{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,26]],"date-time":"2026-10-26T20:11:55Z","timestamp":1793045515618,"version":"4.5.0"},"reference-count":62,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T00:00:00Z","timestamp":1719532800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T00:00:00Z","timestamp":1719532800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100010790","name":"Erasmus+","doi-asserted-by":"publisher","award":["2020-1-DE01-KA203-005677"],"award-info":[{"award-number":["2020-1-DE01-KA203-005677"]}],"id":[{"id":"10.13039\/501100010790","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100012996","name":"University of Cyprus","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100012996","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Educ Inf Technol"],"published-print":{"date-parts":[[2025,2]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>The aim of this study was to develop, implement, and evaluate an intervention program focusing on developing Grade 5 and 6 students\u2019 functional thinking. The innovative aspect lies in addressing simultaneously various aspects of function\u2014input\u2013output, covariation, correspondence, and object\u2014 in terms of manipulating tasks that involve functional relationships. The program adopts promising design principles, including an inquiry-based approach, engaging students in embodied dynamic mathematics learning environments, and making connections to real-world situations. A sample of 104 students took part in the program. The results showed a significant improvement in students\u2019 performance related to functional thinking between the pre- and post-tests. Grade 5 students\u2019 mean value improved from 0.29 to 0.58 and Grade 6 students from 0.37 to 0.60, respectively. Analysis indicated that students with varying performance potential in developing functional thinking are likely to be significantly affected by the program. Regression analysis showed that students\u2019 gender as well as mathematics- and functions-related self-concept and interest did not serve as predictive factors of students\u2019 gain score magnitude. Students' progression goes along with a significant shift in strategies used. While the dominant strategies in the pre-test relied on recursive and single variation, in the post-test, students moved to covariational and correspondence approaches. The findings indicate that upper primary school students are capable of grappling abstract facets of functions. This underscores the potential effectiveness of targeted interventions that adopt innovative design principles, particularly in light of the limitations of conventional curricula in adequately preparing students to explore functional relationships across diverse contexts.<\/jats:p>","DOI":"10.1007\/s10639-024-12865-y","type":"journal-article","created":{"date-parts":[[2024,6,28]],"date-time":"2024-06-28T16:55:15Z","timestamp":1719593715000},"page":"1329-1361","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Enhancing functional thinking in grade 5\u20136 students through a dynamic mathematics intervention program"],"prefix":"10.1007","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3609-7388","authenticated-orcid":false,"given":"Marios","family":"Pittalis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ute","family":"Sproesser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eleni","family":"Demosthenous","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eleni","family":"Odysseos","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,6,28]]},"reference":[{"key":"12865_CR1","doi-asserted-by":"publisher","first-page":"876","DOI":"10.3389\/fpsyg.2020.00876","volume":"11","author":"A Ab\u00edn","year":"2020","unstructured":"Ab\u00edn, A., N\u00fa\u00f1ez, J. C., Rodr\u00edguez, C., Cueli, M., Garc\u00eda, T., & Ros\u00e1rio, P. (2020). Predicting mathematics achievement in secondary education: The role of cognitive, motivational, and emotional variables. Frontiers in psycholog, 11, 876. https:\/\/doi.org\/10.3389\/fpsyg.2020.00876","journal-title":"Frontiers in psycholog"},{"issue":"1","key":"12865_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijcci.2014.07.002","volume":"2","author":"D Abrahamson","year":"2014","unstructured":"Abrahamson, D. (2014). Building educational activities for understanding: An elaboration on the embodied-design framework and its epistemic grounds. International Journal of Child-Computer Interaction, 2(1), 1\u201316. https:\/\/doi.org\/10.1016\/j.ijcci.2014.07.002","journal-title":"International Journal of Child-Computer Interaction"},{"issue":"1","key":"12865_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s41235-016-0034-3","volume":"1","author":"D Abrahamson","year":"2016","unstructured":"Abrahamson, D., & Bakker, A. (2016). Making sense of movement in embodied design for mathematics learning. Cogn Res: Principles Implicat, 1(1), 1\u201313. https:\/\/doi.org\/10.1186\/s41235-016-0034-3","journal-title":"Cogn Res: Principles Implicat"},{"issue":"2","key":"12865_CR4","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1080\/10508406.2016.1143370","volume":"25","author":"D Abrahamson","year":"2016","unstructured":"Abrahamson, D., & S\u00e1nchez-Garc\u00eda, R. (2016). Learning is moving in new ways: The ecological dynamics of mathematics education. Journal of the Learning Science, 25(2), 203\u2013239. https:\/\/doi.org\/10.1080\/10508406.2016.1143370","journal-title":"Journal of the Learning Science"},{"key":"12865_CR5","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1007\/s11858-013-0506-6","volume":"45","author":"M Artigue","year":"2013","unstructured":"Artigue, M., & Blomh\u00f8j, M. (2013). Conceptualizing inquiry-based education in mathematics. ZDM Mathematics Education, 45, 797\u2013810. https:\/\/doi.org\/10.1007\/s11858-013-0506-6","journal-title":"ZDM Mathematics Education"},{"issue":"4","key":"12865_CR6","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1111\/j.1756-8765.2010.01115.x","volume":"2","author":"LW Barsalou","year":"2010","unstructured":"Barsalou, L. W. (2010). Grounded cognition: Past, present, and future. Topics in Cognitive Science, 2(4), 716\u2013724. https:\/\/doi.org\/10.1111\/j.1756-8765.2010.01115.x","journal-title":"Topics in Cognitive Science,"},{"issue":"5","key":"12865_CR7","doi-asserted-by":"publisher","first-page":"511","DOI":"10.5951\/jresematheduc.46.5.0511","volume":"46","author":"M Blanton","year":"2015","unstructured":"Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., & Newman-Owens, A. (2015a). A learning trajectory in 6-year-olds\u2019 thinking about generalizing functional relationships. Journal for Research in Mathematics Education, 46(5), 511\u2013558. https:\/\/doi.org\/10.5951\/jresematheduc.46.5.0511","journal-title":"Journal for Research in Mathematics Education"},{"issue":"1","key":"12865_CR8","doi-asserted-by":"publisher","first-page":"39","DOI":"10.5951\/jresematheduc.46.1.0039","volume":"46","author":"M Blanton","year":"2015","unstructured":"Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., & Kim, J.-S. (2015b). The development of children\u2019s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39\u201387. https:\/\/doi.org\/10.5951\/jresematheduc.46.1.0039","journal-title":"Journal for Research in Mathematics Education"},{"key":"12865_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/s10649-019-09894-7","volume":"102","author":"M Blanton","year":"2019","unstructured":"Blanton, M., Isler-Baykal, I., Stroud, R., Stephens, A., Knuth, E., & Gardiner, A. M. (2019). Growth in children\u2019s understanding of generalizing and representing mathematical structure and relationships. Educational Studies in Mathematics, 102, 193\u2013219. https:\/\/doi.org\/10.1007\/s10649-019-09894-7","journal-title":"Educational Studies in Mathematics"},{"key":"12865_CR10","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.jmathb.2015.10.004","volume":"41","author":"MC Ca\u00f1adas","year":"2016","unstructured":"Ca\u00f1adas, M. C., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about linear functional relationships. The Journal of Mathematical Behavior, 41, 87\u2013103. https:\/\/doi.org\/10.1016\/j.jmathb.2015.10.004","journal-title":"The Journal of Mathematical Behavior"},{"issue":"5","key":"12865_CR11","doi-asserted-by":"publisher","first-page":"352","DOI":"10.2307\/4149958","volume":"33","author":"M Carlson","year":"2002","unstructured":"Carlson, M., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying covariational reasoning while modeling dynamic events: A framework and a study. Journal for Research in Mathematics Education, 33(5), 352\u2013378. https:\/\/doi.org\/10.2307\/4149958","journal-title":"Journal for Research in Mathematics Education"},{"key":"12865_CR12","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/978-3-319-68351-5_5","volume-title":"Teaching and learning algebraic thinking with 5-to 12-year-olds","author":"DW Carraher","year":"2018","unstructured":"Carraher, D. W., & Schliemann, A. D. (2018). Cultivating early algebraic thinking. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 107\u2013138). Springer. https:\/\/doi.org\/10.1007\/978-3-319-68351-5_5"},{"issue":"1","key":"12865_CR13","doi-asserted-by":"publisher","first-page":"66","DOI":"10.2307\/749228","volume":"26","author":"J Confrey","year":"1995","unstructured":"Confrey, J., & Smith, E. (1995). Splitting, covariation, and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26(1), 66\u201386. https:\/\/doi.org\/10.2307\/749228","journal-title":"Journal for Research in Mathematics Education"},{"key":"12865_CR14","doi-asserted-by":"publisher","unstructured":"Cooper, T. J., & Warren, E. (2011). Years 2 to 6 students\u2019 ability to generalise: Models, representations and theory for teaching and learning.\u00a0Early algebraization: A global dialogue from multiple perspectives, 187\u2013214. https:\/\/doi.org\/10.1007\/978-3-642-17735-4_12","DOI":"10.1007\/978-3-642-17735-4_12"},{"key":"12865_CR15","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1007\/s11858-017-0850-z","volume":"49","author":"T Dackermann","year":"2017","unstructured":"Dackermann, T., Fischer, U., Nuerk, H. C., Cress, U., & Moeller, K. (2017). Applying embodied cognition: From useful interventions and their theoretical underpinnings to practical applications. ZDM Mathematics Education, 49, 545\u2013557. https:\/\/doi.org\/10.1007\/s11858-017-0850-z","journal-title":"ZDM Mathematics Education"},{"key":"12865_CR16","first-page":"425","volume-title":"Educational design research Part B Illustrative cases","author":"M Doorman","year":"2013","unstructured":"Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2013). Design research in mathematics education: The case of an ICT-rich learning arrangement for the concept of function. In T. Plomp & N. Nieveen (Eds.), Educational design research Part B Illustrative cases (pp. 425\u2013446). SLO: Netherlands Institute for Curriculum Development."},{"key":"12865_CR17","first-page":"85","volume-title":"The concept of function: Aspects of epistemology and pedagogy","author":"E Dubinsky","year":"1992","unstructured":"Dubinsky, E., & Harel, G. (1992). The nature of the process conception of function. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 85\u2013106). Mathematical Association of America."},{"key":"12865_CR18","doi-asserted-by":"publisher","first-page":"144","DOI":"10.3389\/fpsyg.2017.00144","volume":"8","author":"CA Duijzer","year":"2017","unstructured":"Duijzer, C. A., Shayan, S., Bakker, A., Van der Schaaf, M. F., & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. Frontiers in Psychology, 8, 144. https:\/\/doi.org\/10.3389\/fpsyg.2017.00144","journal-title":"Frontiers in Psychology"},{"key":"12865_CR19","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/s10648-019-09471-7","volume":"31","author":"CA Duijzer","year":"2019","unstructured":"Duijzer, C. A., Van den Heuvel-Panhuizen, M., Veldhuis, M., Doorman, M., & Leseman, P. (2019). Embodied learning environments for graphing motion: A systematic literature review. Educational Psychology Review, 31, 597\u2013629. https:\/\/doi.org\/10.1007\/s10648-019-09471-7","journal-title":"Educational Psychology Review"},{"key":"12865_CR20","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s11858-019-01072-6","volume":"17","author":"CA Duijzer","year":"2020","unstructured":"Duijzer, C. A., den Heuvel-Panhuizen, V., Veldhuis, M., Boom, J., Doorman, L. M., & Leseman, P. P. M. (2020). Moving towards understanding: Students interpret and construct motion graphs. Mediterranean Journal for Research in Mathematics Education, 17, 25\u201351. https:\/\/doi.org\/10.1007\/s11858-019-01072-6","journal-title":"Mediterranean Journal for Research in Mathematics Education"},{"key":"12865_CR21","first-page":"153","volume-title":"The concept of function: Aspects of epistemology and pedagogy","author":"T Eisenberg","year":"1992","unstructured":"Eisenberg, T. (1992). On the development of a sense for functions. In E. Dubinsky & G. Harel (Eds.), The concept of function: Aspects of epistemology and pedagogy (pp. 153\u2013174). Mathematical Association of America."},{"issue":"7","key":"12865_CR22","doi-asserted-by":"publisher","first-page":"1307","DOI":"10.1007\/s11858-020-01165-7","volume":"52","author":"VJ Flood","year":"2020","unstructured":"Flood, V. J., Shvarts, A., & Abrahamson, D. (2020). Teaching with embodied learning technologies for mathematics: Responsive teaching for embodied learning. ZDM, 52(7), 1307\u20131331. https:\/\/doi.org\/10.1007\/s11858-020-01165-7","journal-title":"ZDM"},{"key":"12865_CR23","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/s10763-011-9310-3","volume":"10","author":"JM Francisco","year":"2012","unstructured":"Francisco, J. M., & H\u00e4hki\u00f6niemi, M. (2012). Students\u2018 ways of reasoning about nonlinear functions in guess-my-rule games. International Journal of Science and Mathematics Education, 10, 1001\u20131021. https:\/\/doi.org\/10.1007\/s10763-011-9310-3","journal-title":"International Journal of Science and Mathematics Education"},{"issue":"6","key":"12865_CR24","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1080\/00220270050167170","volume":"32","author":"K Gravemeijer","year":"2000","unstructured":"Gravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777\u2013796. https:\/\/doi.org\/10.1080\/00220270050167170","journal-title":"Journal of Curriculum Studies"},{"key":"12865_CR25","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1007\/s11858-020-01179-1","volume":"52","author":"SM G\u00fcnster","year":"2020","unstructured":"G\u00fcnster, S. M., & Weigand, H. G. (2020). Designing digital technology tasks for the development of functional thinking. ZDM, 52, 1259\u20131274. https:\/\/doi.org\/10.1007\/s11858-020-01179-1","journal-title":"ZDM"},{"issue":"1","key":"12865_CR26","doi-asserted-by":"publisher","first-page":"123","DOI":"10.3102\/00346543052001123","volume":"52","author":"BC Hansford","year":"1982","unstructured":"Hansford, B. C., & Hattie, J. A. (1982). The relationship between self and achievement\/performance measures. Review of Educational Research, 52(1), 123\u2013142. https:\/\/doi.org\/10.3102\/00346543052001123","journal-title":"Review of Educational Research"},{"issue":"1","key":"12865_CR27","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/BF02652735","volume":"32","author":"G Kaiser","year":"2000","unstructured":"Kaiser, G., & Steisel, T. (2000). Results of an analysis of the TIMS study from a gender perspective. ZDM, 32(1), 18\u201324. https:\/\/doi.org\/10.1007\/BF02652735","journal-title":"ZDM"},{"issue":"6","key":"12865_CR28","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1007\/s11858-022-01435-6","volume":"54","author":"C Kieran","year":"2022","unstructured":"Kieran, C. (2022). The multi-dimensionality of early algebraic thinking: background, overarching dimensions, and new directions. ZDM\u2013Mathematics Education, 54(6), 1131\u20131150. https:\/\/doi.org\/10.1007\/s11858-022-01435-6","journal-title":"ZDM\u2013Mathematics Education"},{"issue":"3","key":"12865_CR29","doi-asserted-by":"publisher","first-page":"510","DOI":"10.5951\/jresematheduc.44.3.0510","volume":"44","author":"A Kolovou","year":"2013","unstructured":"Kolovou, A., van den Heuvel-Panhuizen, M., & K\u00f6ller, O. (2013). An intervention including an online game to improve grade 6 students\u2019 performance in early algebra. Journal for Research in Mathematics Education, 44(3), 510\u2013549. https:\/\/doi.org\/10.5951\/jresematheduc.44.3.0510","journal-title":"Journal for Research in Mathematics Education"},{"issue":"3","key":"12865_CR30","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1080\/1554480X.2010.486147","volume":"5","author":"D K\u00fcchemann","year":"2010","unstructured":"K\u00fcchemann, D. (2010). Using patterns generically to see structure. Pedagogies: an International Journal, 5(3), 233\u2013250. https:\/\/doi.org\/10.1080\/1554480X.2010.486147","journal-title":"Pedagogies: an International Journal"},{"key":"12865_CR31","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1007\/s41979-018-0007-1","volume":"1","author":"M Lichti","year":"2018","unstructured":"Lichti, M., & Roth, J. (2018). How to foster functional thinking in learning environments using computer-based simulations or real materials. Journal for STEM Education Research, 1, 148\u2013172. https:\/\/doi.org\/10.1007\/s41979-018-0007-1","journal-title":"Journal for STEM Education Research"},{"key":"12865_CR32","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/BF02652810","volume":"38","author":"C Michelsen","year":"2006","unstructured":"Michelsen, C. (2006). Functions: A modelling tool in mathematics and science. ZDM Mathematics Education, 38, 269\u2013280. https:\/\/doi.org\/10.1007\/BF02652810","journal-title":"ZDM Mathematics Education"},{"key":"12865_CR33","unstructured":"National Council for Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author."},{"key":"12865_CR34","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/978-3-319-68351-5_7","volume-title":"Teaching and learning algebraic thinking with 5-to 12-year-olds","author":"SF Ng","year":"2018","unstructured":"Ng, S. F. (2018). Function tasks, input, output, and the predictive rule: How some Singapore primary children construct the rule. In C. Kieran (Ed.), Teaching and learning algebraic thinking with 5-to 12-year-olds (pp. 167\u2013193). Springer. https:\/\/doi.org\/10.1007\/978-3-319-68351-5_7"},{"issue":"6","key":"12865_CR35","doi-asserted-by":"publisher","first-page":"1315","DOI":"10.1007\/s11858-022-01411-0","volume":"54","author":"J Pang","year":"2022","unstructured":"Pang, J., & Sunwoo, J. (2022). Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook. ZDM\u2013Mathematics Education, 54(6), 1315\u20131331. https:\/\/doi.org\/10.1007\/s11858-022-01411-0","journal-title":"ZDM\u2013Mathematics Education"},{"key":"12865_CR36","first-page":"17","volume-title":"Studies on the educational quality of schools. The final report on the DFG Priority Programme","author":"R Pekrun","year":"2007","unstructured":"Pekrun, R., vom Hofe, R., Blum, W., Frenzel, A. C., Goetz, T., & Wartha, S. (2007). Development of mathematical competencies in adolescence. The PALMA longitudinal study. In M. Prenzel (Ed.), Studies on the educational quality of schools. The final report on the DFG Priority Programme (pp. 17\u201337). Waxmann."},{"issue":"6","key":"12865_CR37","doi-asserted-by":"publisher","first-page":"1865","DOI":"10.1007\/s10763-022-10333-y","volume":"21","author":"M Pittalis","year":"2023","unstructured":"Pittalis, M. (2023). Young Students\u2019 Arithmetic-Algebraic Structure Sense: an Empirical Model and Profiles of Students. International Journal of Science and Mathematics Education, 21(6), 1865\u20131887. https:\/\/doi.org\/10.1007\/s10763-022-10333-y","journal-title":"International Journal of Science and Mathematics Education"},{"key":"12865_CR38","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/s10649-023-10222-3","volume":"113","author":"M Pittalis","year":"2023","unstructured":"Pittalis, M., & Drijvers, P. (2023). Embodied instrumentation in a Dynamic Geometry Environment: Eleven-year-old students\u2019 dragging schemes. Educational Studies in Mathematics, 113, 181\u2013205. https:\/\/doi.org\/10.1007\/s10649-023-10222-3","journal-title":"Educational Studies in Mathematics"},{"issue":"5","key":"12865_CR39","doi-asserted-by":"publisher","first-page":"631","DOI":"10.5951\/jresematheduc-2020-0164","volume":"51","author":"M Pittalis","year":"2020","unstructured":"Pittalis, M., Pitta-Pantazi, D., & Christou, C. (2020). Young students\u2019 functional thinking modes: The relation between recursive patterning, covariation thinking and correspondence relation. Journal for Research in Mathematics Education, 51(5), 631\u2013674. https:\/\/doi.org\/10.5951\/jresematheduc-2020-0164","journal-title":"Journal for Research in Mathematics Education"},{"key":"12865_CR40","doi-asserted-by":"publisher","DOI":"10.1080\/0020739X.2024.2327552","author":"M Pittalis","year":"2024","unstructured":"Pittalis, M., Sproesser, U., & Demosthenous, E. (2024). Graphically Representing Covariational Functional Situations in an Interactive Embodied Digital Learning Environment. International Journal of Mathematical Education in Science and Technology. https:\/\/doi.org\/10.1080\/0020739X.2024.2327552","journal-title":"International Journal of Mathematical Education in Science and Technology"},{"key":"12865_CR41","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s10648-014-9255-5","volume":"26","author":"WT Pouw","year":"2014","unstructured":"Pouw, W. T., Van Gog, T., & Paas, F. (2014). An embedded and embodied cognition review of instructional manipulatives. Educational Psychology Review, 26, 51\u201372. https:\/\/doi.org\/10.1007\/s10648-014-9255-5","journal-title":"Educational Psychology Review"},{"issue":"2","key":"12865_CR42","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s10649-008-9127-3","volume":"70","author":"L Radford","year":"2009","unstructured":"Radford, L. (2009). Why do gestures matter? Sensuous cognition and the palpability of mathematical meanings. Educational Studies in Mathematics, 70(2), 111\u2013126. https:\/\/doi.org\/10.1007\/s10649-008-9127-3","journal-title":"Educational Studies in Mathematics"},{"issue":"3","key":"12865_CR43","doi-asserted-by":"publisher","first-page":"372","DOI":"10.3102\/0034654310374880","volume":"80","author":"CR Rakes","year":"2010","unstructured":"Rakes, C. R., Valentine, J. C., McGatha, M. B., & Ronau, R. N. (2010). Methods of instructional improvement in algebra: A systematic review and meta-analysis. Review of Educational Research, 80(3), 372\u2013400. https:\/\/doi.org\/10.3102\/0034654310374880","journal-title":"Review of Educational Research"},{"issue":"6","key":"12865_CR44","doi-asserted-by":"publisher","first-page":"1393","DOI":"10.1007\/s11858-022-01423-w","volume":"54","author":"R Ram\u00edrez","year":"2022","unstructured":"Ram\u00edrez, R., Ca\u00f1adas, M. C., & Dami\u00e1n, A. (2022). Structures and representations used by 6th graders when working with quadratic functions. ZDM\u2013Mathematics Education, 54(6), 1393\u20131406. https:\/\/doi.org\/10.1007\/s11858-022-01423-w","journal-title":"ZDM\u2013Mathematics Education"},{"issue":"1","key":"12865_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s41979-021-00060-4","volume":"5","author":"T Rolfes","year":"2022","unstructured":"Rolfes, T., Roth, J., & Schnotz, W. (2022). Mono-and multi-representational learning of the covariational aspect of functional thinking. Journal for STEM Education Research, 5(1), 1\u201327. https:\/\/doi.org\/10.1007\/s41979-021-00060-4","journal-title":"Journal for STEM Education Research"},{"issue":"1","key":"12865_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00302715","volume":"22","author":"A Sfard","year":"1991","unstructured":"Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22(1), 1\u201336. https:\/\/doi.org\/10.1007\/BF00302715","journal-title":"Educational Studies in Mathematics"},{"issue":"4","key":"12865_CR47","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1080\/10986065.2021.1983691","volume":"25","author":"A Shvarts","year":"2023","unstructured":"Shvarts, A., & van Helden, G. (2023). Embodied learning at a distance: From sensory-motor experience to constructing and understanding a sine graph. Mathematical Thinking and Learning, 25(4), 409\u2013437. https:\/\/doi.org\/10.1080\/10986065.2021.1983691","journal-title":"Mathematical Thinking and Learning"},{"issue":"1","key":"12865_CR48","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s41235-018-0092-9","volume":"3","author":"A Skulmowski","year":"2018","unstructured":"Skulmowski, A., & Rey, G. D. (2018). Embodied learning: Introducing a taxonomy based on bodily engagement and task integration. Cognitive Research: Principles and Implications, 3(1), 1\u201310. https:\/\/doi.org\/10.1186\/s41235-018-0092-9","journal-title":"Cognitive Research: Principles and Implications"},{"key":"12865_CR49","unstructured":"Sproesser, U., Vogel, M., Doerfler, T., & Eichler, A. (2019). Do students perceive mathematics and the mathematical subdomain of functions differently with regard to their self-concept and interest? In T. Jankvist, M. Van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (No. 22). Utrecht, the Netherlands: Freudenthal Group & Freudenthal Institute, Utrecht University and ERME."},{"issue":"1","key":"12865_CR50","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40594-022-00350-2","volume":"9","author":"U Sproesser","year":"2022","unstructured":"Sproesser, U., Vogel, M., D\u00f6rfler, T., & Eichler, A. (2022). Changing between representations of elementary functions: students\u2019 competencies and differences with a specific perspective on school track and gender. International Journal of STEM Education, 9(1), 1\u201318. https:\/\/doi.org\/10.1186\/s40594-022-00350-2","journal-title":"International Journal of STEM Education"},{"issue":"3","key":"12865_CR51","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/10986065.2017.1328636","volume":"19","author":"AC Stephens","year":"2017","unstructured":"Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Gardiner, A. M. (2017). A learning progression for elementary students\u2019 functional thinking. Mathematical Thinking and Learning, 19(3), 143\u2013166. https:\/\/doi.org\/10.1080\/10986065.2017.1328636","journal-title":"Mathematical Thinking and Learning"},{"issue":"3","key":"12865_CR52","doi-asserted-by":"publisher","first-page":"332","DOI":"10.5951\/jresematheduc-2020-0304","volume":"52","author":"AC Stephens","year":"2021","unstructured":"Stephens, A. C., Stroud, R., Strachota, S., Stylianou, D., Blanton, M., Knuth, E., & Gardiner, A. (2021). What early algebra knowledge persists 1 year after an elementary grades intervention? Journal for Research in Mathematics Education, 52(3), 332\u2013348. https:\/\/doi.org\/10.5951\/jresematheduc-2020-0304","journal-title":"Journal for Research in Mathematics Education"},{"key":"12865_CR53","first-page":"421","volume-title":"Compendium for research in mathematics education","author":"PW Thompson","year":"2017","unstructured":"Thompson, P. W., & Carlson, M. P. (2017). Variation, covariation, and functions: Foundational ways of thinking mathematically. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 421\u2013456). National Council of Teachers of Mathematics."},{"issue":"1","key":"12865_CR54","first-page":"13","volume":"39","author":"H Venkat","year":"2019","unstructured":"Venkat, H., Askew, M., Watson, A., & Mason, J. (2019). Architecture of mathematical structure. For the Learning of Mathematics, 39(1), 13\u201317.","journal-title":"For the Learning of Mathematics"},{"issue":"4","key":"12865_CR55","doi-asserted-by":"publisher","first-page":"356","DOI":"10.2307\/749441","volume":"20","author":"S Vinner","year":"1989","unstructured":"Vinner, S., & Dreyfus, T. (1989). Images and definitions for the concept of function. Journal for Research in Mathematics Education, 20(4), 356\u2013366. https:\/\/doi.org\/10.2307\/749441","journal-title":"Journal for Research in Mathematics Education"},{"issue":"2","key":"12865_CR56","doi-asserted-by":"publisher","first-page":"150","DOI":"10.2304\/ciec.2005.6.2.5","volume":"6","author":"E Warren","year":"2005","unstructured":"Warren, E., & Cooper, T. (2005). Introducing functional thinking in Year 2: A case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150\u2013162. https:\/\/doi.org\/10.2304\/ciec.2005.6.2.5","journal-title":"Contemporary Issues in Early Childhood"},{"issue":"3","key":"12865_CR57","doi-asserted-by":"publisher","first-page":"208","DOI":"10.1016\/j.jmathb.2006.09.006","volume":"25","author":"EA Warren","year":"2006","unstructured":"Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning. The Journal of Mathematical Behavior, 25(3), 208\u2013223. https:\/\/doi.org\/10.1016\/j.jmathb.2006.09.006","journal-title":"The Journal of Mathematical Behavior"},{"issue":"2","key":"12865_CR58","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1564\/tme_v30.2.2","volume":"30","author":"H Wei","year":"2023","unstructured":"Wei, H., Bos, R., & Drijvers, P. (2023). An embodied approach to abstract functional thinking using digital technology: A systematic literature review. International Journal for Technology in Mathematics Education, 30(2), 75\u201394. https:\/\/doi.org\/10.1564\/tme_v30.2.2","journal-title":"International Journal for Technology in Mathematics Education"},{"issue":"2","key":"12865_CR59","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s10763-019-09955-6","volume":"18","author":"KJ Wilkie","year":"2020","unstructured":"Wilkie, K. J. (2020). Investigating students\u2019 attention to covariation features of their constructed graphs in a figural pattern generalisation context. International Journal of Science and Mathematics Education, 18(2), 315\u2013336. https:\/\/doi.org\/10.1007\/s10763-019-09955-6","journal-title":"International Journal of Science and Mathematics Education"},{"key":"12865_CR60","doi-asserted-by":"publisher","first-page":"100917","DOI":"10.1016\/j.jmathb.2021.100917","volume":"65","author":"KJ Wilkie","year":"2022","unstructured":"Wilkie, K. J. (2022). Generalization of quadratic figural patterns: Shifts in student noticing. The Journal of Mathematical Behavior, 65, 100917. https:\/\/doi.org\/10.1016\/j.jmathb.2021.100917","journal-title":"The Journal of Mathematical Behavior"},{"key":"12865_CR61","doi-asserted-by":"publisher","first-page":"2580","DOI":"10.3389\/fpsyg.2018.02580","volume":"9","author":"H Xie","year":"2018","unstructured":"Xie, H., Peng, J., Qin, M., Huang, X., Tian, F., & Zhou, Z. (2018). Can touchscreen devices be used to facilitate young children\u2019s learning? A meta-analysis of touchscreen learning effect. Frontiers in Psychology, 9, 2580. https:\/\/doi.org\/10.3389\/fpsyg.2018.02580","journal-title":"Frontiers in Psychology"},{"key":"12865_CR62","doi-asserted-by":"publisher","unstructured":"Yeung, W. L., & Ng, O. L. (2023). Characterizing touchscreen actions in technology-enhanced embodied learning for mathematics instruction in K-12 setting\u2013A systematic review (2010\u20132023).\u00a0Computers & Education, 104881. https:\/\/doi.org\/10.1016\/j.compedu.2023.104881","DOI":"10.1016\/j.compedu.2023.104881"}],"container-title":["Education and Information Technologies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10639-024-12865-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10639-024-12865-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10639-024-12865-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,6]],"date-time":"2025-02-06T10:38:08Z","timestamp":1738838288000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10639-024-12865-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,28]]},"references-count":62,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["12865"],"URL":"https:\/\/doi.org\/10.1007\/s10639-024-12865-y","relation":{},"ISSN":["1360-2357","1573-7608"],"issn-type":[{"value":"1360-2357","type":"print"},{"value":"1573-7608","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,28]]},"assertion":[{"value":"29 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 June 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author has no relevant financial or non-financial interests to disclose.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Financial interests"}},{"value":"License for conducting the research was provided by the Department of Primary Education of the Ministry of Education, Culture, Youth and Sports in Cyprus and the Center of Educational Research and Evaluation in Cyprus, after examining research ethical compliance.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"There is no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}]}}