in this article, we investigated ninth graders'…

Algorithms for the four basic operations on whole numbers are described; these algorithms provide for sequential recording of all steps in the operations. (SD)

Presented are several methods of introducing nondecimal numeration systems to elementary grade students. Various activities for grouping and/or visual displays are used. Games which incorporate nondecimal grouping ideas are also presented. (JP)

Evidence gathered in a study of 106 students in a course in elementary school mathematics methods shows that work with a nondecimal numeration system involving entirely new number symbols and names can lead to heightened awareness and appreciation of difficulties that children might have in understanding base ten numeration. (Author/CM)

The question is raised: What comes first: rules of calculation or the meaning of concepts? The pressures on the teacher to teach and simplify knowledge to algorithms are discussed. The relation between conceptual and procedural knowledge in school mathematics and consequences for the teacher's professional knowledge are considered. (DC)

Dyscalculia, a poor understanding of the number concept and the number system, is a learning problem affecting many individuals. However, less is known about this disability than about the reading disability, dyslexia, because society accepts learning problems in mathematics as quite normal. This article provides a summary of the research on…

To investigate whether games may serve as useful formative assessment environments, this study examined, experimentally, the effects of two aspects of formative assessment on math achievement, game play, and help-seeking behaviors: (a) making assessment criteria explicit through the explanation of scoring rules and (b) incentivizing the use of…

This set of 13 activities, adapted from "Mathmatters: Developing Computational Skills with Developmental Activity Sequences (by Randall Souviney, Tamara Keyser, and Alan Sarver) was designed to help teachers using the Indigenous Mathematics Project materials (in Papua New Guinea) understand the basic processes involved in computation with…

Directions are presented for the construction and use of line-segment strips. Examples demonstrate activities, integrate elementary geometry and arithmetic instruction. (JP)

This monograph attempts to provide the teacher with examples, techniques, and tips for developing order in number. Topics covered include pre-number order and classification; beginning number activities; number lines; the 100-square counting chart; ordering the integers; fractional numbers; and games, counting rhymes, and other activities. A…

The author argues on theoretical grounds that not all "logical" pre-number activities are equally relevant for numeracy, and concludes with a practical suggestion for the kind of activity which does have particular relevance. (MN)

This study compares three methods of introducing two-digit numeration. It is concluded that teachers should build on the preschool exposure children have in counting past ten, rather than have children begin by counting out groups of tens and ones and only later in the process use the normal number names. (MN)

Teaching sequences designed to develop strategies for comparing numerals in grade two (in France) were analyzed. Children's strategies were noted, and an experiment confirmed underlying misconceptions concerning number. (MNS)