{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,26]],"date-time":"2025-03-26T16:21:47Z","timestamp":1743006107628,"version":"3.40.3"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783031162893"},{"type":"electronic","value":"9783031162909"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,9,5]],"date-time":"2022-09-05T00:00:00Z","timestamp":1662336000000},"content-version":"vor","delay-in-days":247,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Using examples and non-examples is a common technique to demonstrate concepts\u2019 characteristics and boundaries. Based on their properties, certain objects are accepted as examples or non-examples intuitively, while others are accepted or neglected non-intuitively. This 2*2 classification is powerful when designing technology-enhanced learning experiences in which feedback could be provided in real-time. That is, feedback could be based not only on the correctness of student response, but also on the specifics of the objects with which they were engaged. Following this framework, we developed an interactive sorting task that aims at strengthening elementary school students\u2019 understanding of reflective symmetry. We studied learners\u2019 interaction with the objects presented to them, and their success. Our study included 29 elementary school students (ages 9 to 12) from both Israel and Germany. We used screen recording to code participants\u2019 shape-movements, and defined quantitative measures of these movements. Our findings support the need for designing feedback that takes into consideration object\u2019s properties and students\u2019 behavior.<\/jats:p>","DOI":"10.1007\/978-3-031-16290-9_21","type":"book-chapter","created":{"date-parts":[[2022,9,4]],"date-time":"2022-09-04T23:02:47Z","timestamp":1662332567000},"page":"285-298","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Learners\u2019 Strategies in Interactive Sorting Tasks"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2404-6102","authenticated-orcid":false,"given":"Norbert","family":"Noster","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1568-2238","authenticated-orcid":false,"given":"Arnon","family":"Hershkovitz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2869-3032","authenticated-orcid":false,"given":"Michal","family":"Tabach","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1597-7108","authenticated-orcid":false,"given":"Hans-Stefan","family":"Siller","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,5]]},"reference":[{"key":"21_CR1","first-page":"115","volume-title":"Instructional-Design Theories and Models: A new paradigm of instructional theory -","author":"M Hannafin","year":"2009","unstructured":"Hannafin, M., Land, S., Oliver, K.: Open Learning Environments: Foundations, Methods, and Models. In: Reigeluth, C.M. (ed.) Instructional-Design Theories and Models: A new paradigm of instructional theory -, vol. II, pp. 115\u2013140. Routledge, New York, NY (2009)"},{"key":"21_CR2","doi-asserted-by":"publisher","first-page":"399","DOI":"10.3390\/MATH9040399","volume":"9","author":"M Cevikbas","year":"2021","unstructured":"Cevikbas, M., Kaiser, G.: A systematic review on task design in dynamic and interactive mathematics learning environments (DIMLEs). Mathematics. 9, 399 (2021). https:\/\/doi.org\/10.3390\/MATH9040399","journal-title":"Mathematics."},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"81","DOI":"10.3102\/003465430298487","volume":"77","author":"J Hattie","year":"2007","unstructured":"Hattie, J., Timperley, H.: The power of feedback. Rev. Educ. Res. 77, 81\u2013112 (2007). https:\/\/doi.org\/10.3102\/003465430298487","journal-title":"Rev. Educ. Res."},{"issue":"2","key":"21_CR4","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/BF00305619","volume":"12","author":"D Tall","year":"1981","unstructured":"Tall, D., Vinner, S.: Concept image and concept definition in mathematics with particular reference to limits and continuity. Edu. Stud. Math. 12(2), 151\u2013169 (1981). https:\/\/doi.org\/10.1007\/BF00305619","journal-title":"Edu. Stud. Math."},{"key":"21_CR5","doi-asserted-by":"publisher","first-page":"663","DOI":"10.2307\/1162820","volume":"20","author":"CW McKinney","year":"1983","unstructured":"McKinney, C.W., Larkins, A.G., Ford, M.J., Davis, I.I.I., J.C.D.: The effectiveness of three methods of teaching social studies concepts to fourth-grade students: an aptitude-treatment interaction study. Am. Edu. Res. J. 20, 663\u2013670 (1983). https:\/\/doi.org\/10.2307\/1162820","journal-title":"Am. Edu. Res. J."},{"unstructured":"Crowley, M.L.: The van Hiele model of the development of geometric thought. In: Montgomery Lindquis, M. (ed.) Learning and Teahching Geometry, K-12, 1987 Yearbook of the National Council of Teachers of Mathematics, pp. 1\u201316. National Council of Teachers of Mathematics, Reston, VA (1987)","key":"21_CR6"},{"key":"21_CR7","doi-asserted-by":"publisher","first-page":"636","DOI":"10.1007\/978-94-007-4978-8_161","volume-title":"Encyclopedia of Mathematics Education","author":"N Presmeg","year":"2014","unstructured":"Presmeg, N.: Visualization and Learning in Mathematics Education. In: Lerman, S. (ed.) Encyclopedia of Mathematics Education, pp. 636\u2013640. Springer, Berlin, Gremany (2014)"},{"key":"21_CR8","first-page":"12","volume":"9","author":"D Kuchemann","year":"1980","unstructured":"Kuchemann, D.: Children\u2019s difficulties with single reflections and rotations. Math. Sch. 9, 12\u201313 (1980)","journal-title":"Math. Sch."},{"key":"21_CR9","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/0022-2496(69)90001-7","volume":"6","author":"GA Miller","year":"1969","unstructured":"Miller, G.A.: A psychological method to investigate verbal concepts. J. Math. Psychol. 6, 169\u2013191 (1969). https:\/\/doi.org\/10.1016\/0022-2496(69)90001-7","journal-title":"J. Math. Psychol."},{"issue":"1","key":"21_CR10","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/s10758-016-9290-z","volume":"22","author":"H Tang","year":"2016","unstructured":"Tang, H., Clariana, R.: Leveraging a sorting task as a measure of knowledge structure in bilingual settings. Technol. Knowl. Learn. 22(1), 23\u201335 (2016). https:\/\/doi.org\/10.1007\/s10758-016-9290-z","journal-title":"Technol. Knowl. Learn."},{"key":"21_CR11","doi-asserted-by":"publisher","first-page":"628","DOI":"10.1187\/cbe.13-05-0096","volume":"12","author":"JI Smith","year":"2013","unstructured":"Smith, J.I., et al.: Development of the biology card sorting task to measure conceptual expertise in biology. CBE Life Sci. Educ. 12, 628\u2013644 (2013). https:\/\/doi.org\/10.1187\/cbe.13-05-0096","journal-title":"CBE Life Sci. Educ."},{"key":"21_CR12","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s13394-011-0017-0","volume":"23","author":"JA Eli","year":"2011","unstructured":"Eli, J.A., Mohr-Schroeder, M.J., Lee, C.W.: Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Math. Educ. Res. J. 23, 297\u2013319 (2011). https:\/\/doi.org\/10.1007\/s13394-011-0017-0","journal-title":"Math. Educ. Res. J."},{"unstructured":"Miyakawa, T.: Reflective symmetry in construction and proving. In: Proceedings of the 28th International Conference of Psychology of Mathematics Education, pp. 337\u2013344. Bergen, Norway (2004)","key":"21_CR13"},{"key":"21_CR14","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s10649-008-9133-5","volume":"69","author":"P Tsamir","year":"2008","unstructured":"Tsamir, P., Tirosh, D., Levenson, E.: Intuitive nonexamples: the case of triangles. Educ. Stud. Math. 69, 81\u201395 (2008). https:\/\/doi.org\/10.1007\/s10649-008-9133-5","journal-title":"Educ. Stud. Math."},{"key":"21_CR15","volume-title":"Intuition in Science and Mathematics: An Educational Approach","author":"H Fischbein","year":"2002","unstructured":"Fischbein, H.: Intuition in Science and Mathematics: An Educational Approach, 1st edn. Kluwer, New York, NY (2002)","edition":"1"},{"issue":"1","key":"21_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s40561-018-0080-z","volume":"6","author":"MAA Dewan","year":"2019","unstructured":"Dewan, M.A.A., Murshed, M., Lin, F.: Engagement detection in online learning: a review. Smart Learn. Environ. 6(1), 1\u201320 (2019). https:\/\/doi.org\/10.1186\/s40561-018-0080-z","journal-title":"Smart Learn. Environ."},{"key":"21_CR17","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1080\/10508406.2013.837391","volume":"22","author":"JD Gobert","year":"2013","unstructured":"Gobert, J.D., Sao Pedro, M., Raziuddin, J., Baker, R.S.: From log files to assessment metrics: measuring students\u2019 science inquiry skills using educational data mining. J. Learn. Sci. 22, 521\u2013563 (2013). https:\/\/doi.org\/10.1080\/10508406.2013.837391","journal-title":"J. Learn. Sci."},{"key":"21_CR18","doi-asserted-by":"publisher","first-page":"28","DOI":"10.18608\/jla.2021.7161","volume":"8","author":"Y Zhang","year":"2021","unstructured":"Zhang, Y., et al.: Can strategic behaviour facilitate confusion resolution? The interplay between confusion and metacognitive strategies in Betty\u2019s Brain. J. Learn. Anal. 8, 28\u201344 (2021). https:\/\/doi.org\/10.18608\/jla.2021.7161","journal-title":"J. Learn. Anal."},{"key":"21_CR19","doi-asserted-by":"publisher","first-page":"19","DOI":"10.18608\/jla.2020.71.3","volume":"7","author":"SA Crossley","year":"2020","unstructured":"Crossley, S.A., Karumbaiah, S., Ocumpaugh, J., Labrum, M.J., Baker, R.S.: Predicting math identity through language and click-stream patterns in a blended learning mathematics program for elementary students. J. Learn. Anal. 7, 19\u201337 (2020). https:\/\/doi.org\/10.18608\/jla.2020.71.3","journal-title":"J. Learn. Anal."},{"key":"21_CR20","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/978-3-319-64792-0_8","volume-title":"Utilizing Learning Analytics to Support Study Success","author":"K Derr","year":"2019","unstructured":"Derr, K., H\u00fcbl, R., Ahmed, M.Z.: Monitoring the Use of Learning Strategies in a Web-Based Pre-course in Mathematics. In: Ifenthaler, D., Mah, D.-K., Yau, J.-K. (eds.) Utilizing Learning Analytics to Support Study Success, pp. 119\u2013141. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-319-64792-0_8"},{"key":"21_CR21","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1177\/0735633120972057","volume":"59","author":"L Haleva","year":"2021","unstructured":"Haleva, L., Hershkovitz, A., Tabach, M.: Students\u2019 activity in an online learning environment for mathematics: the role of thinking levels. J. Educ. Comput. Res. 59, 686\u2013712 (2021). https:\/\/doi.org\/10.1177\/0735633120972057","journal-title":"J. Educ. Comput. Res."},{"issue":"3","key":"21_CR22","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1007\/s11858-014-0641-8","volume":"47","author":"P Tsamir","year":"2014","unstructured":"Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., Tabach, M.: Early-years teachers\u2019 concept images and concept definitions: triangles, circles, and cylinders. ZDM Math. Educ. 47(3), 497\u2013509 (2014). https:\/\/doi.org\/10.1007\/s11858-014-0641-8","journal-title":"ZDM Math. Educ."},{"key":"21_CR23","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1080\/00461520.1986.9653026","volume":"21","author":"ML Gick","year":"1986","unstructured":"Gick, M.L.: Problem-solving strategies. Educ. Psychol. 21, 99\u2013120 (1986). https:\/\/doi.org\/10.1080\/00461520.1986.9653026","journal-title":"Educ. Psychol."},{"issue":"4","key":"21_CR24","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1007\/s11858-020-01129-x","volume":"52","author":"H Palm\u00e9r","year":"2020","unstructured":"Palm\u00e9r, H., van Bommel, J.: Young students posing problem-solving tasks: what does posing a similar task imply to students? ZDM Math. Educ. 52(4), 743\u2013752 (2020). https:\/\/doi.org\/10.1007\/s11858-020-01129-x","journal-title":"ZDM Math. Educ."},{"doi-asserted-by":"publisher","unstructured":"Harel, R., Olsher, S., Yerushalmy, M.: Designing online formative assessment that promotes students\u2019 reasoning processes. In: Proceedings of the 14th International Conference on Technology in Mathematics Teaching, pp. 181\u2013188 (2019). https:\/\/doi.org\/10.17185\/duepublico\/70762","key":"21_CR25","DOI":"10.17185\/duepublico\/70762"},{"unstructured":"Noster, N., Hershkovitz, A., Siller, Hans.-S., Tabach, M.: Students\u2019 strategies for identifying reflective symmetry of extra-mathematical shapes in a digital environment. In: ERME Topic Conference on Mathematics Education in the Digital Age. Nitra, Slovakia (2022)","key":"21_CR26"}],"container-title":["Lecture Notes in Computer Science","Educating for a New Future: Making Sense of Technology-Enhanced Learning Adoption"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-16290-9_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,4]],"date-time":"2022-09-04T23:17:27Z","timestamp":1662333447000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-16290-9_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031162893","9783031162909"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-16290-9_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"5 September 2022","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EC-TEL","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"European Conference on Technology Enhanced Learning","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Toulouse","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 September 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ectel2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/ea-tel.eu\/ectel2022","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"109","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"30","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"28% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3,17","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"1,5","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"No","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}