Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

People frequently gesture when problem-solving, particularly on tasks that require spatial transformation. Gesture often facilitates task performance by interacting with internal mental representations, but how this process works is not well understood. We investigated this question by exploring the case of mental abacus (MA), a technique in which…

This study aims to introduce a method that is based on the relationship between numbers and geometry, which can be used to show the exact location of rational numbers on the number line, compare rational numbers, make calculations, and examine rational numbers conceptually through parallel lines. It is believed that this method will to contribute…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

The purpose of this study is to investigate pre-service elementary teachers' realistic considerations and difficulties in solving "division with remainder" type of problems which focus on the measurement meaning of division operation. The qualitative research method of case study design was used for the study. The purposive sampling…

Number line models provide a visual aid for students to examine the relationship of integers with each other and facilitate learning of integers and integer operations. Such models are typically used when students are asked real-life problems. This study employs a qualitative case study design to perform an in-depth analysis of how middle grade…

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

This study aims to examine the differences in numerosity estimation on a right-to-left number line between second- to fourth-grade students and undergraduate students, together with whether number-line estimation is related to basic arithmetic tasks (addition and subtraction). Hence, 53 Arabic-speaking children and 63 Arabic-speaking adults…

Developmental dyscalculia (DD) is a specific mathematical learning disability, with a prevalence of around 3%-7% in the school-aged population. It negatively affects individuals, and even the national, development. Previous DD-intervention programs usually targeted on numerosity, number, simple arithmetic, or even general cognitive ability. The…

Algebraic thinking in children can bridge the cognitive gap between arithmetic and algebra. This quantitative study aimed to develop and test a cognitive model that examines the cognitive factors influencing algebraic thinking among Year Five pupils. A total of 720 Year Five pupils from randomly selected national schools in Malaysia participated…

This research aims to explore the use of ethnomathematics in revealing mathematical representations and in the formulation of a calculation system used in the "Marosok" trading tradition by the Minangkabau tribe in West Sumatra. Ethnomathematics studies ideas in various cultural activities practiced by ethnic, social, or professional…

Fraction knowledge has been found to predict later mathematical performance, but many students have difficulty with fractions. Virtual manipulatives (VM) and concrete manipulatives (CM) are effective approaches to teaching fractions, but previous research has not been able to reach a consensus on which manipulatives are the most effective. This…

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been…

This groundbreaking book looks at the development of mathematical thinking in infants and toddlers, with an emphasis on the earliest stage, from zero to three, when mathematical thinking and problem solving first emerge as natural instincts. The text explores the four precursor math concepts--attribute, comparison, change, and pattern--with an…