{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T05:45:26Z","timestamp":1775281526499,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T00:00:00Z","timestamp":1592956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Education Sciences"],"abstract":"<jats:p>The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and option elimination, for which chains of inferences based on premises and rules are accomplished. Focusing on the solutions of children aged 10\u201312 to an analytical reasoning problem proposed in two separate settings\u2014a web-based problem-solving competition and mathematics classes\u2014this study aims to find out what forms of deductive reasoning they undertake and how they express that reasoning. This was done through a qualitative content analysis encompassing 384 solutions by children participating in a beyond-school competition and 102 solutions given by students in their mathematics classes. The results showed that four different types of deductive reasoning models were produced in the two venues. Moreover, several representational resources were found in the children\u2019s solutions. Overall, it may be concluded that moderately complex analytical reasoning tasks can be taken into regular mathematics classes to support and nurture young children\u2019s diverse deductive reasoning models.<\/jats:p>","DOI":"10.3390\/educsci10060169","type":"journal-article","created":{"date-parts":[[2020,6,24]],"date-time":"2020-06-24T08:54:50Z","timestamp":1592988890000},"page":"169","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0746-7258","authenticated-orcid":false,"given":"Susana","family":"Carreira","sequence":"first","affiliation":[{"name":"University of Algarve, 8005-139 Faro, Portugal"},{"name":"UIDEF, Institute of Education, University of Lisbon, 1649-103 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5768-9633","authenticated-orcid":false,"given":"N\u00e9lia","family":"Amado","sequence":"additional","affiliation":[{"name":"University of Algarve, 8005-139 Faro, Portugal"},{"name":"UIDEF, Institute of Education, University of Lisbon, 1649-103 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4768-2080","authenticated-orcid":false,"given":"H\u00e9lia","family":"Jacinto","sequence":"additional","affiliation":[{"name":"Institute of Education, University of Lisbon, 1649-103 Lisboa, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,6,24]]},"reference":[{"key":"ref_1","unstructured":"NCTM (2000). Principles and Standards for School Mathematics, National Council of Teachers of Mathematics."},{"key":"ref_2","unstructured":"MOE (2012). Mathematics syllabus\u2014Primary One to Six, Ministry of Education\u2014Curriculum Planning and Developmental Division."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1023\/A:1003660018579","article-title":"Why Johnny can\u2019t prove","volume":"38","author":"Dreyfus","year":"1999","journal-title":"Educ. Stud. Math."},{"key":"ref_4","unstructured":"Lee, K. (2011). Students\u2019 Logical Reasoning and Mathematical Proving of Implications. [Ph.D. Thesis, Michigan State University]. Available online: https:\/\/d.lib.msu.edu\/etd\/1959."},{"key":"ref_5","first-page":"89","article-title":"Mathematicians and the Selection Task","volume":"Volume 3","author":"Fuglestad","year":"2004","journal-title":"Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway, 14\u201318 July 2004"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1024661004375","article-title":"Which notion of implication is the right one? From logical considerations to a didactic perspective","volume":"53","year":"2003","journal-title":"Educ. Stud. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1080\/10986060701854425","article-title":"Proof in school mathematics: Insights from psychological research into students\u2019 ability for deductive reasoning","volume":"10","author":"Stylianides","year":"2008","journal-title":"Math. Think. Learn."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1080\/10986060701533805","article-title":"Introducing young children to the role of assumptions in proving","volume":"9","author":"Stylianides","year":"2007","journal-title":"Math. Think. Learn."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Carreira, S., Jones, K., Amado, N., Jacinto, H., and Nobre, S. (2016). Youngsters Solving Mathematical Problems with Technology, Springer.","DOI":"10.1007\/978-3-319-24910-0"},{"key":"ref_10","unstructured":"Kaufman, S.B., Ross, H.J., and Silk, E.M. (2019, February 17). Available online: https:\/\/scottbarrykaufman.com\/wp-content\/uploads\/2013\/01\/Kaufman-Etal-2001-GRE-Problems.pdf."},{"key":"ref_11","unstructured":"Cox, R. (1996). Analytical Reasoning with Multiple External Representations. [Ph.D. Thesis, University of Edinburgh]. Available online: https:\/\/www.era.lib.ed.ac.uk\/bitstream\/handle\/1842\/10550\/Cox1996.pdf."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1080\/13546780042000091","article-title":"The processing of negations in conditional reasoning: A meta-analytic case study in mental model and\/or mental logic theory","volume":"7","author":"Schroyens","year":"2001","journal-title":"Think. Reas."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1146\/annurev.psych.50.1.109","article-title":"Deductive reasoning","volume":"50","year":"1999","journal-title":"Annu. Rev. Psychol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1080\/13546789508251508","article-title":"A model point of view","volume":"1","author":"Byrne","year":"1995","journal-title":"Think. Reas."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1080\/13546780244000024","article-title":"Mental model theory versus the inference rule approach in relational reasoning","volume":"8","year":"2002","journal-title":"Think. Reas."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1348\/026151006X153127","article-title":"The contribution of logical reasoning to the learning of mathematics in primary school","volume":"25","author":"Nunes","year":"2007","journal-title":"Br. J. Dev. Psychol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1080\/00029890.2003.11920029","article-title":"The role of logic in teaching proof","volume":"110","author":"Epp","year":"2003","journal-title":"Am. Math. Mon."},{"key":"ref_18","unstructured":"Bak\u00f3, M. (2019, March 12). Why we need to teach logic and how we can teach it. Available online: http:\/\/www.cimt.plymouth.ac.uk\/journal\/bakom.pdf."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1023629608614","article-title":"Students\u2019 understandings of logical implication","volume":"51","author":"Hoyles","year":"2002","journal-title":"Educ. Stud. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10649-008-9136-2","article-title":"Deductive reasoning: In the eye of the beholder","volume":"69","author":"Ayalon","year":"2008","journal-title":"Educ. Stud. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1080\/13546783.2017.1384760","article-title":"The link between deductive reasoning and mathematics","volume":"24","author":"Morsanyi","year":"2018","journal-title":"Think. Reas."},{"key":"ref_22","unstructured":"Lommatsch, C.W. (2018). Learning Logic: A mixed methods study to examine the effects of context ordering on reasoning about conditionals. [Ph.D. Thesis, Utah State University]. Available online: https:\/\/digitalcommons.usu.edu\/etd\/7011."},{"key":"ref_23","first-page":"239","article-title":"Supporting the use of external representations in problem solving: The need for flexible learning environments","volume":"6","author":"Cox","year":"1995","journal-title":"Int. J. Artif. Intell. Educ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/135467898394157","article-title":"Children\u2019s reasoning in solving relational problems of deduction","volume":"4","author":"English","year":"1998","journal-title":"Think. Reas."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1080\/13546780542000023","article-title":"Predicting the difficulty of complex logical reasoning problems","volume":"12","author":"Newstead","year":"2006","journal-title":"Think. Reas."},{"key":"ref_26","unstructured":"Krippendorff, K. (2004). Content Analysis: An Introduction to its Methodology, Sage Publications. [2nd ed.]."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Schreier, M. (2012). Qualitative Content Analysis in Practice, Sage Publications.","DOI":"10.4135\/9781529682571"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1006\/drev.2000.0533","article-title":"The development of conditional reasoning: A mental model account","volume":"22","author":"Markovits","year":"2002","journal-title":"Dev. Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1017\/S0140525X00212442","article-title":"Mental model theory and pragmatics","volume":"23","year":"2000","journal-title":"Behav. Brain Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1037\/1076-898X.7.4.308","article-title":"Mental models and logical reasoning problems in the GRE","volume":"7","author":"Yang","year":"2001","journal-title":"J. Exp. Psychol. Appl."},{"key":"ref_31","first-page":"51","article-title":"O racioc\u00ednio matem\u00e1tico aos seis anos: Caracter\u00edsticas e fun\u00e7\u00f5es das representa\u00e7\u00f5es dos alunos (Mathematical reasoning at age six: Characteristics and functions of students\u2019 representations)","volume":"21","author":"Canavarro","year":"2012","journal-title":"Quadrante"}],"container-title":["Education Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7102\/10\/6\/169\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:42:24Z","timestamp":1760175744000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7102\/10\/6\/169"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,24]]},"references-count":31,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6]]}},"alternative-id":["educsci10060169"],"URL":"https:\/\/doi.org\/10.3390\/educsci10060169","relation":{},"ISSN":["2227-7102"],"issn-type":[{"value":"2227-7102","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6,24]]}}}