Older and younger adults' strategies in approximate quantification

Numerosity comparison, cognitive strategies, and general cognitive functioning in older people

Introduction

Studies have shown age-related differences in numerical cognition, for example, in the level of numerosity comparison ability. Moreover, some studies point out individual differences in the cognitive strategies employed during the performance of numerosity comparison tasks and reveal that they are related to the aging process. One probable cause of these differences is the level of cognitive functioning. The aim of our study was to determine the relationships among numerosity comparison ability, the cognitive strategies utilized in the performance of numerosity comparison tasks and the general cognitive functioning in older people.

Methods

Forty-seven elderly people participated in the study. The participants were examined using overall cognitive functioning scales and computerized numerosity comparison task.

Results

The results showed many correlations between the participants' level of cognitive functioning and the percent of correct responses (PCR) and response time (RT) during numerosity comparison, as well as with the cognitive strategies applied by the participants. Task correctness was positively related to the level of performance in the attention and executive function tasks. In contrast, the long-term memory resources index and visuospatial skills level were negatively correlated with RT regarding numerosity comparison task performance. The level of long-term memory resources was also positively associated with the frequency of use of more complex cognitive strategies. Series of regression analyses showed that both the level of general cognitive functioning and the cognitive strategies employed by participants in numerosity comparison can explain 9-21 percent of the variance in the obtained results.

Discussion

In summary, these results showed significant relationships between the level of cognitive functioning and proficiency in numerosity comparison measured in older people. Moreover, it has been shown that cognitive resources level is related to the strategies utilized by older people, which indicates the potential application for cognitive strategy examinations in the development of new diagnostic tools.

EXPRESS: How negative emotions affect young and older adults' numerosity estimation performance

In this study, we investigated the influence of negative emotions on numerosity estimation and whether this influence changes with aging during adulthood. Young and older adults were asked to estimate and compare the numerosity of collections of elements (cars or dots) with a two-digit number. Collections of elements were preceded by emotionally neutral (e.g., mushrooms) or emotionally negative (e.g., a corpse) pictures. Stimuli were easier (i.e., small-ratio) or harder (i.e., large-ratio) items. Young and older participants obtained similar numerosity estimation performance. Interestingly, participants were less accurate under negative emotions than under neutral emotions when they estimated numerosity of collections of abstract elements (i.e., dots). In contrast, participants improved their performance under negative emotions while estimating collections of non-abstract, daily-life elements (i.e., cars). These findings have important implications for furthering our understanding of the role of negative emotions in numerosity estimation and age-related differences therein.

Extrafoveal Processing in Categorical Search for Geometric Shapes: General Tendencies and Individual Variations

The paper addresses the capabilities and limitations of extrafoveal processing during a categorical visual search. Previous research has established that a target could be identified from the very first or without any saccade, suggesting that extrafoveal perception is necessarily involved. However, the limits in complexity defining the processed information are still not clear. We performed four experiments with a gradual increase of stimuli complexity to determine the role of extrafoveal processing in searching for the categorically defined geometric shape. The series of experiments demonstrated a significant role of extrafoveal processing while searching for simple two-dimensional shapes and its gradual decrease in a condition with more complicated three-dimensional shapes. The factors of objects' spatial orientation and distractor homogeneity significantly influenced both reaction time and the number of saccades required to identify a categorically defined target. An analysis of the individual p-value distributions revealed pronounced individual differences in using extrafoveal analysis and allowed examination of the performance of each particular participant. The condition with the forced prohibition of eye movements enabled us to investigate the efficacy of covert attention in the condition with complicated shapes. Our results indicate that both foveal and extrafoveal processing are simultaneously involved during a categorical search, and the specificity of their interaction is determined by the spatial orientation of objects, type of distractors, the prohibition to use overt attention, and individual characteristics of the participants.

Consumer Decision-Making Creativity and Its Relation to Exploitation-Exploration Activities: Eye-Tracking Approach

Modern consumers face a dramatic rise in web-based technological advancements and have trouble making rational and proper decisions when they shop online. When they try to make decisions about products and services, they also feel pressured against time when sorting among all of the unnecessary items in the flood of information available on the web. In this sense, they need to use consumer decision-making creativity (CDMC) to make rational decisions. However, unexplored research questions on this subject remain. First, in what ways do task difficulty and time constraints affect visual attention on exploitative and exploratory activities differently? Second, how does the location of the reference (i.e., hints) influence the level of visual attention to exploitative and exploratory activities depending on affordance theory? Third, how do exploratory and exploitative activities affect CDMC? Eye-tracking experiments were conducted with 70 participants to obtain relevant metrics such as total fixation duration (TFD), fixation count (FC), and visit count (VC) to answer these research questions. Our findings suggest that task difficulty influences exploitative activity, whereas time constraint is related to the exploratory activity. The result of the location of hints aligns with the affordance theory for the exploitative activity. Besides, exploratory activity positively affected CDMC, but exploitative activity did not show any effect.

Examining aging and numerosity using an integrated diffusion model

Two experiments are presented that use tasks common in research in numerical cognition with young adults and older adults as subjects. In these tasks, one or two arrays of dots are displayed, and subjects decide whether there are more or fewer dots of one kind than another. Results show that older adults, relative to young adults, tend to rely more on the perceptual feature, area, in making numerosity judgments when area is correlated with numerosity. Also, convex hull unexpectedly shows different effects depending on the task (being either correlated with numerosity or anticorrelated). Accuracy and response time (RT) data are interpreted with the integration of the diffusion decision model with models for the representation of numerosity. One model assumes that the representation of the difference depends on the difference between the numerosities and that standard deviations (SDs) increase linearly with numerosity, and the other model assumes a log representation with constant SDs. The representational models have coefficients that are applied to differences between two numerosities to produce drift rates and SDs in drift rates in the decision process. The two tasks produce qualitatively different patterns of RTs: One model fits results from one task, but the results are mixed for the other task. The effects of age on model parameters show a modest decrease in evidence driving the decision process, an increase in the duration of processes outside the decision process (nondecision time), and an increase in the amount of evidence needed to make a decision (boundary separation). (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Alzheimer's disease disrupts domain-specific and domain-general processes in numerosity estimation

INTRODUCTION

This study investigated how Alzheimer's Disease (AD) affects numerosity estimation abilities (e.g., finding the approximate number of items in a collection).

METHOD

Across two experiments, performance from HOA (i.e., Healthy Older Adults; N = 48) and AD patients (N = 50) was compared on dot comparison tasks. Participants were presented with two dot arrays and had to select the more numerous dot array in comparison tasks. They also took a Simon task and a number-line tasks (i.e., number-line tasks in which they had to indicate the position of a number on a line 0 to 100 or on a line 0 to 1,000 in the number-line task).

RESULTS

In Experiment 1, (a) AD patients obtained significantly poorer performance while comparing collections of dots, especially harder (small-ratio) collections, (b) these deficits correlated with poorer performance on the number-line task for larger numerosities (i.e., 0 to 1,000), and (c) AD patients showed poorer performance on incongruent (where numerosity and area occupied by dots mismatched) than on congruent items (where both features matched), while HOA showed no congruency effects. Experiment 2 showed (a) congruency effects in both groups when convex hull was tested as an incongruent feature, and (b) comparable sequential modulations of congruency effects in both groups.

CONCLUSIONS

Our findings showed that numerosity abilities decline in AD patients, and that this decline results from impaired domain-specific processes (i.e., numerosity processing) and domain-general processes (i.e., inhibition). These findings have important implications to further our understanding of how specific and general cognitive processes contribute to numerosity estimation/comparison performance, and how such contributions change during Alzheimer's disease.

Damage to the Intraparietal Sulcus Impairs Magnitude Representations of Results of Complex Arithmetic Problems

Past research investigating the role of the intraparietal sulcus (IPS) in numerical processes focused mainly on quantity and numerical comparisons as well on single digit arithmetic. The present study investigates the involvement of the IPS in estimating the results of multi-digit multiplication problems. For this purpose, the performance a 24-year-old female (JD) with brain damage in the left IPS was compared to an age-matched control group in the computation estimation task. When required to estimate whether the results of multi-digit multiplication problems are smaller or larger than given reference numbers, JD, in contrast to controls, did not show the common patterns of distance and size effects. Her strategy use was also atypical. Most control participants used both the approximated calculation strategy that involves rounding and calculation procedures and the sense of magnitude strategy that relies on an intuitive approximated magnitude representation of the results. In contrast, JD used only the former but not the latter strategy. Together, these findings suggest that the damage to the IPS impaired JD's representations of magnitude that play an important role in this computation estimation task.

Probing the mechanisms underlying numerosity-to-numeral mappings and their relation to math competence

Numerosity estimation performance (e.g., how accurate, consistent, or proportionally spaced (linear) numerosity-numeral mappings are) has previously been associated with math competence. However, the specific mechanisms that underlie such a relation is unknown. One possible mechanism is the mapping process between numerical sets and symbolic numbers (e.g., Arabic numerals). The current study examined two hypothesized mechanisms of numerosity-numeral mappings (item-based "associative" and holistic "structural" mapping) and their roles in the estimation-and-math relation. Specifically, mappings for small numbers (e.g., 1-10) are thought to be associative and resistant to calibration (e.g., feedback on accuracy of estimates), whereas holistic "structural" mapping for larger numbers (e.g., beyond 10) may be supported by flexibly aligning a numeral "response grid" (akin to a ruler) to an analog "mental number line" upon calibration. In 57 adults, we used pre- and post-calibration estimates to measure the range of continuous associative mappings among small numbers (e.g., a base range of associative mappings from 1 to 10), and obtained measures of math competence and delayed multiple-choice strategy reports. Consistent with previous research, uncalibrated estimation performance correlated with calculation competence, controlling for reading fluency and working memory. However, having a higher base range of associative mappings was not related to estimation performance or any math competence measures. Critically, discontinuity in calibration effects was typical at the individual level, which calls into question the nature of "holistic structural mapping". A parsimonious explanation to integrate previous and current findings is that estimation performance is likely optimized by dynamically constructing numerosity-numeral mappings through the use of multiple strategies from trial to trial.

Malleability of mappings between Arabic numerals and approximate quantities: Factors underlying individual differences and the relation to math

Humans tend to be inaccurate and inconsistent when estimating a large number of objects. Furthermore, we modify our estimates when feedback or a reference array is provided, indicating that the mappings between perceived numerosity and their corresponding numerals are largely malleable in response to calibration. However, there is great variability in response to calibration across individuals. Using uncalibrated and calibrated numerosity estimation conditions, the current study explored the factors underlying individual differences in the extent and nature of the malleability of numerosity estimation performance as a result of calibration in a sample of 71 undergraduate students. We found that individual differences in performance were reliable across conditions, and participants' responses to calibration varied greatly. Participants who were less consistent or had more proportionally spaced (i.e., linear) estimates before calibration tended to shift the distributions of their estimates to a greater extent. Higher calculation competence also predicted an increase in how linear participants' estimates were after calibration. Moreover, the effect of calibration was not continuous across numerosities within participants. This suggests that the mechanisms underlying numeral-numerosity mappings may be less systematic than previously thought and likely depend on cognitive mechanisms beyond representation of numerosities. Taken together, the mappings between numerosities and numerical symbols may not be stable and direct, but transient and mediated by task-related (e.g., strategic) mechanisms. Rather than estimation skills being foundational for math competence, math competence may also influence estimation skills. Therefore, numerosity estimation tasks are not a pure measure of number representations.

Aging and Sequential Strategy Interference: A Magnetoencephalography Study in Arithmetic Problem Solving

This study investigated age-related changes in the neural bases of sequential strategy interference. Sequential strategy interference refers to decreased strategy interference (i.e., poorer performance when the cued strategy is not the best) after executing a poorer strategy relative to after a better strategy. Young and older adults performed a computational estimation task (e.g., providing approximate products to two-digit multiplication problems, like 38 × 74) and were matched on behavioral sequential strategy interference effects. Analyses of magnetoencephalography (MEG) data revealed differences between young and older adults in brain activities underlying sequential strategy interference. More specifically, relative to young adults, older adults showed additional recruitments in frontal, temporal, and parietal regions. Also, age-related differences were found in the temporal dynamics of brain activations, with modulations occurring both earlier and later in older than young adults. These results suggest that highly functioning older adults rely on additional mechanisms to process sequential strategy interference as efficiently as young adults. Our findings inform mechanisms by which highly functioning older adults obtain as good performance as young adults, and suggest that these older adults may compensate deleterious effects of aging to efficiently execute arithmetic strategies.

Eye-movement patterns during nonsymbolic and symbolic numerical magnitude comparison and their relation to math calculation skills

A growing body of research suggests that the processing of nonsymbolic (e.g. sets of dots) and symbolic (e.g. Arabic digits) numerical magnitudes serves as a foundation for the development of math competence. Performance on magnitude comparison tasks is thought to reflect the precision of a shared cognitive representation, as evidence by the presence of a numerical ratio effect for both formats. However, little is known regarding how visuo-perceptual processes are related to the numerical ratio effect, whether they are shared across numerical formats, and whether they relate to math competence independently of performance outcomes. The present study investigates these questions in a sample of typically developing adults. Our results reveal a pattern of associations between eye-movement measures, but not their ratio effects, across formats. This suggests that ratio-specific visuo-perceptual processing during magnitude processing is different across nonsymbolic and symbolic formats. Furthermore, eye movements are related to math performance only during symbolic comparison, supporting a growing body of literature suggesting symbolic number processing is more strongly related to math outcomes than nonsymbolic magnitude processing. Finally, eye-movement patterns, specifically fixation dwell time, continue to be negatively related to math performance after controlling for task performance (i.e. error rate and reaction time) and domain general cognitive abilities (IQ), suggesting that fluent visual processing of Arabic digits plays a unique and important role in linking symbolic number processing to formal math abilities.

A Systematic Investigation of Accuracy and Response Time Based Measures Used to Index ANS Acuity

The approximate number system (ANS) was proposed to be a building block for later mathematical abilities. Several measures have been used interchangeably to assess ANS acuity. Some of these measures were based on accuracy data, whereas others relied on response time (RT) data or combined accuracy and RT data. Previous studies challenged the view that all these measures can be used interchangeably, because low correlations between some of the measures had been observed. These low correlations might be due to poor reliability of some of the measures, since the majority of these measures are mathematically related. Here we systematically investigated the relationship between common ANS measures while avoiding the potential confound of poor reliability. Our first experiment revealed high correlations between all accuracy based measures supporting the assumption that all of them can be used interchangeably. In contrast, not all RT based measures were highly correlated. Additionally, our results revealed a speed-accuracy trade-off. Thus, accuracy and RT based measures provided conflicting conclusions regarding ANS acuity. Therefore, we investigated in two further experiments which type of measure (accuracy or RT) is more informative about the underlying ANS acuity, depending on participants’ preferences for accuracy or speed. To this end, we manipulated participants’ preferences for accuracy or speed both explicitly using different task instructions and implicitly varying presentation duration. Accuracy based measures were more informative about the underlying ANS acuity than RT based measures. Moreover, the influence of the underlying representations on accuracy data was more pronounced when participants preferred accuracy over speed after the accuracy instruction as well as for long or unlimited presentation durations. Implications regarding the diffusion model as a theoretical framework of dot comparison as well as regarding the relationship between ANS acuity and math performance are discussed.

Sensori-motor strategic variations and sequential effects in young and older adults performing a Fitts' task

The present study aimed at investigating age-related changes in strategic variations and sequential effects in discrete Fitts' aiming task. Three sequential effects were investigated, namely trial sequential difficulty effects (TSDE), strategy sequential difficulty effects (SSDE), and strategy repetition effects (SRE). After generalizing previously observed aging effects on strategic variations, our results showed that movement times were longer when performed after harder ID level than when following easier ID level (TSDE). We also observed SSDE, such that is movement times were longer when participants executed a strategy of intermediate difficulty (i.e., the progressive-deceleration strategy) after having used a more difficult strategy (i.e., the undershoot strategy) on the previous trial than after an easier strategy (i.e., the one-shot strategy). These sequential difficulty effects related to both difficulty and strategy were similar in young and older adults. In addition, we found that across two successive trials, participants tended to repeat the one-shot strategy the most often and the undershoot strategy the least often, with repetition rates of the progressive-deceleration strategy being in-between (SRE). Finally, age-related differences in strategy repetition effects varied with strategies (e.g., they were largest for the one-shot strategy). These findings have important implications for deciphering processes responsible for sequential effects in sensori-motor tasks as well as in cognitive tasks in general, and for our understanding of processes underlying sensori-motor performance in young and older adults.

Aging and the number sense: preserved basic non-symbolic numerical processing and enhanced basic symbolic processing

Aging often leads to general cognitive decline in domains such as memory and attention. The effect of aging on numerical cognition, particularly on foundational numerical skills known as the number sense, is not well-known. Early research focused on the effect of aging on arithmetic. Recent studies have begun to investigate the impact of healthy aging on basic numerical skills, but focused on non-symbolic quantity discrimination alone. Moreover, contradictory findings have emerged. The current study aimed to further investigate the impact of aging on basic non-symbolic and symbolic numerical skills. A group of 25 younger (18-25) and 25 older adults (60-77) participated in non-symbolic and symbolic numerical comparison tasks. Mathematical and spelling abilities were also measured. Results showed that aging had no effect on foundational non-symbolic numerical skills, as both groups performed similarly [RTs, accuracy and Weber fractions (w)]. All participants showed decreased non-symbolic acuity (accuracy and w) in trials requiring inhibition. However, aging appears to be associated with a greater decline in discrimination speed in such trials. Furthermore, aging seems to have a positive impact on mathematical ability and basic symbolic numerical processing, as older participants attained significantly higher mathematical achievement scores, and performed significantly better on the symbolic comparison task than younger participants. The findings suggest that aging and its lifetime exposure to numbers may lead to better mathematical achievement and stronger basic symbolic numerical skills. Our results further support the observation that basic non-symbolic numerical skills are resilient to aging, but that aging may exacerbate poorer performance on trials requiring inhibitory processes. These findings lend further support to the notion that preserved basic numerical skills in aging may reflect the preservation of an innate, primitive, and embedded number sense.

Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement

A central question in cognitive and educational neuroscience is whether brain operations supporting nonlinguistic intuitive number sense (numerosity) predict individual acquisition and academic achievement for symbolic or "formal" math knowledge. Here, we conducted a developmental functional magnetic resonance imaging (MRI) study of nonsymbolic numerosity task performance in 44 participants including 14 school age children (6-12 years old), 14 adolescents (13-17 years old), and 16 adults and compared a brain activity measure of numerosity precision to scores from the Woodcock-Johnson III Broad Math index of math academic achievement. Accuracy and reaction time from the numerosity task did not reliably predict formal math achievement. We found a significant positive developmental trend for improved numerosity precision in the parietal cortex and intraparietal sulcus specifically. Controlling for age and overall cognitive ability, we found a reliable positive relationship between individual math achievement scores and parietal lobe activity only in children. In addition, children showed robust positive relationships between math achievement and numerosity precision within ventral stream processing areas bilaterally. The pattern of results suggests a dynamic developmental trajectory for visual discrimination strategies that predict the acquisition of formal math knowledge. In adults, the efficiency of visual discrimination marked by numerosity acuity in ventral occipital-temporal cortex and hippocampus differentiated individuals with better or worse formal math achievement, respectively. Overall, these results suggest that two different brain systems for nonsymbolic numerosity acuity may contribute to individual differences in math achievement and that the contribution of these systems differs across development.

The role of feedback and dot presentation format in younger and older adults' number estimation

Numerosity estimation, the rapid assessment of the number of items in a visual scene, is historically inaccurate. We assessed whether providing feedback regarding the correct numerosity on either 0%, 50%, or 100% of the trials would affect younger and older adults' estimation accuracy for randomized, clustered (i.e., groups of 3 or 7 dots), and stacked (i.e., column) dot formats. Participants provided estimates and confidence ratings in six blocks, each containing 48 trials (16 numerosities shown in each format). Feedback frequency was manipulated between participants during blocks 1-4; no feedback was provided during blocks 5 and 6, which contained old and new numerosities and previously estimated presentations rotated 90°. Estimation accuracy was age equivalent across blocks despite younger adults initially being more accurate than older adults. Feedback improved both age groups' accuracy. Stacked presentations were most accurately estimated but were more likely to be over-estimated than clustered and randomized presentations. Older adults gave lower confidence ratings than younger adults despite both age groups showing increased confidence across blocks, for more structured presentation formats, and as feedback frequency increased. These results expand our understanding of the role of presentation format and feedback in producing age equivalence or age-related differences in numerosity estimation.

Underestimating numerosity of items in visual search tasks

Previous research on numerosity judgments addressed attended items, while the present research addresses underestimation for unattended items in visual search tasks. One potential cause of underestimation for unattended items is that estimates of quantity may depend on viewing a large portion of the display within foveal vision. Another theory follows from the occupancy model: estimating quantity of items in greater proximity to one another increases the likelihood of an underestimation error. Three experimental manipulations addressed aspects of underestimation for unattended items: the size of the distracters, the distance of the target from fixation, and whether items were clustered together. Results suggested that the underestimation effect for unattended items was best explained within a Gestalt grouping framework.

Cognitive Strategy Variations During Aging

The last two decades of research in cognitive aging have seen a shift from simply describing age-related changes in cognitive performance to determining the mechanisms underlying these changes. Recent findings on variations in the use of cognitive strategies during aging further our understanding of how these changes in performance occur during adulthood. Data show age-related differences in strategy repertoire, strategy distribution, strategy execution, and strategy selection. I illustrate these findings in cognitive domains as varied as episodic memory, working memory, reasoning, decision making, problem solving, and language. I discuss how strategic variations are best studied both conceptually and methodologically and how investigating strategic variations helps us make significant progress in the study of cognitive aging. As I also show in this article, whichever the cognitive domain being studied, there are no restrictions that would prevent us from adopting a strategy perspective.

Neural correlates of approximate quantification strategies in young and older adults: an fMRI study

Young and older adults assessed the approximate number of dots in collections including between 20 and 50 dots, with two strategies. The benchmark strategy is based on retrieving memory representations of quantities after visually scanning stimulus. The anchoring strategy involves both enumeration and estimation processes. Brain activations and performance were analyzed as a function of strategies, size of collections and age. Executing the benchmark strategy produced faster performance. It was associated with increased activity of a bilateral parieto/occipital and insular cortical network, including the postcentral gyrus, the cuneus, the middle occipital gyrus, and the insula. In addition to these bilateral activations, the benchmark strategy activated right prefrontal area. The anchoring strategy activated right superior parietal lobule, bilateral subcortical structures (putamen), and left dorso-lateral prefrontal cortex. The effects of aging on these cortical networks depended on strategies. These results suggest dissociation between two numerosity estimation strategies underlying different cognitive estimation processes and help to clarify age differences in numerosity estimation.