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…

Widespread concern has been expressed about the persistent low mathematics achievement of students in the US, particularly for students from low-income and minority backgrounds and students with disabilities. Instructional gaming technology, when designed and fictionalized well, has the potential to improve the motivation and mathematics…

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…

This paper examines the way two 10th graders cope with a non-standard generalisation problem that involves elementary concepts of number theory (more specifically linear Diophantine equations) in the geometrical context of a rectangle's area. Emphasis is given on how the students' past experience of problem solving (expressed through interplay…

This report provides evidence of the influence of a tutorial "communication game" on fifth graders' generative understanding of the integer number line. Students matched for classroom and pretest score were randomly assigned to a tutorial (n = 19) and control group (n = 19). The tutorial group students played a 13-problem game in which…

How can teachers encourage their geography students to make sense of big numbers? The key math skills geography students need to apply are ones they learned long ago in fifth grade: estimation and place value. However, in order to recognize the size of a city, or strength of a country's per capita income, or value of a birth rate, they need…

Researchers (Ball, 2003; Ma, 1999; Schulman, 1986) have long investigated how a teacher's subject matter and pedagogical content knowledge impact on students' learning of mathematics. In an attempt to account for the relationship between teacher knowledge and student learning, this study examined four Romanian first grade teachers' knowledge about…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

The purpose of the study was to examine how teachers enhance their knowledge of rational numbers focused on modeling problem tasks using multiple representations. The professional development summer institute and the follow-up Lesson Study (Lewis, 2002) throughout the academic year focused on engaging teachers in rational numbers and proportional…

The different combinations involved in additive and subtractive colour mixing can often be difficult for students to remember. Using transmission graphs for filters of the primary colours and a numerical scheme to write out the relationships are good exercises in analytical thinking that can help students recall the combinations rather than just…

This paper highlights the Indonesian's road transportation contexts, namely, angkot, that used in learning and teaching of addition and subtraction in first grade and second grade MIN-2 Palembang. PMRI approach that adopt from RME [Realistic Mathematics Education] was used in this design research. From teaching experiment was founded that the…

Just as athletes stretch their muscles before every game and musicians play scales to keep their technique in tune, mathematical thinkers and problem solvers can benefit from daily warm-up exercises. Jessica Shumway has developed a series of routines designed to help young students internalize and deepen their facility with numbers. The daily use…

In 2008, the authors worked with a range of schools to trial ideas that assisted young Indigenous students to engage with mathematics as they enter the school environment. This article highlights some key pedagogical strategies that assisted classroom teachers to improve Indigenous students' understanding of mathematics, particularly in the area…

Children are often intrigued by number patterns and games and so it makes sense for teachers to include them in their mathematics lessons. Puzzles encourage the use of critical thinking skills and provide practice in important skills areas. The use of games fosters mathematical learning and encourages the mathematical processes that children use.…

One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…