The purpose of the study was to examine differences in early numerical competencies, as well as subtraction skill, as a function of children's mathematics difficulty (MD) status: computational difficulty (CD), word problem-solving difficulty (PD), concurrent difficulty (CDPD), or neither difficulty (i.e., typically developing; TYP). Based on…

A considerable body of research exists on students' understanding of decimal fractions and the prevalence and persistence of common misconceptions related to this understanding. Results from major studies such as the National Assessment of Educational Progress (NAEP) in the United States and the Concepts in Secondary Mathematics and Science (CSMS)…

This study compared how students with learning difficulties in math (MLD) who were randomly assigned to two instructional conditions answered items on problem solving tests aligned to the Common Core State Standards Initiative for Mathematics. Posttest scores showed improvement in the math performance of students receiving Enhanced Anchored…

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…

Interactive whiteboards are somewhat unimpressive at first and look like the whiteboards that already hang on the walls of many classrooms. However, integrating interactive whiteboard technology in a unit on adding and subtracting integers enhances student engagement and understanding. In this article, the author describes how she used an…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for…

Researchers have long disagreed about whether number concepts are essentially continuous (unchanging) or discontinuous over development. Among those who take the discontinuity position, there is disagreement about how development proceeds. The current study addressed these questions with new quantitative analyses of children's incorrect responses…

As a key concept in early mathematics curriculum, number sense is crucial for children's learning of other mathematics concepts. An earlier curriculum with a strong focus on number sense development presumably helps children perform better in mathematics later on. Chinese students outperformed their United States (U.S.) peers on number sense at…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

Numbers are thought to be represented in space along a mental left-right oriented number line. Number magnitude has also been associated with the size of grip aperture, which might suggest a connection between number magnitude and intensity. The present experiment aimed to confirm this possibility more directly by using force as a response…

Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…

The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…

In this article, I discuss a case of pre-primary and primary school teacher education concerning place value in number representation. In primary school (in Italy, in grades 1 and 2), the topic is usually introduced by means of manipulatives (for instance, abaci and base ten blocks). But it is well known that no artefact is transparent for…

The initial formation of number concept represents one of the essential aspects of learning mathematics at the primary school. Children commonly show strong difficulties and absence of comprehension of symbolic and abstract nature of concept of number. The objective of the present study was to show the effectiveness of original method for…