We define and describe how subitizing activity develops and relates to early quantifiers in mathematics. Subitizing is the direct perceptual apprehension and identification of the numerosity of a small group of items. Although subitizing is too often a neglected quantifier in educational practice, it has been extensively studied as a critical…

Tasks that ask students to label rational number points on a number line are common not only in curricula in the upper elementary school grades but also on state assessments. Such tasks target foundational rational number concepts: A fraction (or a decimal) is more than a shaded part of an area, a part of a pizza, or a representation using…

The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…

In this article we analyze the relations between academic mathematical knowledge and the mathematical knowledge associated with issues mathematics school teachers face in practice, according to the specialized literature, and restricted to the theme "number systems". We present examples that illustrate some areas of conflict between those forms of…

The study compared two methods of teaching an initial place value skill: a concrete, semiconcrete, abstract teaching sequence and an abstract-only presentation. Learning-disabled elementary and middle school students (N=24) using the concrete to abstract teaching sequence performed significantly better on three posttests than students taught the…

This investigation involves first assessing and then designing instruction to resolve student difficulties with addition facts. The ultimate goal was improving students' computational fluency.

This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)

To develop their logico-mathematical foundation of number as described by Piaget (1947/1950, 1967/1971, 1971/1974), 26 low-performing, low-SES first graders were given physical-knowledge activities (e.g., Pick-Up Sticks and "bowling") during the math hour instead of math instruction. During the second half of the school year, when they showed…