Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners' developmental trajectories. Given…

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this article is the origins and nature of those fundamental mechanisms that promoted the emergence of the…

The advancement of technology has substantively changed the practices of numerous professions, including teaching. When an instructor first adopts a new technology, established classroom practices are perturbed. These perturbations can have positive and negative, large or small, and long- or short-term effects on instructors' abilities to teach…

Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children's…

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability…

Reasoning about bedrock abstract concepts such as time, number, and valence relies on spatial metaphor and often on multiple spatial metaphors for a single concept. Previous research has documented, for instance, both future-in-front and future-to-right metaphors for time in English speakers. It is often assumed that these metaphors, which appear…

Mathematics teachers are frequently looking for real-life applications and meaningful integration of mathematics and other content areas. Many genuinely seek to reach out to students and help them make connections between the often abstract topics taught in school. In this article the author presents ideas on integrating literature and mathematics…

Human children possess the ability to approximate numerical quantity nonverbally from a young age. Over the course of early childhood, children develop increasingly precise representations of numerical values, including a symbolic number system that allows them to conceive of numerical information as Arabic numerals or number words. Functional…

Skilled instructors observe consistent errors that young children may make in particular situations and seek ways to help children reform their thinking through conceptual understanding. Such teacher observations as those presented at the beginning of this article, combined with similar observations by teachers in other preschool and kindergarten…

Research Findings: Teachers and parents often use trade books to introduce or reinforce mathematics concepts. To date, an analysis of the early numeracy content of trade books has not been conducted. Consequently, this study evaluated the properties of numbers and counting within trade books. We coded 160 trade books targeted at establishing early…

This research synthesizes studies that used a Digitalized Interactive Component (DIC) to assess K-12 student mathematics performance during Computer-based-Assessments (CBAs) in mathematics. A systematic search identified ten studies that categorized existing DICs according to the tools that provided language assistance to students and tools that…

We examine teachers' use of resources as they prepare to teach the topic of numerical series of real numbers, in order to identify how their "personal relationship" with mathematical content--and its teaching--interacts with their use of a commonly used textbook. We describe this interplay between textbook and personal relationship, a…

This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

Making patterning the basis of mathematics investigations for an entire year produced unexpected results for Bruce Ferrington. A Year 2 class used the spatial tasks from the Pattern and Structure Mathematics Awareness Program (PASMAP) with a specific emphasis on patterning, to develop their thinking mathematically skills. The result was students…