{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T07:16:48Z","timestamp":1773559008791,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,23]],"date-time":"2021-11-23T00:00:00Z","timestamp":1637625600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/50008\/2020 (IT)"],"award-info":[{"award-number":["UIDB\/50008\/2020 (IT)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00194\/2020 (CIDTFF)"],"award-info":[{"award-number":["UIDB\/00194\/2020 (CIDTFF)"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e Tecnologia","doi-asserted-by":"publisher","award":["2020.06821.BD"],"award-info":[{"award-number":["2020.06821.BD"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Education Sciences"],"abstract":"<jats:p>The integration of virtual manipulatives in classroom practices facilitates student learning processes. For this, the teacher must understand how to support students in establishing mathematical connections between the manipulation and their interpretations of the representations. We present a learning scenario that integrates the use of virtual manipulatives in mathematical modelling tasks. It was designed and implemented during initial teacher training, with the aim of helping a group of first-year elementary school students to overcome difficulties identified in their comprehension of the meaning of subtraction. The research, following the principles of design-based research, included three distinct moments: an individual written pre-test, an intervention phase with six micro-cycles, and an individual written post-test. The analysis of the collected data\u2014audio, screen recordings, and written productions\u2014allowed us to identify the most influential structural characteristics of the learning scenario: mathematical communication, collaborative learning, self-regulation, and co-regulation of learning. Our results suggest that differentiated instruction, minimal guidance, and scaffolding played an important role in the support provided by the pre-service teacher to students in the mathematical modelling activities that integrated virtual manipulatives.<\/jats:p>","DOI":"10.3390\/educsci11120757","type":"journal-article","created":{"date-parts":[[2021,11,24]],"date-time":"2021-11-24T02:46:08Z","timestamp":1637721968000},"page":"757","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Learning Scenario to Promote Comprehension of the Meaning of Subtraction"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1866-1283","authenticated-orcid":false,"given":"Ricardo","family":"Silva","sequence":"first","affiliation":[{"name":"Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal"},{"name":"CIDTFF\u2014Centro de Investiga\u00e7\u00e3o em Did\u00e1tica e Tecnologia na Forma\u00e7\u00e3o de Formadores, Universidade de Aveiro, 3810-193 Aveiro, Portugal"},{"name":"Instituto Polit\u00e9cnico de Coimbra, ESEC, NIEFI-PEAPEA, 3030-329 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1812-2300","authenticated-orcid":false,"given":"Fernando","family":"Martins","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico de Coimbra, ESEC, NIEFI-PEAPEA, 3030-329 Coimbra, Portugal"},{"name":"Instituto de Telecomunica\u00e7\u00f5es, Delega\u00e7\u00e3o da Covilh\u00e3, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9962-562X","authenticated-orcid":false,"given":"Cec\u00edlia","family":"Costa","sequence":"additional","affiliation":[{"name":"Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal"},{"name":"CIDTFF\u2014Centro de Investiga\u00e7\u00e3o em Did\u00e1tica e Tecnologia na Forma\u00e7\u00e3o de Formadores, Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5376-6128","authenticated-orcid":false,"given":"Jos\u00e9","family":"Cravino","sequence":"additional","affiliation":[{"name":"Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal"},{"name":"CIDTFF\u2014Centro de Investiga\u00e7\u00e3o em Did\u00e1tica e Tecnologia na Forma\u00e7\u00e3o de Formadores, Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9961-1538","authenticated-orcid":false,"given":"Joaquim Bernardino","family":"Lopes","sequence":"additional","affiliation":[{"name":"Escola de Ci\u00eancias e Tecnologia, Universidade de Tr\u00e1s-os-Montes e Alto Douro, 5000-801 Vila Real, Portugal"},{"name":"CIDTFF\u2014Centro de Investiga\u00e7\u00e3o em Did\u00e1tica e Tecnologia na Forma\u00e7\u00e3o de Formadores, Universidade de Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1080\/02607476.2020.1799709","article-title":"Teacher education in times of COVID-19 pandemic in Portugal: National, institutional and pedagogical responses","volume":"46","author":"Gago","year":"2020","journal-title":"J. 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