Number and Language Processing

A Special Issue of Aphasiology

Xavier Seron

• Publisher: Psychology Press
• Year: 2020
• eBook ISBN: 9781000149920
• Topic: Medicine
• Subtopic: History & Theory in Psychology

There is psychological and neurobiological evidence that number and language processing present some specificities and may dissociate after brain damage. Furthermore, animals and babies seem to be able to discriminate small numerosities in a non-symbolic way. However, one of the specificities of the human species is the development of language and symbolic processes. The acquisition and development of arithmetic is thus bound to the acquisition of language and symbolic notations.In this special issue, the relationship between language and number processing is discussed through the examination of the similarities and divergences of language and number disorders in aphasic subjects, in patients with dementia, and in children with specific acquisition deficits. A separate contribution is also devoted to the rehabilitation of number and calculation deficits in brain-lesioned subjects.

Transcoding and calculation in aphasia

Margarete Delazer and Lisa Bartha
University Clinic of Neurology, Innsbruck, Austria

Aphasia may have deteriorating effects on several numerical skills, such as counting, reading numerals aloud, or writing them to dictation, as these abilities rely on intact language. However, aphasia also seems to have specific effects on the calculation system. Group studies, as well as single-case studies, point to the fact that language-impaired patients have particular difficulties in completing multiplication tasks, while other operations are less impaired. From a theoretical point of view, there is still a debate as to whether this association reflects a general psycholinguistic problem, the effect of aphasia on numerical cognition, or a deficit in non-specific resources underlying both number and language domains. In studies on number transcoding multi-route models have been proposed which parallel semantic and asemantic routes in alphabetical processing. Yet, the review of the empirical evidence suggests that these models still lack relevant theoretical specification.

INTRODUCTION

Aphasic patients frequently have difficulties dealing with numbers, i.e., counting, transcoding numerals between different codes, or answering computations in verbal or written format. This is particularly true for tasks requiring verbal input or output processes. In fact, many numerical skills, such as counting, reading numerals aloud, or writing them to dictation unquestionably rely on intact language processing (Seron & Noël, 1992). There is considerable debate, however, as to whether aphasia has a genuine deteriorating effect on central processes of numerical cognition, in particular on the retrieval of basic arithmetic facts.

Before discussing the relation between aphasia and calculation deficits, we briefly summarise the characteristics of the symbolic systems underlying numerical processing and their relations to language in general. Numbers may be expressed in various forms, such as number words (whether in alphabetical form or in phonological form), Arabic numerals, Roman numerals, arrays of dots, or finger patterns. We will consider in turn the properties of the two most common codes, Arabic numerals and verbal number words.

Arabic numerals constitute a semiotic system that differs from alphabetic language in several respects (Grewel, 1952, 1969; Power & Longuet-Higgins, 1978), but also shares some similarities. Each single element of Arabic script has a meaning in itself, for example the symbol 4 denotes the concept expressed by the word "four". In contrast, single elements of alphabetical script, e.g., the letter "A", do not have meaning by themselves. The system of Arabic notation is a strict one, i.e., the symbols for the digits, such as 2, and for the operations, such as + or x, allow only one interpretation (Grewel, 1969). In contrast, language in general has multiple referents (this is valid for common names, but not for proper names). Numerical symbols may be combined and manipulated according to exactly defined rules that are specific to the notational system. The Arabic notation has a very restricted lexicon, using only 10 different symbols. The first nine numbers are represented by nine different digits; from ten onwards, the place value system is introduced. Thus, the quantity expressed by the single digits within a complex numeral depends on their position in the sequence—the rightmost digit representing the units. 0 is used to indicate the absence of a quantity, but also to function as a "place filler", as in 301 (3 hundreds, 0 tens, 1 unit). Both the identity of single elements (digits) and the position of the single elements within the number carry meaning. The two dimensions (identity and position of the digit) are elaborated separately in transcoding to other codes as suggested in neuropsychological (e.g., Deloche & Seron, 1982a,b; McCloskey & Caramazza, 1987; McCloskey, Caramazza, & Basili, 1985; Noël & Seron, 1995) and developmental studies (Power & Dal Martello, 1990; Seron, Deloche, & Noël, 1992; Seron & Fayol, 1994).

Address correspondence to: Margarete Delazer, University Clinic of Neurology, Innsbruck, Austria, The authors are grateful to Luisa Girelli for helpful comments on a first version of the manuscript

In the verbal code (graphemic or phonemic) numbers are expressed by single words (e.g., nine) or by strings of words (e.g., seventy-three). Although the number of single lexical elements is higher than in the Arabic notation, it is still very limited and includes units (from one to nine), teens (from ten to nineteen), tens (from twenty to ninety) and multipliers (hundred, thousand...). Moreover, the order of elements is exactly defined and thus contrasts to most other lexical classes (exceptions are other ordered classes, such as days of the week, months of the year, or music notes). Single number words or lexical primitives (Seron & Noël, 1992) may be combined to assemble more complex numerals. The ordering of lexical primitives within a complex numeral is defined by the number syntax (Power & Longuet-Higgins, 1978) which specifies the relation between semantic content and lexical realisation. In particular, lexical primitives are represented in sum or product relations. For example, three thousand means three times thousand and thus represents a product relation, whereas twenty three means twenty plus three and accordingly constitutes a sum relation. Number syntax specifies the order of single lexical elements and allows us to discriminate legal (e.g., twenty three) from non-legal numbers (e.g., three twenty).

Overall, both notations, Arabic and verbal, are characterised by a restricted, strictly ordered lexicon with high-frequency elements (Dehaene & Mehler, 1992) and by an exactly defined syntax. One may speculate whether these characteristics lead to particular difficulties in aphasic subjects affecting the production and comprehension of numerical stimuli. While the limited number and the high frequency (both Arabic and verbal) may facilitate the retrieval of lexical elements, the strict one-to-one correspondence between semantic content and lexical output certainly inhibits verbal production, allowing no circumlocution and no ambiguity. The strict sequential order of numerical elements in the lexicon may present further difficulties. In fact, it has been reported that other lexical classes meeting similar linguistic criteria as number words (days of the week or months of the year) lead to qualitatively similar errors (Deloche & Seron, 1984).

Difficulties may also arise from syntactic processing in the comprehension and production of complex numerals. Syntactic processing of numerals is not only a multistep process and thus error prone, but is also strictly defined and allows no simplifications or alterations. Even slight alterations of number syntax or morphology change the meaning of a numeral. For example, hundred-four is different from four-hundred and sixty is different from the phonologically similar sixteen. In conclusion, processing numerals, both in Arabic and verbal code, puts high demands on the language system and may be particularly difficult for aphasic patients.

Research on numerical skills in aphasia is not only of theoretical interest, but has eminent practical relevance. Although the topic has gained more interest in the last few years, there are still surprisingly few studies concerned with the particular difficulties of aphasic patients in numerical tasks. Text books on aphasia rarely address specific problems in number processing. In a short overview of ten standard books on language and aphasia we found nothing specific on number processing in five of them (Caplan, 1992; Code, 1989; Goodglass, 1993; Levelt, 1989; Nickels, 1997), and a single paragraph in three of them (Patterson & Shewell, 1987 [in Coltheart, Sartori, & Job, 1987]; Poeck, 1989; Van Hout, 1999 [in Fabbro, 1999]). A whole chapter is devoted to numbers only in Kaplan and Goodglass (1981; in Sarno, 1981) and Leischner (1987). However, these chapters were written more than ten years ago and cannot account for recent developments.

Unfortunately, the lack of theoretical consideration in standard text books is reflected by a lack of attention in clinical assessment and rehabilitation. Difficulties in number processing certainly do not gain the attenti...

Table of contents

• Cover
• Contents
• Copyright Page
• Preface
• Introduction Number and language processing
• Numerical and arithmetical deficits in learning-disabled children: Relation to dyscalculia and dyslexia
• Transcoding and calculation in aphasia
• Numerical abilities in dementia
• Rehabilitation of number processing and calculation skills