Results 1  10
of
64
First principles organize attention to and learning about relevant data: Number and animateinanimate distinction as examples
 Cognitive Science
, 1990
"... Early cognitive development benefits from nonilnguistic representations of skeietai sets of domainspecific principles and complementary domainrelevant doto obstroction processes. The principles outline the domain, identify relevant inputs, and structure coherently what is learned. Knowledge acquis ..."
Abstract

Cited by 62 (2 self)
 Add to MetaCart
Early cognitive development benefits from nonilnguistic representations of skeietai sets of domainspecific principles and complementary domainrelevant doto obstroction processes. The principles outline the domain, identify relevant inputs, and structure coherently what is learned. Knowledge acquisition within the domoin is a faint function of such domainspecific principles and domaingeneral learning mechanisms. Two examples of early learning illustrate this. Skeietol preverboi counting principles help children sort different linguistic strings into those that function OS the conventional countword OS opposed to labels for obfects in the child’s linguistic community. Skeletal causal principles, working with complementary perceptual processes that abstract information obout biological and nonbiological conditions and patterns of movement, leod to the rapid ocquisition of knowledge about the animateinanimate dlstinction. By 3 years of age children con say whether photographs of unfamiliar nonmammoiion animals, mommois, statues, and wheeled obfectr portray objects capable or incopabie of selfgenerated motion. They also generate answers to questions about the insides
NonVerbal Counting in Humans: The Psychophysics of Number Representation
 Psychological Science
, 1999
"... In nonverbal counting tasks derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed ..."
Abstract

Cited by 56 (5 self)
 Add to MetaCart
In nonverbal counting tasks derived from the animal literature, adult human subjects repeatedly attempted to produce target numbers of key presses at rates that made vocal or subvocal counting difficult or impossible. In a second task, they estimated the number of flashes in a rapid, randomly timed sequence. Congruent with the animal data, mean estimates in both tasks were proportional to target values, as was the variability in the estimates. Converging evidence makes it unlikely that subjects used verbal counting or time durations to perform these tasks. The results support the hypothesis that adult humans share with nonverbal animals a system for representing number by magnitudes that have scalar variability (a constant coefficient of variation). The mapping of numerical symbols to mental magnitudes provides a formal model of the underlying nonverbal meaning of the symbols (a model of numerical semantics). Animal subjects represent both number and duration by mental magnitudes (Church, 1984; Gibbon, Church, & Meck, 1984; Meck & Church, 1983). These representations are formally analogous to points on the real number line. Meck and Church (1983) proposed such a representation to account for animal nonverbal counts of objects or events (Figure 1). According to their theory each item is enumerated by an impulse of activation which is added to an accumulator. The magnitude in the accumulator at the end of the count is read into memory, where it represents the number of the counted set. The noise (trialtotrial variability) in these remembered magnitudes is proportional to the magnitude, a property that Gibbon (1977) called scalar variability . Mathematical modeling of psychophysical data from a variety of tasks indicates that memory is the dominant source of trial...
NonVerbal Numerical Cognition: From the Reals to the Integers
, 2000
"... nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the nonverbal foundations of numerical thinking, which, it is argued, are common to humans and nonverbal animals. In this view, ..."
Abstract

Cited by 56 (4 self)
 Add to MetaCart
nthesis of these findings, the tension between the discrete and the continuous, which has been central to the historical development of mathematical thought, is rooted in the nonverbal foundations of numerical thinking, which, it is argued, are common to humans and nonverbal animals. In this view, the nonverbal representatives of number are mental magnitudes (real numbers) with scalar variability. Scalar variability means that the signals encoding these magnitudes are "noisy;" they vary from trial to trial, with the width of the signal distribution increasing in proportion to (scaled to) its mean. In short, the greater the magnitude, the noisier its representation. These noisy mental magnitudes are arithmetically processedadded, subtracted, multiplied, divided and ordered. Recognition of the importance of arithmetically processed mental magnitudes in the nonverbal representation of number has emerged from a convergence of results from human and animal studies. This is comparative
Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability
 Journal of Experimental Child Psychology
, 2000
"... Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade � 82 months), children with IQ scores in the lowaverage to highaverage range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD) ..."
Abstract

Cited by 27 (11 self)
 Add to MetaCart
Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade � 82 months), children with IQ scores in the lowaverage to highaverage range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n � 42), a group of children who showed variable achievement test performance across grades (n � 16), and a control group of academically normal peers (n � 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children. © 2000 Academic Press Key Words: learning disabilities; mathematical disabilities; reading disabilities; number;
Cognitive addition: Strategy choice and speedofprocessing differences in gifted, normal, and mathematically disabled children
 Developmental Psychology
, 1991
"... Sixty young and 60 elderly adults completed a pencilandpaper addition test and solved 40 computerpresented simple addition problems. Strategies and problem solution times were recorded on a trialbytrial basis and were classified in accordance with the distributions of associations model of stra ..."
Abstract

Cited by 25 (17 self)
 Add to MetaCart
Sixty young and 60 elderly adults completed a pencilandpaper addition test and solved 40 computerpresented simple addition problems. Strategies and problem solution times were recorded on a trialbytrial basis and were classified in accordance with the distributions of associations model of strategy choices. The elderly group showed a performance advantage on the ability measure and for the developmental maturity of the mix of problemsolving strategies, but the young group showed an advantage for overall solution times. A componential analysis of the overall solution times for memory retrieval trials, however, showed no reliable age difference for rate of retrieving addition facts from longterm memory but did suggest that the elderly adults might have been slower than the younger adults for rate of encoding digits and verbally producing an answer. Overall results are interpreted within the context of the strategy choice model. The first purpose of this study was to extend into adulthood normative information on the development of problemsolving strategies in addition. The second purpose was to compare the performance of young and elderly adults on a relatively wellunderstood cognitive task: the mental solution of simple addition
A componential analysis of an early learning deficit in mathematics
 Journal of Experimental Child Psychology
, 1990
"... This study was designed to assess strategy choice and informationprocessing differences in normal and mathematically disabled first and second grade children. Twentythree normal and 29 learning disabled (LD) children solved 40 computerpresented simple addition problems. Strategies, and their assoc ..."
Abstract

Cited by 24 (14 self)
 Add to MetaCart
This study was designed to assess strategy choice and informationprocessing differences in normal and mathematically disabled first and second grade children. Twentythree normal and 29 learning disabled (LD) children solved 40 computerpresented simple addition problems. Strategies, and their associated solution times, used in problem solving were recorded on a trialbytrial basis and each was classified in accordance with the distributions of associations model of strategy choices. Based on performance in a remedial education course, as indexed by achievement test scores, the LD sample was reclassified into an LDimproved group and an LDnochange group. No substantive differences comparing the normal and LDimproved groups occurred in the distribution of strategy choices, strategy characteristics (e.g., error rates), or rate of information processing. The performance characteristics of the LDnochange group, as compared to the two remaining groups, included frequent counting and memory retrieval errors, frequent use of an immature computational strategy, poor strategy choices, and a variable rate of information processing. These performance
Cognitive Foundations of Arithmetic: Evolution and Ontogenisis
 Mind and Language
, 2001
"... Dehaene (this volume) articulates a naturalistic approach to the cognitive foundations of mathematics. Further, he argues that the `number line' (analog magnitude) system of representation is the evolutionary and ontogenetic foundation of numerical concepts. Here I endorse Dehaene's naturalistic ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
Dehaene (this volume) articulates a naturalistic approach to the cognitive foundations of mathematics. Further, he argues that the `number line' (analog magnitude) system of representation is the evolutionary and ontogenetic foundation of numerical concepts. Here I endorse Dehaene's naturalistic stance and also his characterization of analog magnitude number representations. Although analog magnitude representations are part of the evolutionary foundations of numerical concepts, I argue that they are unlikely to be part of the ontogenetic foundations of the capacity to represent natural number. Rather, the developmental source of explicit integer list representations of number are more likely to be systems such as the objectfile representations that articulate midlevel object based attention, systems that build parallel representations of small sets of individuals.
Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability
 Journal of Experimental Child Psychology
, 1999
"... Based on performance on standard achievement tests, firstgrade children (mean age � 82 months) with IQ scores in the lowaverage to highaverage range were classified as at risk for a learning disability (LD) in mathematics, reading, or both. These atrisk children (n � 55) and a control group of a ..."
Abstract

Cited by 21 (9 self)
 Add to MetaCart
Based on performance on standard achievement tests, firstgrade children (mean age � 82 months) with IQ scores in the lowaverage to highaverage range were classified as at risk for a learning disability (LD) in mathematics, reading, or both. These atrisk children (n � 55) and a control group of academically normal peers (n � 35) were administered experimental tasks that assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, and ease of retrieving information from longterm memory. Different patterns of intact cognitive functions and deficits were found for children in the different atrisk groups. As a set, performance on the experimental tasks accounted for roughly 50 % and 10 % of the group differences in mathematics and reading achievement, respectively, above and beyond the influence of IQ. Performance on the experimental tasks thus provides insights into the cognitive deficits underlying different forms of LD, as well as into the sources of individual differences in academic achievement. © 1999 Academic Press Key Words: learning disabilities; mathematical disabilities; number; counting; arithmetic. Quantitative skills influence employability, wages, and onthejob productivity above and beyond the influence of reading abilities, IQ, and a host of other factors (Paglin & Rufolo, 1990; RiveraBatiz, 1992). Despite the economic importance of quantitative abilities, little research has been conducted on the factors that contribute to poor mathematical achievement and to mathematical disabilities (MD), in comparison to the research efforts devoted to understanding poor reading achievement and reading
An investigation of teachers' beliefs of students' algebra development
 Cognition and Instruction
, 2000
"... Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problemsolving difficulty. Teachers also rated their levels of agreement to a variety of reformbased statements on teaching and learning mathematics. Anal ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problemsolving difficulty. Teachers also rated their levels of agreement to a variety of reformbased statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbolprecedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problemsolving develops prior to verbal reasoning. High school teachers were most likely to hold the symbolprecedence view and made the poorest predictions of students ’ performances, whereas middle school teachers ’ predictions were most accurate. The discord between teachers ’ reformbased beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbolprecedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbolbased representations and procedures for students ’ learning introductory algebra. The study of people engaged in cognitively demanding tasks must consider the relation between people’s judgments and actions and the beliefs they hold. Several aspects of people’s decision making are well established. People do not strictly follow the laws of logic and probability when weighing information or following im
DC: Mathematics and learning disabilities
 J Learn Disabil
"... Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlyin ..."
Abstract

Cited by 19 (4 self)
 Add to MetaCart
Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities. The breadth and complexity of the field of mathematics make the identification and study of the cognitive phenotypes that define mathematics learning disabilities (MLD) a formidable endeavor. In theory, a learning disability can result from deficits in the ability to represent or process information in one or all of the