Research on probability judgment has traditionally emphasized that people are susceptible to biases because they rely on "variable substitution": the assessment of normative variables is replaced by assessment of heuristic, subjective variables. A recent proposal is that many of these biases may rather derive from constraints on cognitive…

Numbers are fundamental entities in mathematics, but their cognitive bases are unclear. Abundant research points to linear space as a natural grounding for number representation. But, is number representation fundamentally spatial? We disentangle number representation from standard number-to-line reporting methods, and compare numerical…

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Several recent behavioral studies have shown that the enumeration of a small number of items (a process termed "subitizing") depends on the availability of attentional resources and is not a preattentive process as previously thought. Here we studied the neural correlates of visual enumeration under different attentional loads in a dual-task…

The commentary by Treccani and Umilta (2011) on our recent paper in this journal (Fischer et al., 2010) usefully broadens the perspective on numerical cognition for a general readership and clarifies (or raises) some fundamental issues of cognitive representation. Our response to this commentary is organized into three main sections that focus…

The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were…

In this paper we describe four Indian in-service middle school mathematics teachers' shifts in their roles with respect to the textbook. The shifts occurred through participation in collaborative investigation on the topic of integers in professional development meetings. Analysis of teachers' talk in these meetings indicated a shift in teachers'…

There is a consensus among mathematicians and mathematics educators that creativity plays an essential role in doing mathematics. Creative students are self-regulated students who take control over processes and experience high self-efficacy beliefs. The aim of this case study was to promote mathematical creativity and self-efficacy of elementary…

The purpose of this study was to use calculator-assisted instruction to help two fifth-grade low-achievers learn number sense. The research process includes three stages: (1) pre-test interview to detect what kinds of number sense the students did not have; (2) calculator-assisted instruction to help them develop number sense; and (3) post-test…

Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…

The purpose of this study was to determine the effectiveness of computer-based instruction on teaching students with intellectual disability the skills of telling which emergency services to call in specific emergency situations and reciting the correct telephone number of that specific emergency service. In this study, a multiple probe design…

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Theano, an associate, most likely the wife, of Pythagoras, has some claim to be the first woman to play an active role in mathematics. The question of how far this claim can be supported is here examined.

This study intends to investigate how multi-symbolic representations (text, digits, and colors) could effectively enhance the completion of co-located/distant collaborative work in a virtual reality context. Participants' perceptions and behaviors were also studied. A haptics-enhanced virtual reality task was developed to conduct…