Edited by: Rodrigo Orlando Kuljiš, Zdrav Mozak Limitada, Chile
Reviewed by: Donald Sharpe, University of Regina, Canada; Michael David Kopelman, King's College London, UK
*Correspondence: Carlo Semenza, Dipartimento di Neuroscienze, Università di Padova, Via Giustiniani 5, 35128 Padova, Italy e-mail:
This article was submitted to the journal Frontiers in Aging Neuroscience.
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The aim of this study was to build an instrument, the numerical activities of daily living (NADL), designed to identify the specific impairments in numerical functions that may cause problems in everyday life. These impairments go beyond what can be inferred from the available scales evaluating activities of daily living in general, and are not adequately captured by measures of the general deterioration of cognitive functions as assessed by standard clinical instruments like the MMSE and MoCA. We assessed a control group (
Number processing and calculation are an essential part of our culture. We use numbers for counting, measuring, comparing, putting things in order, etc. Moreover, we constantly need to calculate, understand fractions, proportions and ratios, and to understand and remember PIN codes, telephone numbers, addresses, shoe sizes, and so on. Of course, many occupations need relatively high levels of numerical skill, and poor skills will have an adverse effect on life chances in education and employment, indeed a larger effect than poor literacy skills, as a large-scale cohort study in the UK demonstrates (Parsons and Bynner,
In the past two decades, neuroscience has made a significant progress in the understanding of how the brain represents numerical information and sustains mathematical computation (Butterworth and Walsh,
Despite the many studies of the neural basis of typical and atypical mathematical abilities the impact of such important disturbances on an individual's everyday life is still unclear. Deterioration of mathematical abilities is a very frequent consequence of brain damage, however, and a socially relevant one. In the elderly, even in healthy ones, slowing of arithmetical functions is found, which is often clinically hard to distinguish from that produced by neurological deterioration (Zamarian et al.,
Research with brain-damaged patients has repeatedly demonstrated a range of quite specific deficits. For example, there may be selective deficits in number transcoding from spoken to written numbers, or from written to spoken numbers, arithmetical signs, arithmetical facts and rules, arithmetical procedures and conceptual knowledge have been shown to be selectively disrupted after brain damage (see for reviews Butterworth,
Specific error patterns and relative weaknesses may be a signature of specific neurological pathologies (see Cappelletti et al.,
It seems likely that the different specific deficits could impact in different ways on daily living, though this has up till now not been investigated. The instrument we are developing here can provide the foundation for such an investigation.
In one specific practical area, financial competence, there have been attempts to assess the impact of cognitive difficulties more generally on everyday life. Marson and co-workers provided a theoretical framework and appropriate tools to assess reduced financial competence in the elderly and in pathological conditions such as Alzheimer's disease, MCI or traumatic brain injury (Marson et al.,
However, although these studies answered some important questions, they did not directly address the issue of how a specific deficit relates to the range of tasks that a patient can or cannot do in his or her everyday life. To take one example, Patient CG was a competent bookkeeper and manager of the family hotel, but as a consequence of a focal brain lesion, suffered very severe global acalculia, despite her otherwise spared cognitive skills, and therefore could no longer maintain her previous occupation. Patient BE (Hittmair-Delazer et al.,
To what extent do these specific impairments relate to the difficulties measured by available scales evaluating activities of daily living in general (e.g., Instrumental Activities of Daily Living, IADL, Lawton and Brody,
To what extent does general deterioration of cognitive functions as measured by standard clinical instruments like the MMSE capture numerical deficits?
Four new instruments were specifically designed for this investigation, and were administered to participants along with known clinical batteries.
The way NADL is structured allowed us to collect information about the degree of awareness of the deficit by the patient and by her or his caregivers.
NADL is divided into four parts (for details, see Appendix A, supplementary material).
The Patient Interview (Since this study involves a control group, the Patient Interview is referred to as the Participant Interview).
The Caregiver Interview.
The Informal Test, which is designed to offer a brief clinical assessment to determine whether the Formal Test of numerical abilities needs to be administered.
The Formal Test. This is a detailed assessment of the numerical abilities critical to daily living; these abilities are typically assessed in neuropsychological investigation of numerical and mathematical impairments. Thus, this test may be considered as an external criterion for the other subtests. In clinical practice, this only needs to be administered if there is evidence in the first three parts indicating a deficit in numerical abilities. However, for this study, it was always administered in order to evaluate the validity of the first three parts.
These brief interviews, administered separately to the patient and to the caregiver, are meant to provide a rough assessment of the patient's awareness about his or her numerical deficit. The comparison of the patient's answers with those of the caregiver is designed to provide such information. These interviews consist of 10 simple questions (e.g., “Do you shop by yourself?”; “Do you make your own telephone calls unaided (i.e. do you dial them yourself)” on how well the participant uses numbers in everyday life, with equivalent questions asked of the participant and, in reference to the participant, of the caregiver. The activities were selected as relevant activities of daily living that are likely to be influenced by numerical abilities on the basis of previous literature and of clinical experience (frequent complaints about what patients cannot do any more and similar information).
This test is meant to assess the numerical competence likely to be necessary in everyday life. It encompasses questions in the domains of Time (current date?), Measure (amount of pasta or rice in an average portion?), Transportation (distance between home and hospital?), Communication (own telephone number?), General Knowledge (days in a week?) and Money (cost of a car?). When the question implied an estimate rather than a precise number, the answers was considered correct if within a reasonable quantity interval (e.g., amount of pasta/rice: 80 g ±50 per person), The choice of these domains was made in consideration of previous literature and available instruments (e.g., Katz et al.,
This battery has been designed to assess the numerical abilities of patients using brief graded-difficulty subtests. The battery is organized in four sections consistent with previous neuropsychological batteries for numerical abilities (Delazer et al.,
This section comprises three subtests that test the patient's ability to relate number words and digits to numerical magnitudes: Numerosity Comparison (Comparing the number of squares in two panels presented simultaneously, up to nine squares per panel), Number Line marking (The participant is asked to mark a number on a line defined by its end points), and Digit Comprehension (10 panels, similar to the above, are presented one at a time along with a list of digits 1 to 10. For each panel, the participant points to the appropriate number).
The aim of this section is to assess the ability to transcode between written and spoken numbers. This section is separate from that on calculation, since a dissociation has been observed in individual patients (Cipolotti and van Harskamp,
The aim of this section is to assess the ability to perform simple mental calculation (on spoken presentation). This section consists of three subtests: Mental Addition (e.g., 5 + 7), Mental Subtraction (e.g., 13 − 4), and Mental Multiplication (e.g., 9 × 6).
This section assesses in detail the components of calculation. The section consists of six subtests grouped in two subsections. The first subsection, named Understanding Arithmetical Rules and Principles, assesses the ability to use basic rules (e.g., operations with 0) and principles (e.g., the commutativity of addition) in written form. It consists of subtests for Arithmetical Rules (e.g., 0 + 9; 1 × 7), Addition Principles (e.g., 26 + 37 = 63 → 37 + 26 = ?), and Multiplication Principles (94 × 5 = 470 → 93 × 5= ?). The second subsection assesses the ability to perform more complex operations in writing. This latter subsection, named Written Operations consists of three subtests: Addition (e.g., 463 + 659), Subtraction (548 − 231), Multiplication (429 × 53).
The MMSE (Mini-Mental-State Examination, Folstein et al.,
The MoCA (Montreal Cognitive Assessment, Nasreddine et al.,
IADL (Lawton and Brody,
A total of 323 volunteer participants took part in the study: a control group (
Participants of the control group were recruited in Italy. They were autonomous in their activities of daily living and, at the time of the assessment, they had no pathologies that could have influenced their cognitive status or its assessment. They had no record of developmental learning disorders. This group had a mean age of 53.05 years (
Data from the control group were used to obtain normative cut-offs and some data from the control group were also included in the analysis assessing the psychometric properties of the battery.
Participants in the patient group were mostly recruited at the I.R.C.S.S. San Camillo on the Venice Lido or in the Policlinico of Padova. They gave their informed consent according to the Helsinki Declaration. The diagnosis of these patients was established through the standard protocols for their pathologies. The patient group had a mean age of 58 years (
Details on demographic variables and neurological diagnosis of the patient group are reported in Table
Alzheimer | 74.07 (7.81) | 8.69 (4.85) | 8 (61%) | 13 |
Mild cognitive impairment | 75.08 (7.81) | 8.75 (3.85) | 15 (42%) | 36 |
Parkinson | 64.82 (9.07) | 10.75 (4.91) | 13 (46%) | 28 |
Multiple sclerosis | 51.28 (13.25) | 10.67 (3.87) | 32 (53%) | 60 |
Neurofibromatosis type 1 | 28.40 (9.18) | 12.64 (3.98) | 13 (59%) | 22 |
Corticobasal degeneration | 73 (-) | 5 (-) | 1 (50%) | 1 |
Frontotemporal dementia | 65 (-) | 13 (-) | 0 (0%) | 1 |
Lewy body dementia | 76 (-) | 17 (-) | 0 (0%) | 1 |
Left hemisphere lesion | 56 (13.07) | 11 (4.86) | 5 (71%) | 7 |
Right hemisphere lesion | 67 (1.71) | 11 (5.31) | 1 (25%) | 4 |
Amyotrophic lateral sclerosis | 65 (2.83) | 5 (-) | 1 (50%) | 2 |
Overall patients | 58.23 (18.01) | 10.37 (4.35) | 89 (51%) | 175 |
All participants were tested individually. Testing was administered by trained neuropsychologists, always in the following order: first the
Together with the NADL battery, all participants were administered with MMSE and MoCA. The caregiver was also asked to compile the IADL (Instrumental Activities of Daily Living, Katz,
All statistical analyses were performed with the free statistical software
Several psychometric properties of NADL were investigated. To limit the extent of ceiling effect, this analysis was performed only on patients.
Interview with patients | 0.5 | 0.69 | 0.82 |
Interview with caregiver | 0.62 | 0.98 | 1 |
Informal total | 0.64 | 0.86 | 0.94 |
Formal total | 0.73 | 0.86 | 0.87 |
Numerosity comparison | 0.8 | 0.51 | 0.84 |
Number line | 0.73 | 0.50 | 0.60 |
Digit comparison | 0.71 | 0.32 | 0.9 |
Reading number aloud | 0.37 | 0.20 | 0.68 |
Writing numbers on dictation | 0.19 | 0.24 | 0.2 |
Mental addition | 0.7 | 0.28 | 0.58 |
Mental subtraction | 0.5 | 0.44 | 0.95 |
Mental multiplication | 0.61 | 0.72 | 0.92 |
Written rules | 0.59 | 0.38 | 0.55 |
Written addition | 0.65 | 0.68 | 0.81 |
Written multiplication | 0.63 | 0.46 | 0.62 |
Written operations—addition | 0.6 | 0.60 | 0.66 |
Written operations—subtraction | 0.71 | 0.50 | 0.83 |
Written operations—multiplication | 0.6 | 0.38 | 0.55 |
Total number comprehension | 0.43 | 0.34 | 0.78 |
Total reading and writing Arabic numerals | 0.39 | 0.39 | 0.62 |
Total mental calculation | 0.58 | 0.76 | 0.93 |
Total rules and principles | 0.78 | 0.88 | 0.92 |
Total written calculation | 0.74 | 0.47 | 0.68 |
The
Cut-off scores based on the distribution of scores in the healthy participant group were calculated. Cut-offs were calculated separately for each subtest of the formal test and for the informal test, but also for each section of formal and informal test, and for the global scores of formal and informal tests. To account for the effect of demographic variables (age, education, and gender) on cut-offs we used the results of regressions with the subtest or test scores as dependent variables and the demographic variables as predictors (the analysis are reported in detail in the paragraph
Interview with patients | 10.57 (0.21) | −0.02 (0.004) | – | – | – |
Interview with caregiver | – | – | – | – | – |
Informal total | 23.38 (0.49) | −0.05 (0.008) | – | – | 0.18 |
Formal total | 70.78 (2.45) | −0.10 (0.03) | 0.39 (0.11) | – | 0.26 |
Numerosity comparison | – | – | – | – | – |
Number line | |||||
Digit comprehension | – | – | – | – | – |
Reading number aloud | 4.08 (0.13) | – | 0.04 (0.01) | 0.20 (0.09) | 0.11 |
Writing numbers on dictation | – | – | – | – | – |
Mental addition | – | – | – | – | – |
Mental subtraction | – | – | – | – | – |
Mental multiplication | 4.45 (0.22) | – | 0.07 (0.02) | – | 0.09 |
Written rules | 6.27 (0.38) | −0.02 (0.004) | 0.07 (0.02) | – | 0.30 |
Written addition | 3.42 (0.44) | −0.02 (0.005) | 0.07 (0.02) | – | 0.25 |
Written multiplication | 4.66 (0.21) | −0.02 (0.004) | – | – | 0.21 |
Written operations—addition | – | – | – | – | – |
Written operations—subtraction | 6.49 (0.27) | −0.02 (0.004) | – | – | 0.13 |
Written operations—multiplication | – | – | – | – | – |
Total number comprehension | – | – | – | – | – |
Total reading and writing Arabic numerals | 9.54 (0.17) | – | 0.06 (0.01) | 0.25 (0.12) | 0.14 |
Total mental calculation | 15.96 (0.35) | – | 0.09 (0.03) | – | 0.05 |
Total rules and principles | 13.74 (0.85) | −0.05 (0.01) | 0.17 (0.04) | – | 0.40 |
Total written operations | 17.02 (0.54) | −0.04 (0.01) | – | – | 0.11 |
Since NADL is the first battery with the aim of assessing the impact of numerical deficits in daily living, we cannot use external evidence of actual daily living to assess its validity. However, it is possible to collect evidence on the construct validity of the test by investigating correlations among test sections and among the tests and other external tests. Thus, we inspected the correlation among the parts of NADL and with the other tests administered to investigate if the results support the claim that the parts of NADL are indeed measuring the construct of numerical activities related to numbers. Importantly, the formal test of NADL can be considered as an external criterion for the other parts, since it covers the main domains of neuropsychological models of mathematical and numerical abilities, and it closely resembles other existing batteries (see for example, Delazer et al.,
The results of correlations on NADL global scores and scores on subtests are reported in Table
Interview with caregiver | 0.82 | |||||
Informal total | 0.47 | 0.58 | ||||
Formal total | 0.54 | 0.64 | 0.65 | |||
MMSE | 0.60 | 0.74 | 0.65 | 0.75 | ||
MoCA | 0.46 | 0.61 | 0.51 | 0.58 | 0.74 | |
IADL | 0.73 | 0.81 | 0.51 | 0.57 | 0.65 | 0.54 |
The overall pattern of correlations suggests a source of communality that may underlie the interrelation among scores on the different tests. This is not surprising, because all of the tests are supposed to be influenced by the overall cognitive status of the individual.
These results thus support the construct validity of NADL and suggest that the interview with the caregiver is a better estimate of numerical abilities than the interview with the patient.
The interviews with the participant and with the caregiver give the opportunity to estimate the numerical competence in the life of the patients. Results of the correlations suggest that the estimate of the caregiver on the impact of numerical deficits in daily living is better then the estimate made by the patients themselves (see previous paragraph). The error bias in patients was further explored by comparing the scores on the interviews by means of paired
The main purpose of this study was to obtain an instrument able to assess numerical activities of daily living. The instrument described here, the NADL battery, has been normed on a sufficient number of participants, including control participants varying in the age, and its psychometric properties have been tested on participants affected by a wide variety of pathological conditions.
We have found that the NADL battery shows a good reliability both in terms of test-retest and inter-rater reliability. The internal consistency was satisfactory as well. Construct validity was also satisfactory, as tested by the correlation between NADL parts and cognitive status as assessed by MoCA and MMSE, and with IADL. Importantly, the Patient Interview and Caregiver Interview correlated well with IADL, and with the Informal and Formal parts. The Caregiver Interview was a better predictor of actual numerical ability, with additional finding that the Patient Interview overestimated numerical abilities. This confirms the NADL strategy of using these interviews as a brief clinical screening tool to see whether a more detailed investigation of the patient's numerical abilities is indicated.
Since patients tended to overestimate their own numerical competence, a specialized numerical battery, such as NADL, can be employed to evaluate numerical competence for financial or legal decisions about the ability of an individual to manage his or her own affairs, especially financial affairs. The need of such evaluation is likely to increase with the elderly, irrespective of clear neurological damage (Webber et al.,
It is known that distinct patterns of numerical deficits have been identified for a number of neurological conditions, including progressive diseases, such as Alzheimer's disease, Temporal Lobe Epilepsy, Fronto-temporal Dementia, Semantic Dementia and other forms of Primary Progressive Aphasia, Amyotrophic Lateral Sclerosis, Posterior Cortical Atrophy, Parkinson's Disease and other diseases of basal ganglia (see Palmieri et al.,
In our study, we were able to compare for the first time on the same battery Parkinson's Disease and Multiple Sclerosis. On Total Written Calculation, patients with Parkinson performed worse than patients with Multiple Sclerosis, irrespective of the severity of the condition, general cognitive impairment, age or education. Similarly, neurofibromatosis, a pathological condition for which no previous investigation of numerical abilities was available, and where the pathology shows much earlier than in the above-mentioned degenerative diseases, is characterized by a distinct profile of numerical deficits, especially mental calculation, again independently from severity of the disease, age, and education.
NADL may also be useful in the assessment of “cognitive or brain reserve” the resilience of function in the context of neural damage (see, for example, Nucci et al.,
The NADL battery is an initial step in developing an efficient assessment tool. A shorter version of the Formal part may be needed. However, the detailed and extensive investigation presented here provides the basis on which to proceed. Subsequent analysis of the data from patients and controls may eventually enable us to include only the most discriminating items, and thereby reduce the length of the battery. Importantly, however, the interview with the caregiver seems to provide a first, rough but quite reliable, estimate of a patient's numerical skills. It may thus be used when a thorough evaluation cannot be done, or to guide a screening decision.
The present battery enables the investigation of the consequences of a given numerical defect on numerical activities of daily living. This is work in progress. Factors such as the influence of relative severity will be the focus of subsequent studies. At the present stage, however, this battery can already be employed in its present form to assess patients for their rehabilitation or retraining and to monitor and assess the outcome of rehabilitation and retraining in a real life setting.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
This study was supported by grant RF-2009-1530973 from Ministero della Sanità and by grant STPD11B8HM_004 from the University of Padova to Carlo Semenza.
The Supplementary Material for this article can be found online at: