These studies tested two questions about the developmental origins of children's sensitivity to iconicity with regard to number gestures: (1) whether children initially learn number gestures with sensitivity to the one-to-one correspondence between fingers and quantities or whether they learn them as unanalyzed symbols; and (2) whether sensitivity…

In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts,…

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…

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…

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…

Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

The aim of the study is to examine whether classroom teachers' Pedagogical Content Knowledge (PCK) on numbers develops in the period from their university education to their active teaching profession. Cross-sectional comparative study method was used in this research in order to examine what kind of development classroom teachers? pedagogical…