1. Introduction and problem

In the 3-to-6-year span—kindergarten, preschool, CENDI, infant school—a package of three artefacts has been installed as if it counted as mathematical literacy. The first is an app that “practises” counting: a screen that asks the child to tap, drag or recite a sequence and declares that the child “already counts.” The second is a chatbot that poses problems: a generative system that produces prompts or “number challenges” and delivers them as if the output were mathematical thinking. The third is a model that personalizes worksheets: an algorithm that adjusts sheets, items or paths and presents them as if personalization were number sense. All three are visible and cheap in coordination time. They allow a setting to exhibit that it “already does mathematics with artificial intelligence.” The leap—from completing an item or receiving a generated problem to claiming that there is numeracy—is authorized neither by the evidence on educational apps nor by what classrooms measure when there is number sense, comparison and composition–decomposition.

The thesis of this article is restrictive. An app that drills counting, a chatbot that poses problems or a model that personalizes worksheets do not constitute mathematical literacy in early childhood education. At this stage numeracy is embodied number sense, comparison, composition–decomposition and mathematical conversation with adults and peers about real objects and situations; not digital drill or automatic tutoring. Kim, Gilbert, Yu, and Gale (2021), with thirty-six studies of educational apps from preschool to Grade 3, find a mean effect of +0.31 standard deviations, comparable in mathematics and in literacy, and larger for constrained than for unconstrained skills. That does not authorize translating “there is a counting app” as “there is numeracy.” It authorizes asking what was measured: often recitation, numeral identification or a practice item, not the comparison of collections, not the composition of five as three and two, not conversation about how many remain when a part is hidden. NCTM (2022) warns, explicitly, against narrowing early childhood mathematics to rote counting, number recognition and “answer-getting” activities. An algorithm that generates a “problem of the week” does not converse. It administers a prompt that the profession did not interpret with the body or with the objects in the room.

The problem is worsened by a professional reason that product sheets do not mention. Numeracy at ages 3 to 6 is not the anticipation of a primary-school arithmetic workbook, nor an accumulation of correct taps, nor a personalized path of items. Number is not a property of the interface, but of the use of the body, of the comparison of collections and of conversation with an adult who holds the question about real objects (Björklund, Marton, and Kullberg, 2021; Way and Cartwright, 2025; Turan and De Smedt, 2022; OECD, 2021). Confusing the product—app, prompt, generated worksheet—with the process is the category error this paper names. Outhwaite, Early, Herodotou, and Van Herwegen (2023), analysing twenty-three mathematics apps evaluated in the first three years of schooling, find that practice-based apps are the most common (fifteen of twenty-three) and that the predominant content is basic number representation. Inference, marked as such: the market of “AI for early numeracy” inherits that distribution and automates it. It turns recitation and the drill item into the whole of mathematical literacy.

This paper does not recycle the axes already treated in this series. The question is one of pedagogical category: what counts as numeracy when an early-years setting “does AI and mathematics.” The contributions are three: to reconstruct the state of the art that separates embodied number sense, comparison and composition–decomposition from digital drill; to examine three families of cases; and to offer four tests for deciding when a kindergarten may claim that there is mathematical literacy, and not only an app, a chatbot or a feed of worksheets.

2. State of the art: from numeracy as number sense to the artefact on display

Four strata that the market of “AI for early numeracy” usually mixes should be kept apart. The first is numeracy at ages 3 to 6 as embodied number sense, comparison and composition–decomposition (Björklund, Marton, and Kullberg, 2021; Way and Cartwright, 2025; Roesch et al., 2026; Poletti et al., 2025; Alkaş Ulusoy et al., 2023; Bakker, Torbeyns, Verschaffel, and De Smedt, 2023; Clements, Sarama, Baroody, Kutaka, Chernyavskiy, Joswick, Cong, and Joseph, 2021). The second is mathematical conversation with adults and peers about real objects and situations (Turan and De Smedt, 2022; Ekdahl, 2021; Ferrara and Ferrari, 2023). The third is the evidence on apps, digital practice and AI that interacts, personalizes or proposes (Kim et al., 2021; Outhwaite et al., 2023; Chen, 2024; Su and Yang, 2022; Ljungcrantz, 2026). The fourth is the framework of rights, systems and developmentally appropriate practice, which treats the 3–6-year-old as a subject of process interactions, not as the user of a drill interface (OECD, 2021, 2023; NAEYC, 2022; NCTM, 2022; UNESCO, 2021; Miao and Holmes, 2023; European Commission, 2022).

In the number-sense stratum, Björklund, Marton, and Kullberg (2021) isolate, in 2 184 observations of children aged 4 to 7, what has to be discerned: representation, ordinality, cardinality and part–whole relations. Way and Cartwright (2025) link, over six months and nine children, embodied activities with subitizing, counting and magnitude. Roesch, Conze, and Moeller (2026) find a medium effect of a finger-based intervention, driven by counting, not by cardinality. Poletti et al. (2025) show that training finger counting raises addition from 37.3% to 77.1% in 328 children aged 5 to 6. Alkaş Ulusoy et al. (2023) find that a part–whole strategy outperforms counting alone. Bakker et al. (2023) measure, in 410 children, counting, comparison and arithmetic. Clements et al. (2021), with 291 kindergartners, find that following the trajectory outperforms jumping to the target. Status: finding that early numeracy runs through the body, comparison and part–whole relations. Inference: a recitation app does not cover, by existing, that profession.

In the conversation stratum, Turan and De Smedt (2022) review eighteen studies: mathematical language—quantitative and spatial terms, not only the labels “one, two, three”—is associated with mathematical abilities concurrently and longitudinally, and interventions that work on it move those abilities. Ekdahl (2021) analyses sixty-seven video recordings of nine Swedish teachers who, with 5-year-olds, play the “snake game”: decompose a collection, hide a part, compare finger patterns. Ferrara and Ferrari (2023) observe twenty-five 5-year-olds who first move on a floor strip and then touch a surface: number is made with the body and with matter, not only with a symbol. Status: finding that numeracy is verified in conversation and in the bodily encounter with collections. Inference: a chatbot that “poses a problem” is not that conversation.

In the apps-and-AI stratum, Kim et al. (2021) estimate +0.31, with larger effects on constrained skills. Outhwaite et al. (2023) document that practice apps predominate and that a personalized path appears as an ingredient of those that report gains. Chen (2024) maps eighteen articles, eleven countries and 15 081 children aged 2 to 8, and extracts AI that interacts and AI that personalizes. Su and Yang (2022) and Ljungcrantz (2026) saturate the growth of the field. Status: finding about the field, not that a chatbot or a personalized worksheet constitutes numeracy. Inference: practising, posing and personalizing is what the three artefacts sell as “mathematical literacy with AI is already happening.”

In the systems stratum, OECD (2021) anchors ECEC quality in process interactions. OECD (2023) locates digitalization in staff, protection and meaningful uses, not in a feed of items. NAEYC (2022) requires developmentally appropriate practice. NCTM (2022) requires not narrowing 3–6 mathematics to rote counting and “answer-getting.” UNESCO (2021) requires human oversight. Miao and Holmes (2023) set a threshold of 13 years for independent conversations with generative platforms and require pedagogical validation. The European Commission (2022) and the U.S. Department of Education (2023) agree on not replacing professional judgement. Inference: a four-year-old is not the user of a drill app, a chatbot or a model that “personalizes the worksheet.” The child is the subject of a number sense that a responsible adult exercises with the body, with collections and with the group in view.

3. Review method

A critical narrative review was conducted, not a meta-analysis. The purpose was not to estimate a homogeneous effect size, but to articulate an argument of pedagogical category with verified sources. Inclusion criteria: (a) 2021–2026; (b) numeracy, number sense, comparison, composition–decomposition, mathematical language, mathematics apps or AI in early childhood education, or explicitly marked transfer when the sample is not ages 3–6; (c) relevance to kindergarten, preschool, CENDI or ages 3–6; (d) peer-reviewed journal, DOI, or a NAEYC, NCTM, UNESCO, OECD, European Commission or education-department report; (e) verifiable DOI or publisher page. Axes already used in this series were excluded as a central object, although some appear as a limit.

The search was run on 27 August 2026 on DOI pages, Springer, Elsevier, Wiley, SAGE, Frontiers, MDPI, OECD iLibrary, UNESDOC, ERIC, NAEYC, NCTM, Nature, APA and publisher sites. Each source was checked against at least one of those pages. Empirical finding, conceptual or normative framework, and pedagogical inference marked as such were distinguished.

4. Case 1. Practising counting in an app, receiving a chatbot problem or a personalized worksheet is not doing numeracy

Kim, Gilbert, Yu, and Gale (2021) publish in AERA Open the synthesis that best names the first artefact when it is presented as mathematical literacy. They meta-analyse thirty-six intervention studies and 285 effect sizes of educational apps for children from preschool to Grade 3. The mean weighted effect is +0.31 standard deviations on achievement, comparable in mathematics (+0.29) and in literacy (+0.35). Three moderators matter: the effect is larger in preschool than in K–3; larger with researcher-developed measures than with standardized tests; and larger for constrained than for unconstrained skills. Status of the evidence. Empirical finding of synthesis: educational apps, in programmes that pass the filters, are associated with gains against a counterfactual. It is not a finding that owning a counting app constitutes numeracy, nor that number sense is covered. The datum the market does not cite is constrained skills. Reciting a sequence, identifying a numeral or tapping the correct item are precisely what an app knows how to measure. Pedagogical inference, marked as such: this is the gesture a kindergarten copies when it “does mathematics with an app.” The product is installed, taps or a counting test are measured, and literacy is declared fulfilled. What there is is an artefact. Numeracy, in Björklund, Marton, and Kullberg (2021), in NCTM (2022) and in NAEYC (2022), asks for discerning cardinality, part–whole relations and comparison with objects and with an adult. A drill app does not observe it.

Outhwaite, Early, Herodotou, and Van Herwegen (2023) saturate the portrait with the inventory that best illustrates the category leap. Building on a prior review of fifty studies and seventy-seven apps with 23 981 children in the first three years of schooling, they analyse a subset of twenty-three apps: fifteen are practice-based; twenty-one target basic number skills (representation and relationships). A qualitative comparative analysis finds that observed gains are associated with the combination of a personalized path (programmatic levelling), explanatory feedback and praise. Status: finding on the design of mathematics apps in the first years of school, with marked transfer when the sample is not kindergarten in isolation. It is not a finding that personalization constitutes number sense. Inference, marked as such: the “personalized path” that the third artefact sells as innovation is, in this corpus, a trait of practice apps. A model that personalizes worksheets inherits that logic: it adjusts the item; it does not open comparison or the decomposition of a real collection. Clements and Sarama (2025), reviewing learning trajectories in early mathematics, confirm that developmental progressions describe children’s knowledge and that instruction anchored in them outperforms other approaches in rigorous trials. Inference: personalizing a workbook of items is not following a learning trajectory. It is jumping to the target the interface knows how to score.

Clements, Sarama, Baroody, Kutaka, Chernyavskiy, Joswick, Cong, and Joseph (2021) name the error of “teaching to a target.” Two hundred and ninety-one kindergartners are assigned to instruction one level above their present thinking or to instruction that skips three levels. Those who follow the trajectory learn more, including target knowledge. Status: finding that jumping to the target item is not the most effective path, even for reaching that target. Inference: this is the second gesture the setting copies. A chatbot poses a problem further up, or a model personalizes the worksheet to the grade standard, and numeracy is declared. Chen (2024) maps interaction and personalization. Su and Yang (2022) and Ljungcrantz (2026) saturate the AI-in-ECE field. Miao and Holmes (2023) exclude children under 13 as independent interlocutors of generative platforms. Inference: a system that produces “the problem of the week” personalizes a path; it does not compare collections. A CENDI that delivers the “AI-generated number challenge” has made a product. Numeracy is verified if the group compared, composed and spoke. It is not verified in the prompt.

5. Case 2. What the kindergarten does do when there is numeracy: embodied number sense, comparison and composition–decomposition

Way and Cartwright (2025) publish in Education Sciences the case study that, in this corpus, best names early numeracy as a craft of the body, not as a drill interface. In an Australian preschool they follow, for six months, one teacher and nine children (from 3 years 11 months to 5 years 3 months). They find connections between embodied activities—fingers, drawing, magnitude—and the development of subitizing, counting and magnitude knowledge. Status of the evidence. Empirical finding of process in a small, situated N. It is not a finding about AI, nor that a tapping app reproduces that craft. It is not generalized to a Latin American CENDI. Pedagogical inference, marked as such: this is the object an early-years setting may call embodied number sense. Fingers are not an ornament: they are the medium with which one represents, compares and composes. An app that asks the child to tap the numeral does not place the child as protagonist of a collection. A model that personalizes worksheets does not investigate: it prescribes the item.

Roesch, Conze, and Moeller (2026) saturate the portrait with twelve thirty-minute sessions, using fingers as an embodied manipulative. Thirty-three children aged 5 to 6 receive the programme; thirty-seven, business-as-usual teaching. The effect on early numeracy is medium; there are no equivalent gains in spatial working memory or fluid reasoning. It is driven mainly by counting; cardinality shows no group effect. Finger users outperform non-users. Status: finding that embodying counting moves numeracy, with a ceiling on cardinality in this design. Inference: a kindergarten cannot treat “we already use fingers in the app” as equivalent to that intervention. Poletti, Krenger, Létang, Hennequin, and Thevenot (2025), with 328 children aged 5 to 6 in France, show that those who did not count on their fingers and receive finger-counting training move from 37.3% to 77.1% accuracy in addition, against a passive control from 39.6% to 47.8% (ηp2 = 0.15). Status: finding of addition with the hand, not that the avatar on a screen replaces the finger. Inference: the body that counts is the child’s hand, in an adult’s view.

Alkaş Ulusoy, Kayhan Altay, Özer, and Umay (2023) name composition–decomposition when it is distinguished from counting. In six Turkish public schools, 43 kindergarten children (61–80 months) solve part–whole tasks from 1 to 7 with fingers, visual forms and hidden objects. Those who use a part–whole strategy outperform those who only count. Status: qualitative finding of process, not a trial and not AI. Inference: a kindergarten that “already practises counting on the tablet” may be training, exactly, the weaker strategy in this study. Björklund, Marton, and Kullberg (2021) give the map: without discerning the part–whole relation there is no powerful arithmetic in the range 1–10. Björklund, Ekdahl, and Runesson Kempe (2021) implement a structural approach with 65 five-year-olds; analysis of a group of eight shows that changing the way of experiencing number allows more advanced strategies. Bakker, Torbeyns, Verschaffel, and De Smedt (2023) measure, in 410 children (mean 58.14 months), counting, numeral identification, comparison, ordering and arithmetic, and find four pathways. This article does not convert the home-environment finding—which here does not predict—into a family–school study: the object retained is that numeracy jointly includes counting, comparison and operations. Inference: an app that only scores counting does not describe numeracy. It describes a cut.

6. Case 3. Mathematical conversation with adults and peers about real objects, not the problem a model poses

Turan and De Smedt (2022) publish in Educational Research Review the synthesis that, in this corpus, best names mathematical conversation as an object, not as “more oral language.” After PRISMA and a critical appraisal they retain eighteen studies of sufficient quality. Mathematical language includes terms for numbers and operations, and also quantitative and spatial terms that are not number labels (fewer, the middle one, a few). It is associated, concurrently and longitudinally, with mathematical abilities. Interventions that work on it move those abilities. Status of the evidence. Empirical finding of review: mathematical language is not an ornament of recitation. This article does not convert it into a study of orality or narration: the object retained is the lexicon and the conversation specific to quantity, comparison and spatial relation over mathematical situations. Pedagogical inference, marked as such: a chatbot that “poses a problem” is not that conversation. It is not in the room, does not point to a collection, does not compare one child’s finger pattern with another’s, does not ask “how many are left?” about a hidden object. It produces text. Early numeracy is verified if an adult and peers talked about more, less, parts and wholes, with objects in view.

Ekdahl (2021) saturates the portrait from the profession. Nine Swedish preschool teachers, in collaboration with a research team, enact the same activity—the “snake game,” a decomposition in which a part of a collection is hidden—with 5-year-olds, over three months. Sixty-seven video recordings. The activity becomes mathematically richer when the teacher compares children’s different finger patterns and uses systematically varied examples of number relations. Status: finding of process on enactment, not of AI. Inference: this is the category criterion. Numeracy does not reside in the material (the snake, the objects, the fingers), but in the conversation that makes part–whole relations visible. A model that generates “ten decomposition problems” does not compare finger patterns. It delivers items. Ferrara and Ferrari (2023) observe, in a kindergarten in Northern Italy, twenty-five 5-year-olds in eight three-hour sessions: first a strip on the floor, then a multi-touch application. The focus is physicality and materiality: children, surfaces and number come together provisionally. Status: finding of process on embodied encounters, not that a drill app reproduces that craft. The application in this study is not a counting workbook: it is a surface that is touched after the number has been walked. Inference: a kindergarten cannot treat any “mathematics” screen as equivalent to that encounter. The body on the strip is the first pole. The personalized worksheet does not contain it.

Clements et al. (2021) and Clements and Sarama (2025) confirm, by contrast, that instruction that follows the child’s present thinking—not the system’s target item—produces more learning. NCTM (2022) requires strengthening problem solving and reasoning, not narrowing to rote counting. OECD (2021) anchors quality in process interactions. Inference: AI enters early numeracy, if at all, on the side of the adult who converses with the group—as support for recording a comparison or varying part–whole examples—subject to pedagogical validation (Miao and Holmes, 2023). It does not enter as a chatbot that poses the problem or as a model that prints the worksheet. OECD (2023) locates digitalization in meaningful uses. The European Commission (2022) and the U.S. Department of Education (2023) require not replacing judgement. Inference: a system that generates “the number problem of the day” and measures clicks is not an innovation in mathematical literacy. It is a category error. The conversation that serves is the one an adult holds over a collection the group has in its hands.

7. Inferential framework: four tests for claiming that there is numeracy, not an artefact

The framework that follows is pedagogical inference from this article, anchored in the cases and in the verified instruments. It is not a new international standard. It distinguishes four tests. If a kindergarten, preschool, CENDI or infant school does not pass them, it cannot declare that an app that drills counting, a chatbot that poses problems or a model that personalizes worksheets constitute mathematical literacy.

7.1. Test of embodied number sense, not of the recited sequence. Kim et al. (2021) document app gains, larger on constrained skills. Outhwaite et al. (2023) document the predominance of practice. Way and Cartwright (2025) locate subitizing, fingers and magnitude. Roesch et al. (2026) and Poletti et al. (2025) locate the hand. NCTM (2022) rejects narrowing to rote counting. Inference: evidence of numeracy is verified if the child represented, subitized or structured a quantity with the body and with collections. If the “evidence” that the setting does mathematical literacy is the log of correct taps or the file of generated problems, the setting has done inventory, not number sense.

7.2. Test of comparison and of composition–decomposition, not of the drill item. Bakker et al. (2023) measure comparison alongside counting and arithmetic. Björklund, Marton, and Kullberg (2021) isolate the part–whole relation as a critical aspect. Alkaş Ulusoy et al. (2023) show that a part–whole strategy outperforms counting alone. Björklund, Ekdahl, and Runesson Kempe (2021) show that a structural approach changes the way of experiencing number. Clements et al. (2021) show that jumping to the target yields less. Inference: the 3–6-year-old is not the operator of a personalized worksheet. The child is the subject of a comparison (“where is there more?”) and of a decomposition (“five is three and two”) with objects in view. If AI enters, it enters as the adult’s workshop—for example, to help vary part–whole examples—subject to pedagogical validation. It does not enter as a board of items or as a screen that replaces the collection.

7.3. Test of mathematical conversation about real objects, not of the generated problem. Turan and De Smedt (2022) locate mathematical language as predictor and intervention. Ekdahl (2021) locates the comparison of finger patterns in a shared decomposition. Ferrara and Ferrari (2023) locate the body and matter. Miao and Holmes (2023) exclude children under 13 as independent interlocutors. Inference: early numeracy is not a child who “already solves the chatbot’s problem alone.” It is an adult and peers who talk about quantity, more and less, parts and wholes, over a real situation. A model that poses problems inverts the profession: it delivers the question ready-made and measures fidelity to the item.

7.4. Test of rights and of professional judgement, not of the product catalogue. UNESCO (2021) requires human oversight. Miao and Holmes (2023) require pedagogical validation. The European Commission (2022) and the U.S. Department of Education (2023) require not replacing the teacher. NAEYC (2022) requires developmentally appropriate practice. NCTM (2022) requires not narrowing to rote counting. OECD (2021, 2023) anchors quality in process interactions and in meaningful digital uses. Inference: an early-years setting cannot treat the child as the operator of a drill app, a chatbot or a feed of worksheets. Numeracy is not fulfilled by reciting the sequence better. It is fulfilled by comparing, composing and conversing with the body, with objects and with adults who hold the question.

The framework admits the digital when it is subordinated to embodied number sense and to conversation about real collections (Ferrara and Ferrari, 2023; Way and Cartwright, 2025; Turan and De Smedt, 2022). It admits fingers, decomposition and comparison (Poletti et al., 2025; Roesch et al., 2026; Alkaş Ulusoy et al., 2023; Bakker et al., 2023). It rejects declaring mathematical literacy on the basis of a counting app, a chatbot or a model that personalizes worksheets (Kim et al., 2021; Outhwaite et al., 2023; Chen, 2024; Clements et al., 2021).

8. Discussion

Three tensions organize the discussion. The first is between exhibiting an artefact and discerning number. It is a finding that apps are associated with gains, especially on constrained skills (Kim et al., 2021); that practice and personalization predominate (Outhwaite et al., 2023); and that the AI-in-ECE field grew to thirty-nine studies in 2020–2024 (Ljungcrantz, 2026; Chen, 2024). It is a framework that quality is at stake in process interactions and that mathematics at ages 3–6 must not be narrowed to rote counting (OECD, 2021; NAEYC, 2022; NCTM, 2022). It is not a finding that an app, a chatbot or a personalized worksheet produce the craft that Way and Cartwright (2025), Björklund, Marton, and Kullberg (2021) and Turan and De Smedt (2022) observe. The three artefacts measure what engineering knows how to deliver and declare what only number sense would authorize.

The second is between reciting and relating. Kim et al. (2021) show the bias toward the constrained. Alkaş Ulusoy et al. (2023) show that part–whole outperforms counting alone. Bakker et al. (2023) measure a bundle—counting, comparison, ordering, arithmetic—not a single recitation indicator. Inference: insisting that the kindergarten “already does numeracy” because there is a counting app is an inverted pedagogy. Recitation is made to stand for comparison, composition and conversation. The child is left as operator; the adult, as supervisor of fidelity to the item.

The third is between the adult who converses about a collection and the model that prescribes the problem. Ekdahl (2021) shows that the same activity becomes richer when finger patterns are compared. Miao and Holmes (2023) exclude children under 13. Inference: the only use of AI that does not contradict numeracy at ages 3–6 is the one that remains on the side of the adult who compares, decomposes and talks with the group, subject to pedagogical validation. A chatbot that poses problems because the system needs a product is not that use. An app that is tapped to fill the “digital mathematics” hour is not that use.

9. Limits

This review is narrative. It does not apply PRISMA or estimate combined effects. Kim et al. (2021) cover preschool to Grade 3. Outhwaite et al. (2023) cover the first three years of schooling, with marked transfer. Clements et al. (2021) are kindergarten. Way and Cartwright (2025) are N = 9. Roesch et al. (2026) do not move cardinality. Poletti et al. (2025) measure addition, not the whole of numeracy. Alkaş Ulusoy et al. (2023) are qualitative, N = 43. Ferrara and Ferrari (2023) are an Italian kindergarten. Ekdahl (2021) is Sweden and nine teachers. Turan and De Smedt (2022) review mathematical language, not AI. Chen (2024), Su and Yang (2022) and Ljungcrantz (2026) map AI in ECE, not kindergarten numeracy. NAEYC, NCTM, UNESCO and OECD are framework. Bakker et al. (2023) include the home environment as a covariate that does not predict; this article does not convert that into a family–school study. No Latin American AI trials were located that measure comparison and composition–decomposition against a feed of generated problems in kindergarten. The inferences in section 7 are hypotheses of pedagogical category, not implementation evidence.

10. Conclusions

An app that drills counting, a chatbot that poses problems or a model that personalizes worksheets do not constitute mathematical literacy in an early childhood education setting. The verified evidence does not authorize that declaration. Thirty-six app studies estimate a medium effect, larger on constrained skills (Kim et al., 2021). Twenty-three apps show the predominance of practice and of path personalization (Outhwaite et al., 2023). Two hundred and ninety-one kindergartners learn more when instruction follows the trajectory, not when it jumps to the target (Clements et al., 2021). Eighteen and thirty-nine reviews saturate the growth of AI in ECE without equating it to kindergarten numeracy (Chen, 2024; Su and Yang, 2022; Ljungcrantz, 2026). By contrast, when there is numeracy in the early years, there is body, comparison, part–whole relations and conversation: nine children whose subitizing and magnitude are linked to embodied activities (Way and Cartwright, 2025); fingers that move counting and addition (Roesch et al., 2026; Poletti et al., 2025); part–whole outperforming counting alone (Alkaş Ulusoy et al., 2023; Björklund, Marton, and Kullberg, 2021); comparison as a component of pathways (Bakker et al., 2023); mathematical language that predicts and that is intervened (Turan and De Smedt, 2022); and a decomposition that is enriched when finger patterns are compared (Ekdahl, 2021). Current guidance requires not narrowing to rote counting, human oversight, pedagogical validation and not replacing professional judgement (NCTM, 2022; UNESCO, 2021; Miao and Holmes, 2023; European Commission, 2022; U.S. Department of Education, 2023).

Where the sources do not measure a kindergarten, this article does not claim it. Where they measure an app, a generated problem or a personalized worksheet, it does not translate them into numeracy. Accompanying three- to six-year-olds in mathematical literacy is to exercise embodied number sense, to compare and compose–decompose collections, and to converse with adults and peers about real objects and situations. The rest is digital drill and automatic tutoring. It is not numeracy, and it should not be presented as what it is not.

Editorial Laboratory of NEXTECH.IA / Ingeniero Mitre.

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