To understand misconceptions with rational numbers (i.e., fractions, decimals, and percentages), we administered an assessment of rational numbers to 331 undergraduate students from a 4-year university. The assessment included 41 items categorized as measuring foundational understanding, calculations, or word problems. We coded each student's…

Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, "Let f(x) be a function of a real variable x," implying that the student has a robust sense of the real number continuum. This understanding is a central objective of the school…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

Strategies for rapid mental computation are explained, including multiplying by 11 (or 21, 31, etc.); adding columns of numbers; and multiplying 2-digit numbers. Rapid mental computation is suggested as a motivator for investigating the underlying mathematical principles. (DB)

This yearbook responds to the growing recognition among mathematics educators of the importance of teaching and learning estimation. It makes a strong case for the importance of estimation in such domains as numerosity, computation, and measurement. An important theme is the interdependency between the process of estimating in a particular domain…

The need to include proficiency with estimation and mental arithmetic as goals for the study of computation is presented. Approaches and guidelines are described for developing these skills.

Presents a problem introducing pupils to the ideas of consecutive and integer while practicing addition. Investigates the overall pattern of results with regard to formulating some general results, considers the algebra of the problem, and suggests proofs of why some numbers can and others cannot be formulated in this way. (ASK)

Thirty students (ages 7 to 18) with moderate intellectual disabilities were interviewed individually and their counting skills and number concepts assessed. Results showed a significant difference among the three age groups on all number skills assessed, and learning patterns were similar to those of students with normal intelligence.…

Outlines the embedded mathematics in which important but hidden calculations are being done for communications in commerce. Explains two key concepts, error detecting codes and error correcting codes. Illustrates these ideas using two familiar examples, barcodes and ISBN numbers. (ASK)

Discusses the mistakes of Kirschner, the German philosopher and mathematician, in calculating factorials of large numbers by hand in the 1600s. Uses computer technology to calculate those numbers now. (ASK)

The author redefines basic numeracy as the ability to use a four-function calculator sensibly. He then defines "sensibly" and considers the place of algorithms in the scheme of mathematical calculations. (MN)

The article offers an interpretation of "specially designed instruction" in arithmetic computation for learning disabled students which challenges overreliance on paper-and-pencil methodologies, rule-oriented procedures, and traditional sequences. Long division is used as an example of developing conceptual understanding to undergird computation.…

This publication is designed to help teachers increase awareness of multicultural issues for all students while making science and mathematics more relevant and approachable to children of color. The activities presented in this book are both multicultural and hands-on; they are discoveries to be made by the reader. They will allow teachers and…

A case is made for a comprehensive curriculum that includes strong competencies with not only number ideas and computation, but also with other mathematical topics such as geometry, statistics, probability, and estimation. (MP)

A model for directed numbers, using a sentry moving along the number line, is described. (MNS)