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…

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…

The psychology supporting the use of quantifier words (e.g., "some," "most," "more") is of interest to both scientists studying quantity representation (e.g., number, area) and to scientists and linguists studying the syntax and semantics of these terms. Understanding quantifiers requires both a mastery of the…

A single-case multiple baseline design was used to evaluate the effects of supplemental mathematics instruction with Numicon on the number sense skills of kindergarteners with varying degrees of math difficulty. Nine students participated in the study. Intervention consisted of 20 minutes of supplemental mathematics instruction using the…

Previous research in the area of children's knowledge of number agreement morphology has yielded mixed results. Some researchers have found evidence for sensitivity to agreement morphology at as early as 16 months, while others report that children do not comprehend number agreement morphology until as late as five or six years old. Studies of…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

This study was designed according to the mixed research method in which quantitative and qualitative research methods were used in order to identify the challenges confronted by classroom teacher candidates in solving mathematical problems and the factors affecting how they choose these representations. The population of this study consisted of…