This study examined numerosity comparison in 3-year-old children. Predictions derived from the analog numerical model and the object-file model were contrasted by testing the effects of size and ratio between numerosities to be compared. Different perceptual controls were also introduced to evaluate the hypothesis that comparison by preschoolers…

Research on computational estimation and mental computation has received a considerable amount of attention from mathematics educators during the past decade. These proceedings resulted from a meeting to explore dimensions of number sense and its related fields. The participants came from three groups: mathematics educators actively pursuing…

In this article, I survey the integrated connectionist/symbolic (ICS) cognitive architecture in which higher cognition must be formally characterized on two levels of description. At the microlevel, parallel distributed processing (PDP) characterizes mental processing; this PDP system has special organization in virtue of which it can be…

In 4 experiments, the authors examined the use of the hands in simple arithmetic tasks. Experiments 1 and 2 demonstrated that pointing increases both accuracy and speed in counting arrays of items, whether those items are identical or distinctive. Experiment 3 demonstrated that individuals tend to nod their heads when not allowed to point and that…

Groups of mathematically strong and weak second-, fourth- and sixth-graders were individually confronted with numerosities smaller and larger than 100 embedded in one-, two- or three-dimensional realistic contexts. While one third of these contexts were totally unstructured (e.g., an irregular piece of land jumbled up with 72 cars), another third…

Two studies examined age-related declines in the functioning of working memory. Negative correlations between age and measures of working memory were found. These relations were attenuated by measures of storage capacity, processing efficiency, coordination effectiveness, and simple comparison speed. The greatest attenuation occurred with simple…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

This article provides the rationale for using Fermi questions with eighth graders studying algebra. It describes the students' reaction to such questions as well as their thinking processes and solutions to questions posed to them by their teacher. (Contains 1 figure.)

Patients with corticobasal degeneration (CBD) have calculation impairments. This study examined whether impaired number knowledge depends on verbal mediation. We focused particularly on knowledge of very small numbers, where there is a precise relationship between a cardinality and its number concept, but little hypothesized role for verbal…

Mental computation helps children understand how numbers work, how to make decisions about procedures, and how to create different strategies to solve math problems. Although researchers agree on the importance of mental computation skills, they debate how to help students develop these skills. The present study explored the existing literature in…

Examines some of the issues that underlie the conceptual structure of the computational approach to cognition. Finds that this approach construes symbolization too narrowly, thereby blocking more adequate treatments of learning and acquisition of skills. Discusses the notion of symbol and symbolization and suggests an alternative approach to the…

This paper presents Lewis Carroll's formula for mentally calculating the day of the week of a given date. The paper concludes that such formulas are too complex for individuals of low intelligence to learn by themselves, and thus "idiots savants" who perform such calendar calculations must be using other systems. (JDD)

A 2-high-threshold signal detection (HTSDT) model, a mixture distribution (SON) model, and 2-highthreshold (HT) models with responses distributed over 1 or several response categories were fit to results of 6 experiments from 2 studies on associative recognition: R. Kelley and J. T. Wixted (2001) and A. P. Yonelinas (1997). HTSDT assumes that…

This longitudinal study investigated the academic and cognitive characteristics of persistent mathematics difficulty (MD-p) from first to fourth grade. Ninety-nine children were retrospectively categorized into one of three groups: MD-p, transient mathematics difficulty (MD-t), or typically developing. MD-p was defined as persistently low…

A biologically detailed computational model is described of how categorization judgments become automatic in tasks that depend on procedural learning. The model assumes 2 neural pathways from sensory association cortex to the premotor area that mediates response selection. A longer and slower path projects to the premotor area via the striatum,…