Being numerate involves using mathematical ideas efficiently to make sense of the world, which is much more than just being able to calculate. What is needed is the accurate interpretation of mathematical information and the ability to draw sound conclusions based on mathematical reasoning. This skill may be called "critical numeracy",…

Recently there has been a keen interest in the area of mathematics and finding the best methods of instruction. For instance, the No Child Left Behind Act (NCLB) has placed new levels of accountability on educators for the success of students with their education, especially in mathematics. Certain areas of mathematics, such as Algebra, have been…

Practitioners of education in South Africa (SA) struggle painfully between the extremes of its authoritarian and deeply religious roots that prescribe blind obedience to people in authority and their elders, and the demands of open-mindedness, critical thinking and also solidarity required for democratic citizenship. A particular pedagogy was used…

James Moffett's "Teaching the Universe of Discourse" set out an agenda for the study of development in writing, which influenced James Britton's work in the UK. Subsequently, however, the work of both these thinkers was largely set aside in the approach to writing taken by national strategies in England. In this article, we trace the…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

This article describes Realistic Mathematics Education (RME), a design theory for mathematics education proposed by Hans Freudenthal and developed over 40 years of developmental research at the Freudenthal Institute for Science and Mathematics Education in the Netherlands. Activities from a unit to develop student understanding of logarithms are…

While many researchers in science education have argued that students' epistemological understanding of models and of modelling processes would influence their cognitive processing on a modelling task, there has been little direct evidence for such an effect. Therefore, this study aimed to investigate the relation between students' epistemological…

Alignment between content standards and standardized tests is a significant issue to society, science pedagogy, and test validation. To better understand the issues related to alignment, this study compares the alignment in physics among three education systems: Jiangsu (China), New York State (United States), and Singapore. The same coding…

In today's world, where the volume of knowledge everyone must deal with is increasing exponentially, many educators agree that schools must focus on developing skills for life-long learning. But what does that mean for an area such as algebra? Teachers' goal in school algebra should be to guide students to "work smarter" with algebraic symbols and…

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to…

Students (n = 328) from US and UK universities completed four self-report measures related to intellectual competence: typical intellectual engagement (TIE), openness to experience, self-assessed intelligence (SAI), and learning approaches. Confirmatory data reduction was used to examine the structure of TIE and supported five major factors:…

This paper raises serious questions about the reliability of the learning pyramid as a guide to retention among students. The pyramid suggests that certain teaching methods are connected with a corresponding hierarchy of student retention. No specific credible research was uncovered to support the pyramid, which is loosely associated with the…

A training program in analogical reasoning skills stresses processes of encoding, inferring, mapping, and applying. Initial sessions focus on applications to concrete analogy problems while subsequent sessions present more abstract linguistic analogies and consider applications to other school subjects. (CL)

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…