Frank Domahs

Number processing and calculation--normative data from healthy adults.

Despite the high incidence of numerical deficits in neurological patients, little attention has been paid to the development of diagnostic tools. In fact, most of the published reports on acquired numerical disorders, whether single case or group studies, do not refer to standardised measures of performance providing little, if any, control data specifically collected for the examination. In this study we present data of 282 healthy controls of different age groups and educational levels in a new battery of Number Processing and Calculation (NPC). The NPC battery includes a total of 35 tasks, assessing different counting abilities, various aspects of number comprehension (such as parity and magnitude judgements), numerical transcoding, calculation, arithmetic reasoning and conceptual knowledge. Special attention is paid to the assessment of different calculation abilities, including simple fact retrieval, rule based processing, mental calculation and written calculation in all four operations. Moreover, text problem solving is assessed as well as the understanding of arithmetic principles. Thus, the NPC battery differs from the EC 301 battery proposed by Deloche et al., 1994 (Dellatolas, Deloche, Basso, & Claros-Salinas, 2001) and allows a more fine grained diagnosis which is relevant for planning targeted interventions. The battery is easy to administer and does not require special materials or equipment.

Number processing and basal ganglia dysfunction: a single case study.

Numerical processing has never been investigated in a case of Fahrs disease (FD) and only rarely in cases of basal ganglia dysfunction. The study describes the cognitive decline of a pre-morbidly high-functioning patient (medical doctor) affected by FD and his difficulties in number processing. A MRI scan revealed bilateral calcifications in the basal ganglia and a brain PET showed a massive reduction of glucose metabolism in the basal ganglia and both frontal lobes, but no other brain abnormalities. The patients cognitive deficits included impairments in problem solving, in cognitive set shifting and in mental flexibility, as well as in verbal memory. These deficits are attributed to the disruption of the dorsolateral prefrontal circuit involving the basal ganglia. In number processing, the patient showed a severe deficit in the retrieval of multiplication facts, deficits in all tasks of numerical problem solving and in the execution of complex procedures. Importantly, he also showed a dense deficit in conceptual knowledge, which concerned all test conditions and all operations. The findings confirm the predictions of the triple code model in so far, as a disruption of cortico-subcortical loops involving the basal-ganglia may lead to specific deficits in fact retrieval. However, no verbal deficit, as assumed in the triple code model and reported in similar cases, could be observed. The present findings further add to current knowledge on numerical processing, showing how fronto-executive dysfunction may disrupt conceptual understanding of arithmetic. This study shows that not only parietal lesions may lead to severe deficits in conceptual understanding, but that basal ganglia lesions leading to frontal dysfunction may have a devastating effect.

The Influence of Implicit Hand-Based Representations on Mental Arithmetic

Recently, a strong functional relationship between finger counting and number processing has been suggested. It has been argued that bodily experiences such as finger counting may influence the structure of the basic mental representations of numbers even in adults. However, to date it remains unclear whether the structure of finger counting systems also influences educated adults’ performance in mental arithmetic. In the present study, we pursued this question by examining finger-based sub-base-five effects in an addition production task. With the standard effect of a carry operation (i.e., base-10 crossing) being replicated, we observed an additional sub-base-five effect such that crossing a sub-base-five boundary led to a relative response time increase. For the case of mental arithmetic sub-base-five effects have previously been reported only in children. However, it remains unclear whether finger-based numerical effects in mental arithmetic reflect an important but transitory step in the development of arithmetical skills. The current findings suggest that even in adults embodied representations such as finger counting patterns modulate arithmetic performance. Thus, they support the general idea that even seemingly abstract cognition in adults may at least partly be rooted in our bodily experiences.

To carry or not to carry — Is this the question? Disentangling the carry effect in multi-digit addition

Recent research has suggested addition performance to be determined by both the need for a carry operation and problem size. Nevertheless, it has remained debatable, how these two factors are interrelated. In the current study, this question was pursued by orthogonally manipulating carry and problem size in two-digit addition verification. As the two factors interacted reliably, our results indicate that the carry effect is moderated by number magnitude processing rather than representing a purely procedural, asemantic sequence of processing steps. Moreover, it was found that the carry effect may not be a purely categorical effect but may be driven by continuous characteristics of the sum of the unit digits as well. Since the correct result of a carry problem can only be derived by integrating and updating the magnitudes of tens and units within the place-value structure of the Arabic number system, the present study provides evidence for the idea that decomposed processing of tens and units also transfers to mental arithmetic.

Intensive speech and language therapy in patients with chronic aphasia after stroke: a randomised, open-label, blinded-endpoint, controlled trial in a health-care setting

BACKGROUND Treatment guidelines for aphasia recommend intensive speech and language therapy for chronic (≥6 months) aphasia after stroke, but large-scale, class 1 randomised controlled trials on treatment effectiveness are scarce. We aimed to examine whether 3 weeks of intensive speech and language therapy under routine clinical conditions improved verbal communication in daily-life situations in people with chronic aphasia after stroke. METHODS In this multicentre, parallel group, superiority, open-label, blinded-endpoint, randomised controlled trial, patients aged 70 years or younger with aphasia after stroke lasting for 6 months or more were recruited from 19 inpatient or outpatient rehabilitation centres in Germany. An external biostatistician used a computer-generated permuted block randomisation method, stratified by treatment centre, to randomly assign participants to either 3 weeks or more of intensive speech and language therapy (≥10 h per week) or 3 weeks deferral of intensive speech and language therapy. The primary endpoint was between-group difference in the change in verbal communication effectiveness in everyday life scenarios (Amsterdam-Nijmegen Everyday Language Test A-scale) from baseline to immediately after 3 weeks of treatment or treatment deferral. All analyses were done using the modified intention-to-treat population (those who received 1 day or more of intensive treatment or treatment deferral). This study is registered with ClinicalTrials.gov, number NCT01540383. FINDINGS We randomly assigned 158 patients between April 1, 2012, and May 31, 2014. The modified intention-to-treat population comprised 156 patients (78 per group). Verbal communication was significantly improved from baseline to after intensive speech and language treatment (mean difference 2·61 points [SD 4·94]; 95% CI 1·49 to 3·72), but not from baseline to after treatment deferral (-0·03 points [4·04]; -0·94 to 0·88; between-group difference Cohens d 0·58; p=0·0004). Eight patients had adverse events during therapy or treatment deferral (one car accident [in the control group], two common cold [one patient per group], three gastrointestinal or cardiac symptoms [all intervention group], two recurrent stroke [one in intervention group before initiation of treatment, and one before group assignment had occurred]); all were unrelated to study participation. INTERPRETATION 3 weeks of intensive speech and language therapy significantly enhanced verbal communication in people aged 70 years or younger with chronic aphasia after stroke, providing an effective evidence-based treatment approach in this population. Future studies should examine the minimum treatment intensity required for meaningful treatment effects, and determine whether treatment effects cumulate over repeated intervention periods. FUNDING German Federal Ministry of Education and Research and the German Society for Aphasia Research and Treatment.

Is math lateralised on the same side as language? Right hemisphere aphasia and mathematical abilities

The main purpose of the present study was to learn how mathematical abilities are located and develop in the brain with respect to language. Mathematical abilities were assessed in six right-handed patients affected by aphasia following a lesion to their non-dominant hemisphere (crossed aphasia) and in two left-handed aphasics with a right-sided lesion. Acalculia, although in different degrees, was found in all cases. The type of acalculia depended on the type of aphasia, following patterns that have been previously observed in the most common aphasias resulting from left hemisphere lesions. No sign of right hemisphere or spatial acalculia (acalculia in left lateralised right-handed subjects) was detected. These results suggest that, as a rule, language and calculation share the same hemisphere. A primitive computational mechanism capable of recursion may be the precursor of both functions.

Rehabilitation of arithmetic fact retrieval via extensive practice: A combined fMRI and behavioural case-study

The present study investigates the effects of a training of arithmetic fact retrieval in a patient suffering from particular difficulties with multiplication facts. Over a period of four weeks simple multiplication facts were trained extensively. The outcome of the training was assessed behaviourally and changes in cerebral activation patterns were investigated using fMRI. The training led to a change in calculation strategies: Prior to training, the patient used predominantly time-consuming back-up strategies, after training he relied increasingly on the direct retrieval of arithmetic facts from long-term memory. Regarding the fMRI results, prefrontal activations were observed for untrained problems, which can be attributed to the application of back-up strategies strongly relying on fronto-executive functions. Interestingly, significant foci of activation for both trained and untrained items were found in the angular gyrus of the right hemisphere, which, however, differed in their exact localisation. For the trained condition, activations were observed in anterior parts of the angular gyrus which may be related to the training-based automatisation in fact retrieval. Activations in the untrained condition were found in a more posterior portion of the angular gyrus, that might be attributable to one of the patients back-up strategies, namely to recite a whole multiplication row to get to the correct answer.

Categorical and continuous - disentangling the neural correlates of the carry effect in multi-digit addition

BackgroundRecently it was suggested that the carry effect observed in addition involves both categorical and continuous processing characteristics.MethodsIn the present study, we aimed at identifying the specific neural correlates associated with processing either categorical or continuous aspects of the carry effect in an fMRI study on multi-digit addition.ResultsIn line with our expectations, we observed two distinct parts of the fronto-parietal network subserving numerical cognition to be associated with either one of these two characteristics. On the one hand, the categorical aspect of the carry effect was associated with left-hemispheric language areas and the basal ganglia probably reflecting increased demands on procedural and problem solving processes. Complementarily, the continuous aspect of the carry effect was associated with increased intraparietal activation indicating increasing demands on magnitude processing as well as place-value integration with increasing unit sum.ConclusionsIn summary, the findings suggest representations and processes underlying the carry effect in multi-digit addition to be more complex and interactive than assumed previously.

Going on with optimised feet: Evidence for the interaction between segmental and metrical structure in phonological encoding from a case of primary progressive aphasia

Background: Our knowledge about the interaction between segmental and metrical levels of representation in word production is still largely underspecified. In particular, there is only sparse evidence of how syllables are hierarchically organised into higher‐level prosodic structures such as prosodic feet and words. Furthermore, the question whether stress assignment in German is sensitive to syllable weight is unresolved so far. While quantity‐insensitive accounts state that stress is predominantly assigned to a default position (i.e., to the penultimate syllable) and other stress patterns are exceptional, quantity‐sensitive accounts assume that stress assignment is determined by the weight of the final two syllables. The present investigation was supported by the German Science Foundation (project WI 853/7‐1) and by the START programme of the faculty of Medicine at the RWTH Aachen University (AZ 37/07). We would like to thank patient HT for participating in our studies, Anna‐Lisa Schelwies for her assistance in transcribing some of the data, and Ingrid Aichert for kindly providing us with syllable frequency counts. Aims: Impaired lexical retrieval may lead to regularisations of stress assignment. Such an error pattern will be examined to gain insights into the interrelation between different tiers of prosodic representations (e.g., syllable, foot, prosodic word). Methods & Procedures: A reading and a repetition task were conducted with German‐speaking patient HT, suffering from primary progressive aphasia, which especially affected her retrieval of lexical information. The material consisted of polysyllabic words with varying stress patterns and syllable structures. Outcomes & Results: In reading, HT produced hardly any segmental errors, but a substantial amount of stress errors. Importantly, the patient not only over‐generalised the “default” penultimate stress as would have been predicted by quantity‐insensitive approaches. Instead, she over‐applied different stress patterns depending on the weight of the last two syllables. In repetition, HTs output can be characterised as phonological jargon. Crucially, however, she hardly produced any stress errors. Rather, thorough analyses revealed that segmental deviations in her output led to optimised prosodic structures. For instance, insertions of rhyme segments could be observed mainly in strong syllables, i.e., syllables bearing main or secondary stress, whereas deletions occurred predominantly in weak, unstressed syllables. Conclusions: The present data provide evidence for specific forms of interaction between segmental and metrical knowledge: On the one hand, segmental information influenced the patients stress assignment errors in reading. On the other hand, prosodic information modified segmental errors even in severe jargon observed in repetition. With respect to the prosodic system of German, the observed error patterns show that the structure of the final syllable determines how syllables of a word are parsed into prosodic feet and, accordingly, which syllable has to be prominent. Thus, our results support quantity‐sensitive approaches of stress assignment.

Multimodal semantic quantity representations: further evidence from Korean Sign Language.

Korean deaf signers performed a number comparison task on pairs of Arabic digits. In their response times profiles, the expected magnitude effect was systematically modified by properties of number signs in Korean sign language in a culture-specific way (not observed in hearing and deaf Germans or hearing Chinese). We conclude that finger-based quantity representations are automatically activated even in simple tasks with symbolic input although this may be irrelevant and even detrimental for task performance. These finger-based numerical representations are accessed in addition to another, more basic quantity system which is evidenced by the magnitude effect. In sum, these results are inconsistent with models assuming only one single amodal representation of numerical quantity.