Approximate quantification in young, healthy older adults’, and Alzheimer patients

https://doi.org/10.1016/j.bandc.2008.12.004Get rights and content

Abstract

Forty young adults, 40 healthy older adults, and 39 probable AD patients were asked to estimate small (e.g., 25) and large (e.g., 60) collections of dots in a choice condition and in two no-choice conditions. Participants could choose between benchmark and anchoring strategies on each collection of dots in the choice condition and were required to use either benchmark or anchoring on all configurations in the no-choice conditions (one per strategy). The benchmark strategy involves visual estimation processes whereas the anchoring strategy involves both enumeration and estimation processes. Results showed that strategy use was influenced by collection, participant, and strategy characteristics. Age-related and dementia-related differences were found in both strategy use and strategy execution. The findings have implications for our understanding of aging effects in approximate quantification, strategic variations in Alzheimer’s patients, and sources of cognitive decline during early stages of Alzheimer’s disease.

Introduction

The present study investigated how young, healthy older adults, and individuals diagnosed with probable Alzheimer’s disease (AD) process approximate quantification tasks. Approximate quantification refers to our ability to provide a quick and rough estimate of a magnitude. Addressing this issue is important for different reasons. First, everyday, we are bombarded by a lot of numerical information. Due to environmental constraints (e.g., time pressure), we often process this numerical information in an approximate manner. For instance, in a supermarket, to choose the checkout where we shall wait for, we generally approximate the number of persons waiting for each checkout and choose the one with the fewest persons. Similar processes are involved when we want to determine if the available place to park our car is sufficiently large or if the quantity of food in our plate is reasonable. So, approximate quantification is a pervasive and central ability for understanding our social and physical environment, and adapting to it.

Second, recent brain-imaging studies have revealed that quantity-related processes crucially activate the temporo-parietal lobe (e.g., Ansari et al., 2006, Gandini et al., 2008, Piazza et al., 2004, Piazza et al., 2006). Interestingly, AD patients suffer from early lesions of temporal and parietal regions (e.g., Chétélat et al., 2003, Hirao et al., 2005). As no previous studies documented AD patients’ performance in approximate quantification, we do not know whether such lesions lead to disrupted performance in AD patients. Also, given the few studies on effects of normal cognitive aging on approximate quantification skills, the present study aimed at further our understanding of how normal aging changes approximate quantification performance. We begin by reviewing relevant findings in aging and approximate quantification and then, before outlining the logic of the present project, we review previous findings on AD and numerical processes.

Few studies investigated the effect of age on approximate quantification skills. Most of these tested only small numerosities (i.e., less than 10 elements) and showed that counting (i.e., ability to enumerate more than four items) is unaffected by normal aging whereas subitizing speed (i.e., ability to quickly enumerate 1–4 items) decreases with increasing age (Geary and Lin, 1998, Kotary and Hoyer, 1995, Nebes et al., 1992, Sliwinski, 1997, Trick et al., 1996, Watson et al., 2005, Watson et al., 2002). Nevertheless, recent studies showed that two types of factors crucially influence participants’ performance in approximate quantification. These are the semantic features of stimuli (i.e., the size of collections) and participants’ strategies.

First, several studies have shown that participants’ estimates are a direct power function of the number of items presented. Indeed, estimates are reliably predicted with a power function of actual numerosity of the form E = kNb, where E is the estimated numerosity, N is the correct numerosity, b is the power-function exponent, and k is a constant (e.g., Krueger, 1982). With regards to aging, Lemaire and Lecacheur (2007) have shown that young and older individuals’ estimates were well predicted with a power function of actual numerosity. Both groups had comparable power function exponents. Mean exponents were 0.90 and 0.93, in young and older adults, respectively, meaning that the two age groups tended to underestimate numerosities. Moreover, comparable exponents of power functions in young and older adults suggest that memory representations for large numerosities remain stable with age.

The second important findings from previous research on approximate quantification concern the strategies that participants use. Indeed, several recent studies showed that, when participants have to find how many items there are approximately in a collection, they use several strategies (e.g., Crites, 1992, Gandini et al., 2008, Luwel et al., 2005, Luwel et al., 2003a, Luwel et al., 2003b, Siegel et al., 1982). For example, Gandini, Lemaire, and Dufau (2008) showed that both young and healthy older adults used the same set of six different strategies, but varied in how well they executed each strategy (resulting in poorer performance in older adults compared to younger ones), how often they used each strategy, and how the type of collections influenced their strategy use. More precisely, this study emphasized the existence of the benchmark strategy, which involved visual estimation processes, and the anchoring strategy, which involved both enumeration and estimation processes. These are the focus of the present work, as the authors found that both young and older adults use these two strategies spontaneously.

In sum, previous studies of aging suggest that, to understand how approximate quantification performance changes with age and during Alzheimer’s disease, it is important to vary the size of collections that participants have to quantify and to investigate strategic aspects of their performance, which is what we did in the present study. Indeed, investigating strategic aspects of a cognitive task appears crucial to adequately and precisely describe effects of age on performance. It helps not only to determine patterns of preserved/impaired performance, but also to provide a better mechanistic account (in terms of underlying processes) of these patterns of performance.

A number of studies have tested the effects of AD on numerical processes. The main reason is that numerical impairment is an early sign of dementia (Deloche et al., 1995, Grafman et al., 1989, Mantovan et al., 1999, Marterer et al., 1996, Parlato et al., 1992, Pesenti et al., 1994) and may represent a reliable hallmark for the diagnosis of AD (Carlomagno et al., 1999, Deloche et al., 1995, Kaufmann et al., 2002, Mantovan et al., 1999, Marterer et al., 1996, Rosselli et al., 1998). Several previous findings are relevant for our project. These concern the effects of AD on enumeration ability.

Several authors have found differences between normal and abnormal aging on visual enumeration. Most of the studies tested only small numerosities (i.e., less than 10 elements). For instance, Kaufmann and colleagues (Kaufmann et al., 2002) compared AD patients and controls in calculation, enumerating 1–9 dots, and number comparison tasks. Results showed that calculation processes were impaired, while processes such as number comparison and subitizing were not affected in AD. However, for the counting dot task, the group difference was approximately twice as great for larger numbers as for small numbers, which is consistent with generalized slowing (e.g., Watson et al., 2002, Watson et al., 2005). Thus, the results of Kaufmann et al.’s study indicated that there may be qualitative differences between enumeration performance in normal and abnormal aging, which is what Maylor et al. (Maylor, Watson, & Muller, 2005) have shown. These authors investigated enumeration ability on probable AD patients and in age-matched controls. Results showed that counting rate was significantly slower (451 vs. 349 ms/items), and especially subitizing span was significantly reduced in AD patients compared to controls (2.3 vs. 3.5 items). Above and beyond the results concerning the effects of abnormal aging on enumeration ability, this pattern of performance also suggests a specific AD patients’ difficulty to process visual information. Indeed, the most comprehensive explanation proposed to account for subitization is the FINST theory (Trick and Pylyshyn, 1993, Trick and Pylyshyn, 1994). This proposes that the visual system is able to selectively tag up to about four items that are individuated at a preattentive level of processing. Thus, any reduction in the number of FINSTs would be expected to have an impact on the efficiency of visual functioning in everyday tasks beyond those related to enumeration. It is therefore predicted that AD patients should be similarly impaired in other tasks where visual indexing is crucial, such as our approximate quantification task. As no prior study documented effects of AD on participants’ performance in approximate quantification tasks involving relatively large numerosities, we compared AD patients and healthy older adults while they had to find estimates of collections of 20–65 dots briefly presented on a computer screen.

Forty healthy young adults, 40 healthy older adults, and 39 probable AD patients were asked to estimate 51 collections of dots once in a choice-condition and twice in two no-choice conditions. Participants could choose between benchmark (consisting in retrieving a numerical representation in long-term memory) and anchoring strategies (consisting in counting a first group of dots, and then estimating the remaining dots based on the first counting). Participants had to choose between these two strategies in the choice condition but were required to use benchmark on all configurations in the first no-choice condition, and anchoring in the second one. Based on previous studies of approximate quantification, we tested two types of collections according to their size. Half of the collections were small (i.e., including 20–39 dots) and half were large collections (i.e., with 40–65 dots).

Mean percentages of use of benchmark enabled us to compare strategy use in each of the three groups under the choice condition. In particular, it was of interest to determine whether AD patients had degraded memory representations of numerosities and used mostly anchoring strategy and whether the other two groups would use both benchmark and anchoring strategies. Performance with benchmark and anchoring strategies under the no-choice conditions enabled us to investigate group differences in strategy execution. Regarding performance, we expected to replicate Gandini, Lemaire, and Dufau (2008) findings. That is, participants’ performance should vary with their strategy (i.e., the benchmark strategy should be faster, though less accurate, than the anchoring strategy), with their age (young adults should have better performance than older adults), with problem characteristics (performance should be better with small than with large collections, especially for the anchoring strategy), and interactions among these factors. If AD exacerbates aging effects, even poorer performance was expected in probable AD patients. Furthermore, if as suggested by previous results on arithmetic performance (Allen et al., 2005, Arnaud et al., 2008, Duverne et al., 2003) that AD does not affect strategy selection, we expected to find systematic strategy choices in all three groups as a function of either configuration or strategy characteristics. If group differences on strategy execution and no group differences on strategy use were found, then this would suggest that normal and abnormal aging were characterized by only quantitative changes (i.e., the same approximate quantification processes are used by the three groups, but these processes are executed more poorly in healthy older adults and in probable AD patients). However, if group differences in both strategy execution and strategy use were found, then this would suggest that changes during (normal and/or abnormal) aging were accompanied by quantitative and qualitative modifications.

Section snippets

Participants

Three groups of participants were selected according to their age and their health-status: Forty healthy younger adults (26 women; mean age: 23; age range: 17–30), 40 healthy older adults (22 women; mean age: 74; age range: 60–85), and 39 individuals diagnosed with probable Alzheimer’s disease (27 women; mean age: 77; age range: 60–87).

Healthy controls were recruited in the community. Participants were all screened for global cognitive functioning using the Mini Mental State Examination (MMSE;

Group differences in strategy use

Analyses of strategy use aimed at determining whether individuals accomplish the approximate quantification task with only one strategy or with both strategies and at comparing strategy use in each group on small and large collections. This section analyzes strategy use in the choice condition.

As can be seen in Table 1, in each group, some participants used only one strategy whereas others used both the benchmark and anchoring strategies. For example, the number of single-strategy users (i.e.,

General discussion

This study documented group differences in approximate quantification. A strategy perspective enabled us to not only compare young adults, older adults, and probable AD patients’ performance, but to also examine how participants found approximate numerosities of collections of dots. It replicated previous findings regarding normal aging and documented group differences in strategic aspects unknown before. Two sets of interesting findings, each concerning strategy use and strategy execution,

References (58)

  • M.C. Mantovan et al.

    The breakdown of calculation procedures in Alzheimer’s disease

    Cortex

    (1999)
  • A. Marterer et al.

    Calculation abilities in dementia of Alzheimer’s type and in vascular dementia

    Archives of Gerontology and Geriatrics

    (1996)
  • M. Pesenti et al.

    Selective impairment as evidence for mental organisation of arithmetical facts: BB, a case of preserved subtraction?

    Cortex

    (1994)
  • M. Piazza et al.

    Tuning curves for approximate numerosity in the human intraparietal sulcus

    Neuron

    (2004)
  • M. Piazza et al.

    Exact and approximate judgements of visual and auditory numerosity: An fMRI study

    Brain Research

    (2006)
  • P.A. Allen et al.

    Influence of probable Alzheimer’s disease on multiplication verification and production

    Aging, Neuropsychology, and Cognition

    (2005)
  • A.D. Baddeley et al.

    The decline of working memory in Alzheimer’s disease: A longitudinal study

    Brain

    (1991)
  • A.D. Baddeley et al.

    Dementia and working memory

    Quarterly Journal of Experimental Psychology

    (1986)
  • S. Carlomagno et al.

    Dyscalculia in the early stages of Alzheimer’s disease

    Acta Neurologica Scandinavica

    (1999)
  • G. Chétélat et al.

    Mild cognitive impairment: Can FDG-PET predict who is to rapidly convert to Alzheimer’s disease?

    Neurology

    (2003)
  • F. Collette et al.

    Working memory deficits in Alzheimer’s disease

    Brain and Cognition

    (1998)
  • T. Crites

    Skilled and less skilled estimators’ strategies for estimating discrete quantities

    The Elementary School Journal

    (1992)
  • G.R. Deloche et al.

    Calculation and number processing in mild Alzheimer’s disease

    Journal of Clinical and Experimental Neuropsychology

    (1995)
  • J. Dunlosky et al.

    Aging and deficits in associative memory: What is the role of strategy production?

    Psychology and Aging

    (1998)
  • J. Dunlosky et al.

    Measuring strategy production during associative learning: The relative utility of concurrent versus retrospective reports

    Memory & Cognition

    (2001)
  • R. El Yagoubi et al.

    Effects of aging on arithmetic problem-solving: An event-related brain potential study

    Journal of Cognitive Neuroscience

    (2005)
  • D.C. Geary et al.

    Simple and complex mental subtraction: Strategy choice and speed-of-processing differences in younger and older adults

    Psychology and Aging

    (1993)
  • D.C. Geary et al.

    Numerical cognition: Age-related differences in the speed of executing biologically and biologically secondary processes

    Experimental Aging Research

    (1998)
  • D.C. Geary et al.

    Cognitive addition: Strategy choices and speed-of-processing differences in young and elderly adults

    Psychology and Aging

    (1991)
  • Cited by (24)

    • Learning, Aging, and the Number Brain

      2016, Continuous Issues in Numerical Cognition: How Many or How Much
    • Chapter 6 - Adaptive Decision Making and Aging

      2015, Aging and Decision Making: Empirical and Applied Perspectives
    • Number skills are maintained in healthy ageing

      2014, Cognitive Psychology
      Citation Excerpt :

      If these continuous variables are not taken into account, for example if in all trials an increase in numerosity always corresponds to an increase in cumulative area (e.g., Gandini et al., 2008), it is unclear whether participants judged changes in numerosity or in these continuous variables. Finally, participants’ performance cannot be fully characterised when only measured as percentage of correct answers rather than in terms of finer psychophysical measures like the wf (Gandini et al., 2008, 2009; Lemaire & Lecacheur, 2007; Watson et al., 2005). A recent internet-based mega-study showed a different patter of results, indicating that the ability to discriminate numerosities (as indexed by the wf) may indeed be sensitive to ageing (Halberda et al., 2012).

    • Dissociation between numerosity and duration processing in aging and early Parkinson's disease

      2012, Neuropsychologia
      Citation Excerpt :

      Investigation of numerical processing in an aging population highlighted different patterns of performance, suggesting that numerical cognition is one of the cognitive domains where aging has mixed effects (Duverne & Lemaire, 2005). Even when elderly adults have no difficulty with visual enumeration (e.g., Li et al., 2010; Trick, Enns, & Brodeur, 1996; Watson, Maylor, & Bruce, 2005) or approximate quantification tasks (Gandini, Lemaire, & Michel, 2009; Lemaire & Lecacheur, 2007), their subitizing and counting speed decreases slightly with aging (Geary & Lin, 1998; Li et al., 2010; Sliwinski, 1997; Trick et al., 1996; Watson, Maylor, & Manson, 2002). Moreover, elderly adults use multiple strategies when solving arithmetical problems and are influenced by problem difficulty (Arnaud, Lemaire, Allen, & Michel, 2008; Gandini, Lemaire, & Dufau, 2008; see Duverne & Lemaire, 2005 for a review).

    • Inhibition and shifting capacities mediate adults' age-related differences in strategy selection and repertoire

      2011, Acta Psychologica
      Citation Excerpt :

      Results showed that older adults selected less frequently the best strategy on each problem than young adults. This decrease in the capacity at selecting the best strategy on each problem has been replicated in arithmetic (e.g., Arnaud et al., 2008; Duverne et al., 2003) and found in other cognitive domains (e.g., Gandini, Lemaire, & Michel, 2009; Taconnat et al., 2009). One of the main aging issues then is why strategy selection decreases with age during adulthood.

    View all citing articles on Scopus
    View full text