Discusses the relationship between computational fluency and number sense in early childhood mathematical development. (Author/NB)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes the work that students and teachers do to develop computational fluency for subtraction. Examines the orchestration of whole-class discourse and presents a collection of common strategies. (Author/NB)

Suggests ways to increase students' computational fluency using concrete materials, engaging tasks, and reflection time to increase number automaticity, flexibility in thinking about numbers, and use of efficient problem-solving strategies to find sums and differences. (Author/NB)

In two experiments, large effects of variations in the form and timing of the cardinality question suggested that preschoolers' cardinality responses were situation-specific. Results suggested that children had no initial understanding of the relation between cardinality responses and numerosity. (RH)

Uses interviews with 72 pupils in grades 2-6 to investigate awareness of the relation between situation and computation in simple quotitive and partitive division problems as informally and formally experienced. Concludes that formal division, understood as related to everyday situations, only depends in interplay with informal knowledge.…

Reacts to an article published in a previous issue of this journal on the effects of graphing calculators and computer algebra systems (CAS) on students' manual calculation skills. Asks enthusiasts of CAS to learn from history and avoid pitfalls. (ASK)

Describes the use of a soroban, a base-10 computer which is a relative of the Chinese abacus, for developing concepts of number sense, place value, operation sense, and mental computation. Provides pictures of the soroban. (MKR)

Describes a lesson on long division using chip trading which follows that algorithm for long division. (MKR)

We investigated processing of numerical order information and its relation to mechanisms of numerical quantity processing. In two experiments, performance on a quantity-comparison task (e.g. 2 5; which is larger?) was compared with performance on a relative-order judgment task (e.g. 2 5; ascending or descending order?). The comparison task…

This paper explores the changing conditions of the Swedish minority in bilingual Finland. It describes the framework for Finland's bilingualism and the present situation of the Swedish minority in Finland. It concludes with a discussion of the recent debate in Finland about whether the increased use of languages other than L1 is to be seen as a…

Participants at the Summer Institute Pattern Exploration: Integration Math and Science in the Middle Grades used and developed a method treat arithmetic, algebra and geometry as one entity. The use of iterative geometric constructions is seen to reinforce the concepts of exponents, ratios and algebraic expressions for the nth stage of the…

Working memory has been implicated in the early acquisition of arithmetic skill, but the relations among different components of working memory, performance on different types of arithmetic problems, and development have not been explored. Preschool and Grade 1 children completed measures of phonological, visual-spatial, and central executive…

A quadrilateral is arithmetic if its area is an integer and its sides are integers in an arithmetic progression, and it is cyclic if it can be inscribed in a circle. The author shows that no quadrilateral is both arithmetic and cyclic.

This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., 5 + 4 + 9 + 5 = ?) and mathematical equivalence problems (e.g., 4 + 3 + 6 = 4 + ? or 6 + 4 + 5 = ? + 5). Next, they completed an encoding task in which they reconstructed…