{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T10:52:58Z","timestamp":1791370378638,"version":"4.3.1"},"reference-count":34,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T00:00:00Z","timestamp":1791331200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Developmental Science"],"published-print":{"date-parts":[[2026,11]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>In this study, the developmental trajectory of children's finger\u2010based strategies for addition is described for the first time using a longitudinal design involving 207 children aged 4 \u00bd at the first testing point. Children were observed individually twice a year over a three\u2010year period. The trajectory typically followed by children corresponds to the one theoretically described in the literature as supporting the gradual internalization of finger strategies and leading to the complete mentalization of the solving process. More precisely, children progressed from a modeling strategy in which each operand of an addition is represented on the fingers of each hand, through a concrete counting\u2010on strategy, in which both operands are still represented but enumerated in a single continuous process, to a counting\u2010on strategy, in which only one operand is kept in mind while the other is tracked on fingers. The frequent use of the concrete counting\u2010on strategy between modeling and counting\u2010on strategies supports Baroody's proposition that it serves as a transitional step between concrete and more abstract forms of numerical representation. However, the concrete counting\u2010on strategy was associated with poor addition performance, suggesting that it corresponds to a reconstructive stage in which children gain new insights about numbers but lack the cognitive resources to fully capitalize on them. Overall, this study provides the first detailed description of the evolution of finger\u2010based strategies toward the internalization of the addition solving process.<\/jats:p>","DOI":"10.1111\/desc.70293","type":"journal-article","created":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T10:17:41Z","timestamp":1791368261000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Evolution of Finger Counting Strategies in Addition: A Three\u2010Year Longitudinal Study in Young Children"],"prefix":"10.1111","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7002-3924","authenticated-orcid":false,"given":"Marie","family":"Krenger","sequence":"first","affiliation":[{"name":"Institute of Psychology University of Lausanne  Lausanne Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3323-8467","authenticated-orcid":false,"given":"Jeanne","family":"Bagnoud","sequence":"additional","affiliation":[{"name":"Department of Psychology University of Hong Kong  Hong Kong SAR China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4997-1882","authenticated-orcid":false,"given":"Catherine","family":"Thevenot","sequence":"additional","affiliation":[{"name":"Institute of Psychology University of Lausanne  Lausanne Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,10,7]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0140525\ufffd;08005578"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2024.106154"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.2307\/749248"},{"key":"e_1_2_11_5_1","unstructured":"Barton K.2023. \u201cMuMIn: Multi\u2010Model Inference (R package version 1.47.5).\u201dhttps:\/\/cran.r\u2010project.org\/web\/packages\/MuMIn\/index.html."},{"key":"e_1_2_11_6_1","volume-title":"The Mathematical Brain","author":"Butterworth B.","year":"1999"},{"key":"e_1_2_11_7_1","first-page":"9","volume-title":"Addition and Subtraction: a Cognitive Perspective","author":"Carpenter T. P.","year":"1982"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/748348"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/20445911.2017.1396990"},{"key":"e_1_2_11_10_1","first-page":"3","volume-title":"Handbook of Mathematical Cognition","author":"Fayol M.","year":"2005"},{"key":"e_1_2_11_11_1","unstructured":"Education Endowment. Foundation.2023. \u201cHow to support children to \u201ccount on\u201d.\u201dhttps:\/\/educationendowmentfoundation.org.uk\/early\u2010years\/counting\u2010on."},{"key":"e_1_2_11_12_1","volume-title":"An R Companion to Applied Regression","author":"Fox J.","year":"2019"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/2041\u2010210X.12584"},{"key":"e_1_2_11_14_1","first-page":"67","volume-title":"Addition and Subtraction: A Cognitive Perspective","author":"Fuson K. C.","year":"1982"},{"key":"e_1_2_11_15_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3754-9","volume-title":"Children's Counting and Concepts of Number","author":"Fuson K. C.","year":"1988"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467\u20107687.2008.00715.x"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2026.106651"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cogdev.2024.101431"},{"key":"e_1_2_11_19_1","unstructured":"Krenger M. Bagnoud J. andThevenot C..2015.Finger counting strategies [Dataset]. Open Science Framwework.https:\/\/osf.io\/543yr\/overview?view_only=5937fa7b3412495f9849e60c629c1368."},{"key":"e_1_2_11_20_1","doi-asserted-by":"crossref","unstructured":"Krenger M. andC.Thevenot.2025. \u201cFinger Counting Is Not a Dead End: Early Finger Use as a Marker of Arithmetic Development.\u201dJournal of Cognition and Development1\u20139.https:\/\/doi.org\/10.1080\/15248372.2025.2606280.","DOI":"10.1080\/15248372.2025.2606280"},{"key":"e_1_2_11_21_1","doi-asserted-by":"crossref","unstructured":"Krenger M. andC.Thevenot.2026. \u201cThe Role of Children's Finger Counting History on Their Addition Skills.\u201dDevelopmental Psychology.https:\/\/doi.org\/10.1037\/dev0002099.<\/bib.","DOI":"10.1037\/dev0002099"},{"key":"e_1_2_11_22_1","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v082.i13"},{"key":"e_1_2_11_23_1","unstructured":"Lenth R. V.2025. \u201cemmeans: Estimated Marginal Means aka Least\u2010Squares Means (R package version 1.11.2).\u201dhttps:\/\/cran.r\u2010project.org\/web\/packages\/emmeans\/index.html."},{"key":"e_1_2_11_24_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478722"},{"issue":"1","key":"e_1_2_11_25_1","first-page":"268","article-title":"What Do Teachers Think About Finger\u2010Counting?","volume":"12","author":"Mutlu Y.","year":"2020","journal-title":"International Journal of Curriculum and Instruction"},{"key":"e_1_2_11_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10648\u2010023\u201009722\u20108.<\/bib"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2024.106031"},{"key":"e_1_2_11_28_1","volume-title":"The Child's Construction of Quantities: Conservation and Atomism","author":"Piaget J.","year":"1964"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.3390\/children9020132"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1111\/cdev.14146"},{"key":"e_1_2_11_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.actpsy.2023.104079"},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dr.2026.101252"},{"key":"e_1_2_11_33_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780195077872.001.0001","volume-title":"Emerging Minds: The Process of Change in Children's Thinking","author":"Siegler R. S.","year":"1996"},{"key":"e_1_2_11_34_1","first-page":"83","volume-title":"Addition and Subtraction: a Cognitive Perspective","author":"Steffe L. P.","year":"1982"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jecp.2024.106156.<\/bib"}],"container-title":["Developmental Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/desc.70293","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/desc.70293","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/desc.70293","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T10:17:45Z","timestamp":1791368265000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/desc.70293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,7]]},"references-count":34,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2026,11]]}},"alternative-id":["10.1111\/desc.70293"],"URL":"https:\/\/doi.org\/10.1111\/desc.70293","archive":["Portico"],"relation":{},"ISSN":["1363-755X","1467-7687"],"issn-type":[{"value":"1363-755X","type":"print"},{"value":"1467-7687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,7]]},"assertion":[{"value":"2025-12-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-09-18","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-10-07","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70293"}}