Learning the meaning of number words is a lengthy and error-prone process. In this review, we highlight outstanding issues related to current accounts of children's acquisition of symbolic number knowledge. We maintain that, despite the ability to identify and label small numerical quantities, children do not understand initially that number words…

This chapter describes instances of play within a teaching episode on integer addition and subtraction. Specifically, this chapter makes the theoretical distinction between integer play and playing with integers. Describing instances of integer play and playing with integers is important for facilitating this type of intellectual play in the…

Math fact fluency involves the quick, accurate retrieval of basic arithmetic combinations and the ability to use this fact knowledge efficiently. Math fact retrieval is typically considered fluent when performed accurately within 2 to 3 seconds, and "efficiency" refers to students' ability to apply fact knowledge to more complex…

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses,…

To increase opportunities for students to take more advanced math courses in high school, many school districts enroll grade 8 students in Algebra I, a gateway course for advanced math. But students who take Algebra I in grade 8 and skip other math courses, such as grade 8 general math, might miss opportunities to develop the foundational…

The collection of studies in this special issue make an important contribution to our understanding and measurement of the core cognitive and noncognitive factors that influence children's emerging quantitative competencies. The studies also illustrate how the field has matured, from a time when the quantitative competencies of infants and young…

In this article Jessica Hunt explores the use of clinical interviews to gain a deep understanding of students' knowledge. Examples of clinical interviews are provided and advice for planning, giving and interpreting the results of interviews is also included.

The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. Difficulties occur in moving from intuitive understandings to formal mathematical representations of operations with negative and positive integers. This paper describes a series of…

Number lines are part of people's everyday life and are frequently used in primary mathematics as instructional aids, in texts, and for assessment purposes on mathematics tests. There are two types of number lines; (1) structured number lines, which are the focus of this paper; and (2) empty number lines. Structured number lines represent…

Human cognition is founded, in part, on four systems for representing objects, actions, number, and space. It may be based, as well, on a fifth system for representing social partners. Each system has deep roots in human phylogeny and ontogeny, and it guides and shapes the mental lives of adults. Converging research on human infants, non-human…

Suggests that political apathy among young people is the result of not having the conceptual tools necessary to comprehend present issues. Argues that to grasp many issues, students need to be mathematically literate, which many are not. Suggests that instructors should expose students to comparative numbers more often. (DSK)