In a 1-hour teaching interview, 20 children (aged 7 to 11) discovered how to tell whether objects might be made of the same material by using ratios of measures of weight and size. We examine progress in the children's reasoning about measurement and proportional relations, as well as design features of instruments, materials, and tasks crafted to…

Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students' spontaneous focusing on…

The relations among various spatial and mathematics skills were assessed in a cross-sectional study of 854 children from kindergarten, third, and sixth grades (i.e., 5 to 13 years of age). Children completed a battery of spatial mathematics tests and their scores were submitted to exploratory factor analyses both within and across domains. In the…

Presents a short biography of one of the winners of the American Psychological Association's Award for Distinguished Scientific Early Career Contributions to Psychology (2012). Thomas L. Griffiths won the award for bringing mathematical precision to the deepest questions in human learning, reasoning, and concept formation. In his pioneering work,…

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of…

Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…

The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

One of most notable features of existing body of research in transition seems to be the absence of a theoretical model. The suggestion we present in this paper--to view and understand the high school to university transition in mathematics as a modern-day rite of passage--is an attempt at defining such framework. Although dominantly reflecting…

The article "Is Google Making Us Stupid?" in last Summer's "Atlantic Monthly," raised a number of provocative, and indeed worrisome, questions about computer usage and cognitive development. For instance, persons with considerable experience of reading for the sake of pleasure report that, after a couple of years using computers a great deal, they…

This article focuses on the cognitive factors that impact on students in the middle school years experiencing learning difficulties in basic mathematics. It begins with a review of selected literature providing information about the learning difficulties in mathematics. Focus then shifts to an implementation of the "Quicksmart"…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

An outline of a model that provides a new perspective on the conceptual foundations of mathematics and a new approach for the study of children's acquisition of numerical operations is proposed. Attention is viewed as a pulse-like succession of moments and is supported by recent data from neurophysiology. (MP)

Performance differences between male and female students in proportional reasoning tasks were analyzed with respect to task characteristics. The student performance was also compared to their visual-spatial ability to determine whether such ability correlates with a better performance. The task characteristics tested were ratio complexity,…