How Language and Numbers Work Together
Human numerical cognition emerges through interactions among quantity perception, memory, language, cultural practices, and mathematical symbols. Number words such as “three,” “twenty,” and “one hundred” provide conventional tools for identifying exact quantities, counting objects, communicating numerical relations, and coordinating calculations. Yet quantities can be compared before a child learns to count, and numerous numerical judgments are possible without saying or reading a number. The central scientific question concerns which components of numerical thinking depend on language, how language changes their organization, and what cognition can accomplish through other representational systems. A major 2026 review distinguishes phonological, morphological, lexical, semantic, conceptual, and visuospatial routes through which spoken and signed languages interact with number learning Berteletti et al. (2026).
Numerical cognition includes perceiving and comparing quantities, determining cardinality, understanding numerical order, retrieving arithmetic facts, making estimates, using written numerals, and reasoning about mathematical relations. Language has different roles in each achievement. Matching two visible small sets can draw on object tracking. Learning that the last word in a count gives a set's size requires an acquired counting system and conceptual insight. Exact multi-digit arithmetic can engage verbal memory, positional notation, magnitude representations, and attentional control simultaneously. A differentiated framework is supported by infant experiments, developmental research, cross-cultural studies, neuroimaging, and mathematical learning research Feigenson et al. (2004); Carey and Barner (2019).
The most coherent current account is that language provides powerful tools for constructing, stabilizing, extending, and communicating exact number concepts, while nonverbal quantity systems make their own substantial contributions. Whether a verbal count sequence is indispensable for an exact numerical performance depends upon how exactness is defined, what a task requires, and which alternatives are accessible. Studies with different counting vocabularies show both constraints associated with verbal knowledge and numerical performance supported by nonverbal strategies Frank et al. (2008); Butterworth et al. (2008); Pitt et al. (2022).
What Is a Number Representation?
Numerosity, cardinality, order, and notation
Numerosity is the number of individual objects in a collection. Cardinality concerns exactly how many objects belong to that collection, while ordinal information specifies a position in an ordered sequence. The written numeral 27, spoken “twenty-seven,” a corresponding signed number expression, and 27 dots can denote one cardinal value but engage different sensory and cognitive routes. Researchers must distinguish the quantity referred to from the representation used to refer to it. A participant may match seven visible objects with seven other objects using one-to-one correspondence without demonstrating a flexible, memory-stable abstract concept for the integer seven.
The distinction is experimentally decisive. One person can answer by counting; another can use direct visual matching, finger configurations, spatial grouping, or a remembered sequence. The same score can conceal different mechanisms. Investigators therefore vary timing, memory demand, opportunity for correspondence, linguistic input, and response modality before inferring which representation was involved Frank et al. (2008).
Approximate quantity and small exact sets
The approximate number system supports rough judgments of magnitude without sequential counting. Under appropriate stimulus controls, distinguishing eight objects from sixteen is easier than distinguishing eight from nine, showing a ratio-dependent signature. Experiments must also control area, density, spacing, individual size, and duration so that participants cannot reliably use correlated visual features. Broad research supports approximate quantity discrimination in infants and adults and connects it to comparative work with other species Feigenson et al. (2004).
Another set of processes supports tracking a small number of individual objects. An observer can notice the disappearance of one of two items or follow two moving objects without explicitly deriving cardinality using number words. Object tracking may preserve separate identities rather than representing a generalized integer concept. Theoretical debate concerns exactly how these small-set representations combine with approximate magnitude mechanisms and subsequently acquired numerical symbols Feigenson et al. (2004); Carey and Barner (2019).
Number words and written numerals
Number words are conventional expressions in a language; numerals are written or otherwise encoded signs for number. Counting routines are ordered procedures connecting labels to successive objects or events. Place-value notation gives a digit different values depending on its position. These are linked systems acquired through learning, not interchangeable abilities. A child may recite twenty number words without identifying twenty objects accurately. An adult may recognize the written symbol 24 but hesitate when translating a complex spoken expression into digits. Proper scientific assessment separates vocabulary, sequence knowledge, exact cardinality, magnitude, and symbol conversion Sarnecka and Carey (2008).
How Children Learn Exact Number Words
Reciting a sequence and understanding its meaning
Children often memorize the conventional count list before assigning exact cardinal meanings to all its words. An experimenter can investigate this using a give-a-number task: ask for one toy, then two, three, four, and larger sets. Some children reliably fulfill “one” but cannot consistently distinguish larger requests, even while reciting the count list fluently. Others become two-knowers or three-knowers before understanding the cardinal principle that connects the final word in a count with the set's exact size. These developmental stages provide evidence that sequence recitation and numerical concept learning are partially separable Le Corre and Carey (2007); Sarnecka and Carey (2008).
The cardinal principle
The cardinal principle coordinates one-to-one mapping, a stable verbal sequence, and understanding that the final count word gives the total. A cardinal-principle knower can count previously unfamiliar collections and extend exact labeling beyond a few memorized values. The count sequence also makes successor relations salient: the next label denotes a collection with one more object under the counting procedure. The exact trajectory varies across learners and linguistic environments. Researchers continue to debate whether children construct integer meanings from small-set concepts, an acquired successor structure, or several interacting cognitive resources Carey and Barner (2019).
Number talk and everyday experience
Counting toys, describing ages, comparing portions, and explaining “one more” or “one fewer” connect number language to experience. Levine and colleagues found that variation in caregivers' number talk was associated with subsequent differences in young children's number knowledge. The longitudinal observational design supports a role for early numerical language experience while leaving confounding by shared environment, prior skill, and parental practices as an important issue. It does not establish that a given number of spoken words causally guarantees a particular mathematical outcome Levine et al. (2010).
Counting objects and checking their final total yields different evidence than simply chanting a list. Comparing “three” and “four” while adding an object illustrates a numerical relation; discussing the same quantity across rearranged objects illustrates cardinal invariance. Such activities are plausible evidence-informed ways to link language, symbols, and numerical meaning, while individual learning outcomes remain dependent on wider educational experience.
Can People Think About Exact Numbers Without Words?
The importance of carefully defined tasks
Research among speakers of languages with small conventional number vocabularies makes an unusual contribution to the science of thought. Such studies separate skills that commonly develop together in heavily schooled decimal-number cultures. At the same time, comparisons are influenced by formal education, familiarity with experimental materials, everyday counting practices, cultural conventions, and memory requirements. Investigators must avoid equating performance on one laboratory procedure with intellectual capacity or treating a language community as cognitively homogeneous Gordon (2004); Butterworth et al. (2008).
Pirahã: remembering exact number and directly matching objects
Gordon's 2004 study with Pirahã speakers reported difficulty on exact-number tasks beyond small sets in the absence of an extensive conventional exact-number lexicon. Its interpretation linked number words to precise numerical representation. Frank and colleagues subsequently distinguished tasks permitting simultaneous visual correspondence from tasks requiring quantity information to be carried across a delay or transformation. Their participants succeeded at certain exact one-to-one matching tasks without numerals for the corresponding set sizes, while more demanding memory-based performance was limited Gordon (2004); Frank et al. (2008).
The evidence suggests that immediate exact correspondence and a portable exact numerical code are distinct achievements. If objects can be aligned side by side, the observer can preserve equality by matching them without determining a verbal total. If the objects disappear or the same quantity must be communicated to someone else, a countable symbol sequence becomes particularly useful. These results explain why “can match exact quantities” and “has generalized exact integer concepts” should not be treated as identical claims. The studies do not imply any deficiency of reasoning among the participants.
Mundurukú: approximate arithmetic outside the verbal count range
In a landmark investigation, Pica and colleagues found that Mundurukú participants could make approximate numerical calculations for quantities beyond their available exact number vocabulary while exact computations were more constrained. The result shows that adding approximate magnitudes and calculating a unique integer answer involve different cognitive requirements. Approximate number is useful for predicting which group will be larger or whether a result is broadly plausible, even when a precise total cannot be named Pica et al. (2004).
These findings count as evidence of mathematical processing independent of an extensive verbal number list. They do not demonstrate that the full apparatus of written arithmetic, large integer representation, and learned formal mathematics develops identically in every linguistic context. The research instead separates the numerical operations under investigation.
Indigenous Australian children: alternative routes to numerical thought
Butterworth and colleagues studied Indigenous Australian children using languages with restricted traditional number vocabularies and found numerical competencies that challenged an absolute dependence on a lengthy verbal number list. Depending on the task, children can use spatial patterns, object-based matching, and quantitative relationships. The findings are particularly valuable because they remind researchers that a test built around familiar school number words may underestimate numerical reasoning learned and expressed through other systems Butterworth et al. (2008).
Tsimane' adults: the learned count range predicts exact responding
Pitt, Gibson, and Piantadosi investigated thirty Tsimane' adults whose knowledge of verbal counting varied within one population. In an exact matching task, the estimated point at which participants shifted from exact to approximate responding was bounded by their known number-word ranges. Within-community variation avoids some of the language-and-culture confounds of comparisons between unrelated populations and gives substantive support to the role of verbal counting in representing larger exact quantities Pitt et al. (2022).
The authors interpreted this result as evidence that large exact-number concepts are enabled by language. The direct observation remains tied to the participants and procedure: an individual's exact responding was associated with the verbal count range in the tested circumstances. Other studies reveal tasks where exact one-to-one matching is possible without naming cardinalities. A full theory must accommodate both phenomena by specifying the kind of exact representation being measured.
Awetý numerical expressions: an important 2026 comparison
A 2026 study examined numerical cognition among speakers of Awetý, an Amazonian language with a consistent set of exactly twenty conventional number words. The research enriches comparison across languages because number lexicons need not be classified simply as either extensive or absent. Different systems organize available quantities in specific ways, and their speakers may have varied experiences of numerical practices and language contact. The investigation uses small participant groups and culturally specific tasks, so it provides novel evidence for comparative theory rather than establishing a final universal causal law da Silva Sinha et al. (2026).
Why Number-Word Structure Matters
Transparent base-ten naming systems
Number languages differ in the extent to which their word structure expresses units, tens, and higher bases consistently. A system analogous to “two-ten-three” for twenty-three makes a compositional decimal relation acoustically or visually apparent. In English, historical expressions such as “eleven,” “twelve,” and various teen forms are less transparent. Learners must map both regular and irregular expressions onto Arabic numerals whose digit positions encode value systematically Berteletti et al. (2026).
Transparency can facilitate the learning of certain linguistic-to-numerical correspondences, particularly early place-value mapping. It does not make mathematical achievement automatic. A review by Ng and Rao found that attempts to explain East Asian students' broader mathematical achievement primarily through Chinese number-word regularity face mixed evidence and major cultural and educational influences. Language must be understood as one component of a larger learning system Ng and Rao (2010).
Number-word inversion: when units are named before tens
Some languages place the ones component before the tens component in spoken two-digit names. German “vierundzwanzig” literally corresponds to “four and twenty,” whereas the written numeral is 24. The linguistic sequence and the left-to-right digit sequence therefore present different orders. Children learning to write spoken number names as Arabic numerals may reverse digit positions, produce incorrect strings, or require additional processing time. Such errors are called transcoding errors and are especially informative when their form follows a predictable word-order pattern Klein et al. (2013).
Research on inversion extends to multi-digit comparison, estimation, and arithmetic. A 2025 review examined how inverted number naming can increase demands on place-value conversion and working memory and evaluated proposed instructional supports. Results are moderated by the task and the learner's familiarity with the linguistic structure; fluent adults may use learned compensation and familiar procedures. Evidence about average task effects should not be turned into judgments about the abilities of speakers of German, Dutch, or other languages Woo and Schiller (2025).
Base-twenty structures, irregularities, and context
Numerical languages can encode decimal and vigesimal patterns, mixed structural systems, or special forms for culturally important quantities. A naming system can support one decomposition of a problem while making another symbol conversion comparatively demanding. The cognitively relevant question is how easily the linguistic expression maps onto the numerical relations required by the task. It is not whether a language possesses some natural hierarchy of intelligence. Researchers increasingly study the combined roles of morphological order, symbol familiarity, schooling, and numerical base in number acquisition Berteletti et al. (2026).
Cognitive Architecture and Brain Mechanisms
Exact calculation and approximate magnitude engage different resources
A seminal study by Dehaene and colleagues combined behavioral experiments and neuroimaging to examine exact and approximate arithmetic across language conditions. Their findings supported a distinction between language-linked pathways important for exact learned calculation and representations useful for approximate magnitude judgments. An observer estimating that one group contains twice as many dots as another can rely on quantity processing, whereas retrieving a memorized multiplication fact can involve verbal learning and retrieval Dehaene et al. (1999).
Numerical tasks recruit distributed cognitive and neural processes. Quantity judgments often engage parietal networks; number-word retrieval can recruit language-related networks; reading Arabic symbols engages visual processing; holding intermediate arithmetic results engages working memory and executive control. This distribution changes with mathematical expertise, developmental stage, task format, and chosen strategy. Imaging evidence establishes task-sensitive associations, not an isolated anatomical organ dedicated to every aspect of number Dehaene et al. (1999); Berteletti et al. (2026).
Verbal, visual, and magnitude codes
A widely used family of models distinguishes the verbal form of a number, its visual Arabic notation, and a representation of quantity or magnitude. Converting spoken “twenty-four” into 24 recruits links between verbal and visual formats. Comparing a display of 24 dots with 30 dots relies substantially on magnitude. Recalling the product of six and seven may depend on a learned verbal fact, a written algorithm, or another strategy. The different routes can cooperate, and the same numerical problem can be solved through different combinations of representations Dehaene et al. (1999).
No single observed effect establishes that all numerical information is linguistically encoded. Naming a number aloud additionally requires lexical retrieval and speech production; writing the corresponding digits requires graphic symbol mapping. Experimental tasks should distinguish which phase carries the burden. Model comparisons are strongest when they yield different predictions about errors, timing, interference, or generalization beyond the training context.
Working memory, rehearsal, and mathematical procedures
Verbal rehearsal provides a compact way to maintain a count sequence or intermediate calculation. A person can hold “forty-eight” internally while processing “plus fifty-two,” and may organize longer strings into familiar chunks. Yet verbal memory also creates bottlenecks when number names are long or unfamiliar and when mathematical instructions consume the same resources needed to hold a result. Other strategies, including finger representations, external marks, written algorithms, and visual grouping, can reduce dependence on a verbal sequence Garcia et al. (2021).
Interference studies help identify these dependencies. Repeating irrelevant syllables during a calculation may reduce available verbal processing resources, whereas a visuospatial secondary task can disrupt a different route. Appropriate control tasks are essential: a secondary task also consumes attention and may reduce performance for reasons unrelated to verbal number concepts. Researchers therefore compare several interference conditions and response modalities rather than drawing a direct inference from any single decrease in accuracy.
Exact Arithmetic, Approximate Arithmetic, and Formal Mathematical Thought
Estimating a sum and deriving a precise result
Approximate addition produces an estimate of a combined quantity; exact addition produces a unique integer. An individual may recognize that combining two large dot arrays yields roughly one hundred items without being able to distinguish exactly ninety-nine from one hundred. Numerical estimation can be used to check plausibility, compare quantities, and choose among broad alternatives. Exact arithmetic requires procedures or representations that maintain the discrete result throughout calculation Pica et al. (2004).
Number words often support exact procedures, but written notation also redistributes memory demands. The problem 48 + 52 can be treated as forty plus fifty and eight plus two, or as a columnar operation that preserves partial results externally. Place-value knowledge permits decomposition, while procedural fluency determines whether the learner can coordinate the steps. The mathematical relation remains one hundred whether communicated in English, another language, sign, or digits.
Arithmetic facts, algorithms, and learned associations
Arithmetic uses strategies with different learning histories. A multiplication-table answer might be retrieved as a memorized verbal sequence; a learner can calculate the same product through repeated addition, decomposition, or visual arrays. Correct performance alone does not identify the strategy. A task that disrupts verbal rehearsal may affect a memorized fact more than a familiar written algorithm. Strategy questions, error analysis, and experimental manipulation of information format are more informative than the assumption that one computational pathway governs all mathematics Dehaene et al. (1999).
From arithmetic to higher mathematics
Complex mathematics draws on mathematical notation, spatial reasoning, working memory, learned symbolic conventions, and language for definitions, proof, and communication. Ordinary number words help establish early exact integer meanings, but advanced mathematics develops formal resources that are only partly dependent on everyday linguistic form. Algebraic expressions and diagrams can represent relations more compactly than full spoken explanations. The question of whether language supports a particular proof or calculation must specify the formal system, strategy, and prior learning involved. Evidence that number naming affects early place-value conversion cannot be directly generalized into a theory of every advanced mathematical discovery.
Bilingual and Multilingual Number Processing
The language in which facts were learned
A bilingual may encounter arithmetic facts in one classroom language, use another language in everyday conversation, and read Arabic numerals in both. A learned number-fact association can be easier to retrieve in the language practiced during instruction. Spoken word length, familiarity with numerical forms, proficiency, schooling, and the mathematical task all contribute. Some bilingual people shift readily between linguistic routes, while others incur costs when switching the format of a fact learned through repeated verbal rehearsal Garcia et al. (2021).
A meta-analysis of 38 within-participant studies and 1,861 bilingual participants reported an overall first-language advantage on certain speed and accuracy measures, moderated by second-language proficiency, language of schooling, age of acquisition, and task. The result identifies conditional processing differences, not a general bilingual mathematical disadvantage. The same person may perform magnitude comparisons equally well across languages while retrieving a memorized multiplication fact faster in the language associated with school practice Garcia et al. (2021).
Numerical comprehension versus language proficiency
Mathematics assessment can underestimate understanding if a student cannot easily parse the language of the problem. A learner who produces the right equation from a diagram but misinterprets a word problem may need assistance with quantitative sentence structure rather than basic arithmetic. Conversely, understanding every word of an equation story does not guarantee knowledge of the procedure. Fair assessment separates decoding, vocabulary, situational interpretation, magnitude representations, symbol mapping, and calculation Daroczy et al. (2015).
Sign Language, Homesign, and Language Access
The numerical possibilities of signed languages
Numerical language is not restricted to speech. Signed languages are fully structured natural languages with conventional ways of expressing number and relationships. Their visual-manual modality can offer handshape, spatial, and sequential structures that differ from speech and thereby reveal which linguistic properties matter for quantitative learning. A major 2026 review explicitly integrates signed and spoken language evidence rather than treating speech as the sole linguistic pathway to number concepts Berteletti et al. (2026).
Homesign and shared numerical systems
Spaepen and colleagues investigated adults using homesign systems developed without access to a conventional shared linguistic model. Participants faced limitations on tasks requiring exact representation of larger sets despite possessing manual communicative strategies. The evidence bears on acquisition of productive, shared numerical conventions. Homesign is distinct from an established signed language, and a finding about limited conventional linguistic input is not a finding that signing itself impairs numerical cognition Spaepen et al. (2011).
Language experience among deaf and hard-of-hearing children
Research on deaf and hard-of-hearing children requires a distinction between hearing status and access to language. Santos and colleagues studied oral deaf and hard-of-hearing preschoolers with restricted early access to spoken language. They documented group differences in numerical discrimination and number knowledge, with numerical group differences attenuated after taking account of time with auditory access to language. The results suggest a relationship between language experience and numerical development while leaving broader causes, individual differences, and intervention effects for further investigation Santos et al. (2023).
Timely access to a complete and comprehensible language, including a fully accessible sign language when appropriate, supports participation in numerical conversations and instruction. Research does not justify describing signed language as a lesser mathematical medium or making assumptions about the mathematical abilities of an individual from hearing status. The relevant history includes actual language access, educational experience, and opportunities to learn number concepts Santos and Cordes (2022).
Language in Mathematical Word Problems
From a sentence to a quantitative model
A mathematics word problem requires the learner to identify quantities, understand relational language, construct a situation model, and then choose or calculate an operation. The same arithmetic relationship can be expressed through sentences with markedly different linguistic complexity. “More than,” “less than,” “altogether,” “each,” “per,” and “remaining” can signal important relationships, but none is a universally reliable shortcut to one specific operation Daroczy et al. (2015).
Consider: “Lena has three more stones than Amir. Lena has eleven stones. How many does Amir have?” The phrase “more stones” occurs, yet solving requires recovering the unknown smaller quantity from a comparison. A child may know 11 − 3 while misunderstanding who has the larger collection or which set is unknown. Asking the learner to explain the relational structure can identify a comprehension difficulty before arithmetic computation begins.
Syntax, pronouns, temporal ordering, embedded comparisons, and irrelevant details add processing demands. A student who fails a story problem may successfully complete a mathematically equivalent symbolic calculation. Conversely, comprehending the sentence does not guarantee understanding how to calculate the answer. Evaluations that separately test linguistic interpretation and mathematical procedure provide a clearer picture of the learner's needs Daroczy et al. (2015).
Specialized mathematical vocabulary
Mathematics assigns technical meanings to terms such as “difference,” “equivalent,” “product,” “factor,” and “ratio.” Students must learn how the formal meaning connects to examples, diagrams, and equations. A verbal definition can be recited without being understood, just as a correct arithmetic operation can be memorized without an explanation. Effective instruction links everyday explanations to formal symbols and progressively introduces precise mathematical language.
How Researchers Test Language Effects on Number
Cross-format matching and give-a-number experiments
A cross-format task may show a set of objects and ask a participant to respond with a number word, written symbol, finger pattern, or second object set. A give-a-number task asks a learner to produce a requested cardinality. Manipulating whether collections remain visible, how much time is available, and whether counting is permitted helps distinguish perceptual correspondence from memorized labels and generalized cardinal concepts Sarnecka and Carey (2008); Pitt et al. (2022).
Controlled dot-array and approximate calculation tasks
Numerosity comparison experiments must distinguish number from total area, density, spacing, and element size. Brief presentation can discourage counting, while randomized variation of visual features makes nonnumerical shortcuts less reliable. Accuracy under different numerical ratios is analyzed alongside speed and potential individual differences. Studies of approximate arithmetic may also compare estimation before and after instruction in conventional number words Feigenson et al. (2004).
Transcoding, interference, and longitudinal designs
Transcoding tasks convert between spoken or signed number expressions and written digits. Word-order-related errors provide evidence about language-specific mapping demands, especially with multi-digit values. Dual-task experiments manipulate verbal rehearsal or visuospatial attention, ideally with difficulty-matched controls. Longitudinal studies examine whether early vocabulary and number processing predict later numerical achievement. Each method addresses a different causal question, and convergence among methods is stronger evidence than a single correlation or single-language result Klein et al. (2013); Levine et al. (2010).
Theoretical Disagreements and Research Boundaries
Strong linguistic necessity versus linguistic scaffolding
A strong account proposes that a productive count-word system is necessary for generalized exact integers beyond small sets. A scaffolding account emphasizes how symbols stabilize, transmit, and expand numerical capacities while allowing nonverbal alternatives for some exact tasks. Within-person count-range findings support a meaningful link between counting and portable exact-number representation; direct matching in Pirahã studies and findings among Indigenous Australian children demonstrate that exact performance can sometimes be achieved through different routes Pitt et al. (2022); Frank et al. (2008); Butterworth et al. (2008).
The disagreement becomes more precise when researchers define “exact representation.” A stable symbolic integer transferable across environments, a simultaneous one-to-one relation, and the memory of a set's cardinality after a delay are experimentally distinguishable. They may depend on language to different degrees. Research therefore needs explicit operational definitions, meaningful controls, and measurement approaches that respect diverse cultural and linguistic settings.
Established results and contested interpretations
Established evidence supports nonverbal approximate magnitude discrimination, developmental differentiation between count-list recitation and cardinal understanding, and language-sensitive effects on some number-transcoding tasks. Cross-method evidence supports important relationships between numerical language experience and exact-number learning. More limited evidence concerns how much a particular transparent number-naming structure improves broad educational achievement. Strict universal necessity claims about exact number concepts remain contested because the operational criteria vary. Theories explaining how successor knowledge constructs integers should be treated as theoretical interpretations grounded in evidence rather than observations of a single isolated mechanism Carey and Barner (2019); Ng and Rao (2010).
Cultural, developmental, and measurement limitations
Language groups differ in school exposure, numeracy practices, written notation, socioeconomic history, and test familiarity. Group contrasts therefore cannot independently establish that vocabulary caused an observed performance difference. Studies with small samples can reveal theoretically important patterns without resolving every alternative explanation. Tasks that require spoken answers may confound lexical retrieval with quantity processing, while tasks that allow simultaneous matching may permit nonverbal correspondence strategies. Longitudinal findings can improve temporal inference but still require attention to prior differences and shared environmental causes Butterworth et al. (2008); da Silva Sinha et al. (2026).
Implications for Education and Assessment
Instruction can coordinate concrete quantities, number words, signed expressions, written digits, and base-ten decompositions. Teachers can explicitly show why twenty-four consists of two tens and four units, even when the spoken form names the units first. Number lines, manipulatives, counting routines, and written algorithms provide complementary representations. Children benefit from tasks that connect labels to counted sets and ask them to explain what changes when one object is added or removed Sarnecka and Carey (2008); Woo and Schiller (2025).
A learner struggling with mathematics may experience a bottleneck in numerical vocabulary, place-value mapping, parsing a word problem, recalling a fact, or performing the calculation itself. These are distinct instructional targets. Language proficiency and accessible communication should be considered when interpreting a child's performance; a difficulty on an informal task does not establish a learning disorder. Condition-specific diagnostic evaluation belongs to appropriate clinical and educational specialists and requires more evidence than a single linguistic or arithmetic error.
Frequently Asked Questions
Can people understand number without having number words?
Yes, people can compare approximate magnitudes and track small sets without learned numerical expressions. Some exact correspondence tasks are also possible without naming cardinalities. Generalized exact integer reasoning across memory and contexts is strongly supported by a structured count sequence. The conclusion depends upon which numerical ability is being tested Frank et al. (2008).
Does a more regular number-naming language make students better at math?
Regular naming can simplify certain number-to-digit and place-value mappings. Overall mathematics achievement also depends on instruction, practice, educational systems, conceptual learning, and other factors. Broad comparisons do not isolate a universal language effect Ng and Rao (2010).
Does reciting a count list prove a child understands exact numbers?
No. Children can memorize a verbal sequence before assigning cardinal meanings to each expression. Researchers assess understanding using set-production tasks and the cardinal principle Sarnecka and Carey (2008).
Why do some bilinguals calculate more easily in one language?
Arithmetic facts learned in a particular language may be more rapidly retrieved through familiar verbal associations. Proficiency, age, school language, and the calculation procedure affect the pattern Garcia et al. (2021).
Do signed languages support exact numerical concepts?
Yes. Established signed languages provide conventional number expressions, and their visual-manual forms enrich scientific comparisons with speech. Findings about limited early language access do not describe a limitation of sign languages Berteletti et al. (2026).
Does difficulty with mathematics mean a person has a language disorder?
Numerical performance depends on multiple learned and cognitive components. Problems with a word question, verbal count sequence, or written symbol cannot alone establish either a language disorder or a mathematics learning disorder. Assessment must address the full pattern of knowledge, experience, and functional difficulties.
Are large language models numerical thinkers in the same way humans are?
A model's ability to produce mathematical language, write calculations, or solve selected problems does not establish that it uses the same perceptual numerosity mechanisms, developmental learning pathways, or subjective processes as humans. Mechanistic comparison requires specifically matched tasks and independent evidence. Human numerical development and artificial language generation are scientifically distinct research targets.
Scientific Synthesis
Language and numerical cognition operate through interacting perceptual, conceptual, linguistic, symbolic, and educational systems. Quantity perception and small-set tracking provide early numerical capacities. Number words make exact relations easier to name, preserve, communicate, and extend; written notation and formal procedures add further tools. Language-specific number naming influences particular pathways, especially counting, place-value conversion, verbal fact retrieval, and sentence-based calculation. Its effects are moderated by language access, proficiency, schooling, cognitive strategy, and the demands of the task.
The evidence supports a substantial role for language in scalable exact-number thinking while recognizing nonverbal foundations and alternative procedures. Scientific progress requires precise definitions of numerical concepts, culturally attentive methods, and careful distinctions between correlation, causal manipulation, and theoretical inference. Those distinctions explain why words matter profoundly for mathematics without reducing mathematical thought to the phonological form of number words Berteletti et al. (2026); Pitt et al. (2022).
Related Articles
Cluster Language, Thought and Psycholinguistics — the scientific overview of language processing and linguistic contributions to human thought.
Psycholinguistics: How Language Is Processed in the Mind — an account of mental language representations, comprehension, and learning.
Language Processing in the Brain: Cognitive Networks and Neural Systems — neural and cognitive systems participating in language processing.
Word Recognition: How the Mind Identifies Spoken and Written Words — word recognition and lexical access relevant to number-word comprehension.
References
Berteletti, I., Andin, J., Langdon, C., and Berch, D. B. (2026). Influences of spoken and signed language on numerical cognition. Nature Reviews Psychology, 5, 157–172. https://doi.org/10.1038/s44159-025-00530-1.
Butterworth, B., Reeve, R., Reynolds, F., and Lloyd, D. (2008). Numerical thought with and without words: Evidence from indigenous Australian children. Proceedings of the National Academy of Sciences, 105, 13179–13184. https://doi.org/10.1073/pnas.0806045105.
Carey, S., and Barner, D. (2019). Ontogenetic origins of human integer representations. Trends in Cognitive Sciences, 23, 823–835. https://doi.org/10.1016/j.tics.2019.07.004.
da Silva Sinha, V., Sabino, W. K., Göbel, S. M., and Majid, A. (2026). Numerical cognition in speakers of an Amazonian language with exactly twenty number words. Psychological Research, 90, Article 83. https://doi.org/10.1007/s00426-026-02300-x.
Daroczy, G., Wolska, M., Meurers, W. D., and Nuerk, H.-C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348. https://doi.org/10.3389/fpsyg.2015.00348.
Dehaene, S., Spelke, E., Pinel, P., Stanescu, R., and Tsivkin, S. (1999). Sources of mathematical thinking: Behavioral and brain-imaging evidence. Science, 284, 970–974. https://doi.org/10.1126/science.284.5416.970.
Feigenson, L., Dehaene, S., and Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8, 307–314. https://doi.org/10.1016/j.tics.2004.05.002.
Frank, M. C., Everett, D. L., Fedorenko, E., and Gibson, E. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108, 819–824. https://doi.org/10.1016/j.cognition.2008.04.007.
Garcia, O., Faghihi, N., Raola, A. R., and Vaid, J. (2021). Factors influencing bilinguals' speed and accuracy of number judgments across languages: A meta-analytic review. Journal of Memory and Language, 118, 104211. https://doi.org/10.1016/j.jml.2020.104211.
Gordon, P. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306, 496–499. https://doi.org/10.1126/science.1094492.
Klein, E., Bahnmueller, J., Mann, A., Pixner, S., Kaufmann, L., Nuerk, H.-C., and Moeller, K. (2013). Language influences on numerical development—Inversion effects on multi-digit number processing. Frontiers in Psychology, 4, Article 480. https://doi.org/10.3389/fpsyg.2013.00480.
Le Corre, M., and Carey, S. (2007). One, two, three, four, nothing more: An investigation of the conceptual sources of the verbal counting principles. Cognition, 105, 395–438. https://doi.org/10.1016/j.cognition.2006.10.005.
Levine, S. C., Suriyakham, L. W., Rowe, M. L., Huttenlocher, J., and Gunderson, E. A. (2010). What counts in the development of young children's number knowledge? Developmental Psychology, 46, 1309–1319. https://doi.org/10.1037/a0019671.
Ng, S. S. N., and Rao, N. (2010). Chinese number words, culture, and mathematics learning. Review of Educational Research, 80, 180–206. https://doi.org/10.3102/0034654310364764.
Pica, P., Lemer, C., Izard, V., and Dehaene, S. (2004). Exact and approximate arithmetic in an Amazonian indigene group. Science, 306, 499–503. https://doi.org/10.1126/science.1102085.
Pitt, B., Gibson, E., and Piantadosi, S. T. (2022). Exact number concepts are limited to the verbal count range. Psychological Science, 33, 371–381. https://doi.org/10.1177/09567976211034502.
Santos, S., Brownell, H., Coppola, M., Shusterman, A., and Cordes, S. (2023). Language experience matters for the emergence of early numerical concepts. npj Science of Learning, 8, Article 57. https://doi.org/10.1038/s41539-023-00202-w.
Santos, S., and Cordes, S. (2022). Math abilities in deaf and hard of hearing children: The role of language in developing number concepts. Psychological Review, 129, 199–211. https://doi.org/10.1037/rev0000303.
Sarnecka, B. W., and Carey, S. (2008). How counting represents number: What children must learn and when they learn it. Cognition, 108, 662–674. https://doi.org/10.1016/j.cognition.2008.05.007.
Spaepen, E., Coppola, M., Spelke, E. S., Carey, S. E., and Goldin-Meadow, S. (2011). Number without a language model. Proceedings of the National Academy of Sciences, 108, 3163–3168. https://doi.org/10.1073/pnas.1015975108.
Woo, V., and Schiller, L. K. (2025). How the inversion property in number-naming impedes mathematical performance, potential interventions to minimize its impact. Psychological Research, 89, Article 147. https://doi.org/10.1007/s00426-025-02177-2.