Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…

To date, researchers investigating nonsymbolic number processes devoted little attention to the visual properties of their stimuli. This is unexpected, as nonsymbolic number is defined by its visual characteristics. When number changes, its visual properties change accordingly. In this study, we investigated the influence of different visual…

Children in developing countries often lack sufficient support for early learning skills prior to beginning school. This research evaluates an educational media intervention using an animated cartoon program, "Akili and Me." The program was originally created in Tanzania to teach early learning skills. This program was adapted in content…

Quantity recognition in whole number representations is a fundamental skill children need to acquire in their mathematical development. Despite the observed correlation to mathematics achievement, however, the ability to recognize quantities in structured whole number representations has not been studied extensively. In this article, we…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

This research was designed to investigate the conceptualisations and thinking strategies Indigenous Australian students use in counting tasks. Eighteen Aboriginal students, in years 1 to 11 at a remote community school, were interviewed using standard counting tasks and a "counting" task that involved fetching "maku" (witchetty…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

Previously, researchers have relied on asking young children to plot a given number on a 0-to-10 number line to assess their mental representation of numbers 1 to 9. However, such a ("conventional") number-to-position (N-P) task may underestimate the accuracy of young children's magnitude estimates and misrepresent the nature of their…

In the past years, rote learning, especially in the teaching and process was the usual practice. This takes the form of indoctrination; Children do not learn through rote memorization, it is only an end in itself. True learning is that which is achieved through the understanding and insight of the problem at stake. An application of philosophy…

The Approximate Number System (ANS) supports basic arithmetic computation in early childhood, but it is unclear whether the ANS also supports the more complex computations introduced later in formal education. "Solving for x" in addend-unknown problems is notoriously difficult for children, who often struggle with these types of problems…

Research has established that executive functions, the skills required to monitor and control thought and action, are related to achievement in mathematics. Until recently research has focused on working memory, but studies are beginning to show that inhibition skills--the ability to suppress distracting information and unwanted responses--are…

Braille-character recognition is one of the foundational skills required for teachers of braille. Prior research has evaluated computer programming for teaching braille-to-print letter relations (e.g., Scheithauer & Tiger, 2012). In the current study, we developed a program (the Visual Braille Trainer) to teach not only letters but also…

The current research examined whether peripherally presented numerical information can affect the speed of number processing. In 2 experiments, participants were presented with a target matrix flanked by a distractor matrix and were asked to perform a comparative judgment (i.e., decide whether the target was larger or smaller than the reference…

This paper deals with a brief history of the most remarkable Euler numbers "e,"?"i"?and?"?" in mathematical sciences. Included are many properties of the constants "e,"?"i"?and?"?" and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special…

Several researchers have documented prospective teachers' (PTs') conceptions of various mathematical topics. However, less is known about how PTs' conceptions develop. To address this gap, I designed two tasks with the goals of addressing the PTs' initial conceptions of multidigit whole numbers and helping them develop more sophisticated ones. I…