In this article, the authors share a European perspective on teaching linear equations in Finland, Flanders, and Hungary. They begin with an assertion that it is through observation, in its broadest sense, and opportunities for participation, that people assimilate themselves into the culture in which they are raised. They discuss three approaches…

This is the second of three articles that draw on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". The report was soundly based on research about how children learn mathematics, much of it done in the UK in the '80s. Most of the findings about algebra are very…

As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…

Despite the emphasis that children should have a robust sense of number and a thorough understanding of fraction (National Mathematics Advisory Panel, 2008), many students continue to struggle with these concepts. Booker Diagnostic Assessment Framework (Booker, 2011) can inform decision about teaching that improves students' learning outcomes.…

This study aimed at investigating the progress of students' learning on multiplication fractions with natural numbers through the five activity levels based on Realistic Mathematics Education (RME) approach proposed by Streefland. Design research was chosen to achieve this research goal. In design research, the Hypothetical Learning Trajectory…

The role of a teacher is different from that in traditional mathematics instruction when the implementation of a lesson is based on students' ideas. The author's experience teaching the same lesson (of the latter format) to two different classes of pre-service teachers in an elementary mathematics methods course is described. Since whole-class…

Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…

One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…

The aim of this exploratory study was to investigate the quality of arithmetic education for children with cerebral palsy. The use of individual educational plans, amount of arithmetic instruction time, arithmetic instructional grouping, and type of arithmetic teaching method were explored in three groups: children with cerebral palsy (CP) in…

The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…

In a meta-analysis of 164 studies, Alfieri, Brooks, Aldrich, and Tenenbaum (2010) found that assisted discovery learning was more effective than explicit instruction or unassisted discovery learning and that explicit instruction resulted in more favorable outcomes than unassisted discovery learning. In other words, "unassisted discovery does…

This article portrays action research conducted in relation to students' faulty use of the equality sign in a Grade Four mathematics classroom in Sweden. Substantial background on teacher-researcher collaboration that prepares ground for the action research is offered. Drawing on cultural-historical and activity theory perspectives, the conduct of…

One of the most fundamental math skills for students to learn is basic computational skills. Students who have difficulty learning math skills may benefit from representational approaches, such as TouchMath. A multiprobe, multiple baseline, across-participants design was used in this study to investigate the use of TouchMath with students with…