Mark H Ashcraft

• PhD
• Professor (Full) at University of Nevada, Las Vegas

This book provides a comprehensive overview of numerical cognition by bringing together writing by leading researchers in psychology, neuroscience, and education, covering work using different methodological approaches in humans and animals. During the last decade there had been an explosion of studies and new findings with theoretical and translat...

For some, doing mathematics is enjoyable, and represents an opportunity to learn and excel. For others, the mere thought of doing mathematics can induce anxiety, fear, and avoidance. What are the factors behind such emotions, and how do they affect math learning and performance? This chapter explores the positive and negative avenues through which...

Because of wide disparities in college students' math knowledge-that is, their math achievement-studies of cognitive processing in math tasks also need to assess their individual level of math achievement. For many research settings, however, using existing math achievement tests is either too costly or too time consuming. To solve this dilemma, we...

We tested children in Grades 1 to 5, as well as college students, on a number line estimation task and examined latencies and errors to explore the cognitive processes involved in estimation. The developmental trends in estimation were more consistent with the hypothesized shift from logarithmic to linear representation than with an account based o...

We review a foundational finding in the area of mathematical cognition, the problem size effect, as it has been studied and modeled across the past 30 years. Early research on the effect indicated a substantial role for memory retrieval, as opposed to simple counting-based performance, leading to research on the nature of the memory representation...

The authors provide a brief review of the history and assessment of math anxiety, its relationship to personal and educational consequences, and its important impact on measures of performance. Overall, math anxiety causes an "affective drop," a decline in performance when math is performed under timed, high-stakes conditions, both in laboratory te...

A national survey on researchers' experiences with their institutional review boards (IRBs) is presented, focused exclusively on social and behavioral researchers. A wide range of experiences is apparent in the data, especially in terms of turnaround time for submitted protocols, incidence of data collection without prior IRB approval, and stated r...

The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective...

Four experiments examined performance on the 100 "basic facts" of subtraction and found a discontinuous "stair step" function for reaction times and errors beginning with 11 - n facts. Participants' immediate retrospective reports of nonretrieval showed the same pattern in Experiment 3. The degree to which elementary subtraction depends on working...

Anxiety-related responding and skill deficits historically are associated with performance-based problems such as mathematics anxiety, yet the relative contribution of these variables to substandard performance remains poorly understood. Utilizing a 7% carbon dioxide (CO2) gas to induce anxiety, the present study examined the impact of anxious resp...

Highly math-anxious individuals are characterized by a strong tendency to avoid math, which ultimately undercuts their math competence and forecloses important career paths. But timed, on-line tests reveal math-anxiety effects on whole-number arithmetic problems (e.g., 46 + 27), whereas achievement tests show no competence differences. Math anxiety...

Individuals with high math anxiety demonstrated smaller working memory spans, especially when assessed with a computation-based span task. This reduced working memory capacity led to a pronounced increase in reaction time and errors when mental addition was performed concurrently with a memory load task. The effects of the reduction also generalize...

Individuals with high math anxiety demonstrated smaller working memory spans, especially when assessed with a computation-based span task. This reduced working memory capacity led to a pronounced increase in reaction time and errors when mental addition was performed concurrently with a memory load task. The effects of the reduction also generalize...

The problem size effect in adult arithmetic performance is generally attributed to direct retrieval processes operating on a network representation in long-term memory. J. LeFevre and her colleagues (J. LeFevre, J. Bisanz, et al., 1996; J. LeFevre, G. S. Sadesky, & J. Bisanz, 1996) challenged this explanation using verbal report evidence that adult...

The problem size effect in adult arithmetic performance is generally attributed to direct retrieval processes operating on a network representation in long-term memory. J. LeFevre and her colleagues (J. LeFevre, J. Bisanz, et al., 1996; J. LeFevre, G. S. Sadesky, & J. Bisanz, 1996) challenged this explanation using verbal report evidence that adult...

Presents a brief overview of the mathematics anxiety literature, discussing in turn the normative and psychometric evidence on maths anxiety, the effects of attitudes and gender, and the consequences of maths anxiety in terms of maths competence. The mathematical cognition area in terms of basic empirical effects, the importance of procedural knowl...

It has recently been demonstrated that highly math-anxious individuals may be less proficient on arithmetic tasks, particularly those that involve complex problems. The processing efficiency theory postulates that in highly anxious individuals, working memory resources are consumed by “worry,” thereby leaving fewer resources available for task comp...

A current theory of anxiety effects in cognition claims that anxiety disrupts normal processing within the working memory system. We examined this theory in the context of a reading task, for participants who were high or low in assessed mathematics anxiety. The task was designed to measure the ability to inhibit attention to distracting informatio...

A current theory of anxiety effects in cognition claims that anxiety disrupts normal processing within the working memory system. We examined this theory in the context of a reading task, for participants who were high or low in assessed mathematics anxiety. The task was designed to measure the ability to inhibit attention to distracting informatio...

Two experiments report on the relationship between level of mathematics anxiety and timed performance on simple and complex addition problems. In both experiments, subjects at differing levels of mathematics anxiety responded to one- and two-column addition problems in a verification task. Anxiety effects on the simple one-column addition problems...

We tabulated the frequency with which simple addition and multiplication facts occur in elementary school arithmetic texts for grades 1-6. The results indicated a strong "small-fact bias" in both addition and multiplication. "Large" facts, with operands larger than 5, occurred up to half as frequently as those with operands in the 2-5 range. As was...

We tabulated the frequency with which simple addition and multiplication facts occur in elementary school arithmetic texts for grades 1–6. The results indicated a strong “small-fact bias” in both addition and multiplication. “Large” facts, with operands larger than 5, occurred up to half as frequently as those with operands in the 2–5 range. As was...

Two exploratory studies were conducted to determine if mathematics anxiety, as assessed by the Mathematics Anxiety Rating Scale (MARS), is related to the underlying mental processes of arithmetic performance. MARS scores were higher when the test was administered by computer, vs. the standard paper-and-pencil format, and were higher for female than...

The article presents a first-person account of a transient anomia or word-finding deficit; the assumption is that such an account, reported by someone with a professional background in memory, cognition, and language processes, may shed additional light on the nature of an anomic episode and on the subjective experience of memory and language disru...

two complimentary topics are of special interest in the study of cognitive skills, first the involvement of working memory resources in successful performance, and second the role of automaticity in the component processes of such performance / [these issues] have only recently begun to receive direct investigation in the area of mental arithmetic...

In 2 experiments, younger and older adults were presented with simple multiplication problems (e.g., 4 x 7 = 28 and 5 x 3 = 10) for their timed, true or false judgments. All of the effects typically obtained in basic research on mental arithmetic were obtained, that is, reaction time (a) increased with the size of the problem, (b) was slowed for an...

In 2 experiments, younger and older adults were presented with simple multiplication problems (e.g., 4 X 7 = 28 and 5 X 3 = 10) for their timed, true or false judgments. All of the effects typically obtained in basic research on mental arithmetic were obtained, that is, reaction time (a) increased with the size of the problem, (b) was slowed for an...

The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of...

Children and adolescents with unilateral left- or right-hemisphere lesions were administered a standardized test of mathematics ability and a battery of experimental tests that examined the components of numerical and arithmetic processing. All lesioned groups showed at least marginally lower scores on the standardized test than the controls. More...

Many undergraduates harbor a variety of misbeliefs about physical objects in motion--for instance, that a bomb will fall straight down when dropped from a moving airplane. The evidence that these misbeliefs are resistant to correction by college-level physics courses, however, has often been based on methodologies that lack adequate internal validi...

Simple multiplication skills of subjects from third grade through college were studied. Data from Experiment 1 indicated that to solve simple multiplication problems, even third graders rely heavily on memory retrieval rather than on reconstructive procedures such as counting. Reaction time was predicted better by normative measures of problem diff...

This chapter is about children’s mental arithmetic, the knowledge that is acquired across the school years, the early representation of that knowledge in memory, and the evolution of the mental representation and processes across childhood. The largest portion of the chapter is devoted to a model of children’s knowledge and performance in a simple...

Widely usedmathematics textbooks from kindergarten, first, second, and third grades were evaluated both for the frequency and the order of presentation of the basic 100 addition facts 0 + 0 through 9 + 9. A striking result was that the frequency of occurrence distributions for the basic facts were markedly skewed. There were many fewer presentation...

Students in Grades 1, 4, 7, and 10 were timed as they solved simple and complex addition problems, then were presented similar problems in an untimed interview. A manipulation of confusion between addition and multiplication, in which multiplication answers were given to addition problems (3 + 4 = 12), revealed evidence for the hypothesized interre...

Baroody (1985) suggests repeatedly that rules and procedures can provide the answers to the basic number combinations in simple arithmetic. My research with older children and adults indicates they do not, at least in the general case. After correcting Baroody's description of my network retrieval model, I indicate five weaknesses in his argument....

Baroody (1985) suggests repeatedly that rules and procedures can provide the answers to the basic number combinations in simple arithmetic. My research with older children and adults indicates they do not, at least in the general case. After correcting Baroody's description of my network retrieval model, I indicate five weaknesses in his argument....

We respond to A. Baroody's comment (1984, Developmental Review, 4, 148–156) with an empirical comparison of the production and verification tasks. With the exception of performance at the first grade level, the two tasks yield essentially identical conclusions. The results of an adjunct task, in which the rate of mental counting was assessed, sugge...

Based on a review of reaction time studies, a model of mental arithmetic performance which emphasizes the process of fact retrieval from organized memory representations was proposed (M. H. Ashcraft, Developmental Review, 1982, 2, 213–236). In contrast to this view A. J. Baroody (Developmental Review, 1983, 3, 225–230) proposes that most mental ari...

Argues that comments by C. A. Bridgewater et al (see record 1982-26541-001) raise some troubling issues concerning the nature and purpose of tenure. It is contended that the problem of departments top-heavy with tenured faculty is not an argument against tenure per se, but against one of the consequences of tenure from the standpoint of college an...

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations; and...

The development of mental arithmetic is approached from a mathematical perspective, focusing on several process models of arithmetic performance which have grown out of the chronometric methods of cognitive psychology. These models, based on hypotheses about the nature of underlying mental operations and structures in arithmetic, generate quantitat...

Evaluated 40 undergraduates' performance on a simple mental multiplication task and the adequacy of several different models of mental addition as extended to multiplication. Exps I and II revealed that the performance of multiplication resembles simple mental addition, showing similar effects of problem size and of split (the numerical difference...

Research on mental arithmetic has suggested that young children use a counting algorithm for simple mental addition, but that adults use memory retrieval from an organized representation of addition facts. To determine the age at which performance shifts from counting to retrieval, children in grades 3, 4, and 6 were tested in a true/false verifica...

Three explanations of adults’ mental addition performance, a counting-based model, a direct-access model with a backup counting procedure, and a network retrieval model, were tested. Whereas important predictions of the two counting models were not upheld, reaction times (RTs) to simple addition problems were consistent with the network retrieval m...

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a transitional age...

Two experiments, each with 12 undergraduates, examined simple addition processes in which single integer problems were presented for true–false verification. The stated sums of the false problems were incorrect by a reasonable (X 1 or 2) or unreasonable (X 4 or 5) amount from the correct sums. The reaction time (RT) to unreasonable wrong problems w...

A description is presented of normative data for property responses to 121 words—17 category labels, three typical and three atypical members of each category, and the words “plant” and “animal.” The production frequency of properties is considered a measure of property dominance or semantic relatedness, and has been validated for the present data...

Reaction time to verify property statements was examined in the context of two semantic distance factors—typicality of the category member in the subject of the statement, and dominance of the category member's property in the predicate. Reaction times were slower for statements with low dominant properties and for statements with atypical category...

Retrieval from semantic memory was examined by means of reaction times to property statements (e.g., sparrow has beak). The variables of interest were normatively defined property dominance (frequency), type of priming between related sentences (sparrow-sparrow vs. sparrow-robin), and separation or lag between related sentences. Statements assertin...

This research was concerned with retrieval processes which underlie conceptual clustering. In a free recall task with categorized lists, fifth graders' and adults' retrieval was examined temporally by means of interword response times. List organization and retrieval cue factors were manipulated in order to assess the developmental relevance of an...

The relationships between rehearsal and subsequent retrieval characteristics were examined in the context of free recall of categorized lists. The results indicated a direct correspondence between the frequency of rehearsal and the order and speed of retrieval within categories. The same relationship obtained for the categories themselves. It was s...

Studied the flow of information from input through output in a free-recall task by means of S-paced presentation times, externalized rehearsal, and interword response times. In this context, storage and retrieval of categorized material were examined for 40 10-yr-old normal and 40 16-yr-old mentally retarded children of the same mental age. As indi...

The major purpose of the present research was to examine the temporal characteristics of storage and retrieval while manipulating variables related to the organization of free recall. In this context, two experiments evaluated the effects of a retrieval plan and degree of list organization. The provision of a specific retrieval plan led to a decrea...

discuss the notion of strategies as it applies to research on mental arithmetic performance a review of this research, and the accompanying theories, is presented in order to highlight the various strategies of arithmetic that have been investigated discuss some difficulties in extending current work to older children and adults, then offer thr...