Given that both children and adults struggle with fractions in mathematics education, we investigated the processing of nonsymbolic fractions in a continuous form of part-of-the-whole. Continuous features of nonsymbolic numbers (e.g., the size of dots in an array) were found to influence numerosity judgment, but it should be noted that the…

The goal of the paper is to pay attention to some important techniques and approaches including adequate designations as a tool for unambiguous understanding and a key to success in solving problems, vivid visual images as a mnemonic techniques, and special formulas as a universal tool for solving typical problems, when teaching medical students…

Over the past few decades, there has been extensive debate as to whether humans represent number abstractly and, if so, whether perceptual features of a set such as cumulative surface area or contour length are extracted more readily than number from the external world. Here we show that 7-month-old infants are sensitive to smaller ratio changes…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

Recent findings have suggested that adults' and children's approximate number system (ANS) acuity may be malleable through training, but research on ANS acuity has largely been conducted with adults and children who are from middle- to high-income homes. We conducted 2 experiments to test the malleability of ANS acuity in preschool-aged children…

Representations that create informative visual displays are powerful tools for communicating mathematical concepts. The National Council of Teachers of Mathematics encourages the use of manipulatives (NCTM 2000). Manipulative materials are often used to present initial representations of basic numerical principles to young children, and it is…

In this article we present an activity theory based framework that can capture the complex situations that arise when modern technology like multi-touch devices are introduced in classroom situations. As these devices are able to cover more activities than traditional technologies, even computerbased, media, we have to accept that they now take a…

Lim and Leek (2012) presented a formalization of information along object contours, which they argued was an alternative to the approach taken in our article (Feldman & Singh, 2005). Here, we summarize the 2 approaches, showing that--notwithstanding Lim and Leek's (2012) critical rhetoric--their approach is substantially identical to ours,…

In this article, the author offers two well-known mathematical images--that of a dot moving around a circle; and that of the tens chart--and considers their power for developing mathematical thinking. In his opinion, these images each contain the essence of a particular topic of mathematics. They are contrasting images in the sense that they deal…

This study examined the hypothesis of superior quantification abilities of persons with high functioning autism (HFA). Fourteen HFA individuals (mean age: 15 years) individually matched with 14 typically developing (TD) participants (gender, chronological age, full-scale IQ) were asked to quantify as accurately and quickly as possible…

A series of experiments, all concerned with the topic of mathematical concept learning by the young child, were conducted. The concept mainly focused upon was that of inequalities. Five experiments were run. These are: (1) acquisition of mathematical concepts under experimental situation and in traditional pedagogical situation, (2) cued vs.…

Using arrays of dots and grids many numerical concepts can be illustrated for students. (SD)

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) The Affective Views of Primary School Children (Peter Grootenboer); (2) Theoretical Model of Analysis of Rate Problems in Algebra (Jose Guzman, Nadine Bednarz and Fernando Hitt); (3) Locating Fractions on…