{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T06:54:12Z","timestamp":1775026452842,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2014,1,29]],"date-time":"2014-01-29T00:00:00Z","timestamp":1390953600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Tech Know Learn"],"published-print":{"date-parts":[[2014,10]]},"DOI":"10.1007\/s10758-014-9213-9","type":"journal-article","created":{"date-parts":[[2014,1,28]],"date-time":"2014-01-28T19:16:27Z","timestamp":1390936587000},"page":"287-315","source":"Crossref","is-referenced-by-count":18,"title":["A Model for Task Design with Focus on Exploration, Explanation, and Generalization in a Dynamic Geometry Environment"],"prefix":"10.1007","volume":"19","author":[{"given":"Maria","family":"Fahlgren","sequence":"first","affiliation":[]},{"given":"Mats","family":"Brunstr\u00f6m","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,1,29]]},"reference":[{"issue":"2","key":"9213_CR1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s10649-008-9149-x","volume":"69","author":"L Alcock","year":"2008","unstructured":"Alcock, L., & Inglis, M. (2008). Doctoral students\u2019 use of examples in evaluating and proving conjectures. Educational Studies in Mathematics, 69(2), 111\u2013129.","journal-title":"Educational Studies in Mathematics"},{"issue":"3","key":"9213_CR2","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1007\/BF02655708","volume":"34","author":"F Arzarello","year":"2002","unstructured":"Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practises in cabri environments. ZDM the International Journal on Mathematics Education, 34(3), 66\u201372.","journal-title":"ZDM the International Journal on Mathematics Education"},{"issue":"3","key":"9213_CR3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/s10758-010-9169-3","volume":"15","author":"A Baccaglini-Frank","year":"2010","unstructured":"Baccaglini-Frank, A., & Mariotti, M. A. (2010). Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225\u2013253.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"1","key":"9213_CR4","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/BF01809606","volume":"21","author":"D Chazan","year":"1990","unstructured":"Chazan, D. (1990a). Quasi-empirical views of mathematics and mathematics teaching. Interchange, 21(1), 14\u201323.","journal-title":"Interchange"},{"issue":"8","key":"9213_CR5","doi-asserted-by":"crossref","first-page":"628","DOI":"10.5951\/MT.83.8.0628","volume":"83","author":"D Chazan","year":"1990","unstructured":"Chazan, D. (1990b). Students\u2019 microcomputer-aided exploration in geometry. Mathematics Teacher, 83(8), 628\u2013635.","journal-title":"Mathematics Teacher"},{"key":"9213_CR6","first-page":"17","volume":"24","author":"M Villiers De","year":"1990","unstructured":"De Villiers, M. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17\u201324.","journal-title":"Pythagoras"},{"issue":"5","key":"9213_CR7","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1080\/0020739042000232556","volume":"35","author":"M Villiers De","year":"2004","unstructured":"De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers\u2019 understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703\u2013724.","journal-title":"International Journal of Mathematical Education in Science and Technology"},{"issue":"5","key":"9213_CR8","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1007\/s11858-007-0043-2","volume":"39","author":"M Doorman","year":"2007","unstructured":"Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in the Netherlands. ZDM the International Journal on Mathematics Education, 39(5), 405\u2013418.","journal-title":"ZDM the International Journal on Mathematics Education"},{"issue":"2","key":"9213_CR9","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s10649-010-9254-5","volume":"75","author":"P Drijvers","year":"2010","unstructured":"Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: Instrumental orchestrations in the technology-rich mathematics classroom. Educational Studies in Mathematics, 75(2), 213\u2013234.","journal-title":"Educational Studies in Mathematics"},{"issue":"3","key":"9213_CR10","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1023\/A:1009711521492","volume":"2","author":"LD Edwards","year":"1997","unstructured":"Edwards, L. D. (1997). Exploring the territory before proof: Student\u2018s generalizations in a computer microworld for transformation geometry. International Journal of Computers for Mathematical Learning, 2(3), 187\u2013215.","journal-title":"International Journal of Computers for Mathematical Learning"},{"key":"9213_CR11","first-page":"404","volume":"2","author":"F Furinghetti","year":"2003","unstructured":"Furinghetti, F., & Paola, D. (2003). To produce conjectures and to prove them within a dynamic geometry environment: A case study. Proceedings of the Twenty Seventh Annual Conference of the International Group for the Psychology of Mathematics Education, 2, 404.","journal-title":"Proceedings of the Twenty Seventh Annual Conference of the International Group for the Psychology of Mathematics Education"},{"issue":"3","key":"9213_CR12","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s10758-008-9129-3","volume":"13","author":"B Guven","year":"2008","unstructured":"Guven, B. (2008). Using dynamic geometry software to gain insight into a proof. International Journal of Computers for Mathematical Learning, 13(3), 251\u2013262.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"1","key":"9213_CR13","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1023\/A:1012781005718","volume":"44","author":"N Hadas","year":"2000","unstructured":"Hadas, N., Hershkowitz, R., & Schwarz, B. B. (2000). The role of contradiction and uncertainty in promoting the need to prove in dynamic geometry environments. Educational Studies in Mathematics, 44(1), 127\u2013150.","journal-title":"Educational Studies in Mathematics"},{"issue":"1","key":"9213_CR14","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1012737223465","volume":"44","author":"G Hanna","year":"2000","unstructured":"Hanna, G. (2000). Proof, explanation and exploration: An overview. Educational Studies in Mathematics, 44(1), 5\u201323.","journal-title":"Educational Studies in Mathematics"},{"key":"9213_CR15","first-page":"877","volume-title":"International handbook of mathematics education","author":"G Hanna","year":"1996","unstructured":"Hanna, G., & Jahnke, H. N. (1996). Proof and proving. In A. J. Bishop, M. A. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 877\u2013908). Dordrecht: Kluwer."},{"issue":"3","key":"9213_CR16","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1023\/A:1013305627916","volume":"6","author":"L Healy","year":"2002","unstructured":"Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235\u2013256.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"2","key":"9213_CR17","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s10758-009-9151-0","volume":"14","author":"F Hitt","year":"2009","unstructured":"Hitt, F., & Kieran, C. (2009). Constructing knowledge via a peer interaction in a CAS environment with tasks designed from a task\u2014technique\u2014theory perspective. International Journal of Computers for Mathematical Learning, 14(2), 121\u2013152.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"1","key":"9213_CR18","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1023\/A:1011464425023","volume":"6","author":"R H\u00f6lzl","year":"2001","unstructured":"H\u00f6lzl, R. (2001). Using dynamic geometry software to add contrast to geometric situations\u2014a case study. International Journal of Computers for Mathematical Learning, 6(1), 63\u201386.","journal-title":"International Journal of Computers for Mathematical Learning"},{"key":"9213_CR19","first-page":"121","volume-title":"Perspectives on the teaching of geometry for the 21st century","author":"C Hoyles","year":"1998","unstructured":"Hoyles, C., & Jones, K. (1998). Proof in dynamic geometry contexts. In C. Mammana & V. Villani (Eds.), Perspectives on the teaching of geometry for the 21st century (pp. 121\u2013128). Dordrecht: Kluwer."},{"key":"9213_CR21","first-page":"393","volume-title":"Research on technology and the teaching and learning of mathematics: Vol. 2, cases and perspectives","author":"C Kieran","year":"2008","unstructured":"Kieran, C., & Saldanha, L. (2008). Designing tasks for the codevelopment of conceptual and technical knowledge in CAS activity: An example from factoring. In G. W. Blume & K. M. Heid (Eds.), Research on technology and the teaching and learning of mathematics: Vol. 2, cases and perspectives (pp. 393\u2013414). Charlotte, NC: Information Age Publishing."},{"issue":"3","key":"9213_CR22","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1023\/A:1013309728825","volume":"6","author":"C Laborde","year":"2002","unstructured":"Laborde, C. (2002). Integration of technology in the design of geometry tasks with cabri-geometry. International Journal of Computers for Mathematical Learning, 6(3), 283\u2013317.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"3","key":"9213_CR23","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s11858-011-0329-2","volume":"43","author":"A Leung","year":"2011","unstructured":"Leung, A. (2011). An epistemic model of task design in dynamic geometry environment. ZDM the International Journal on Mathematics Education, 43(3), 325\u2013336.","journal-title":"ZDM the International Journal on Mathematics Education"},{"issue":"2","key":"9213_CR24","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1023\/A:1021195015288","volume":"7","author":"A Leung","year":"2002","unstructured":"Leung, A., & Lopez-Real, F. (2002). Theorem justification and acquisition in dynamic geometry: A case of proof by contradiction. International Journal of Computers for Mathematical Learning, 7(2), 145\u2013165.","journal-title":"International Journal of Computers for Mathematical Learning"},{"key":"9213_CR25","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/978-94-007-2129-6_13","volume-title":"Proof and proving in mathematics education. the 19th ICMI study","author":"FL Lin","year":"2012","unstructured":"Lin, F. L., Yang, K. L., Lee, K. H., Tabach, M., & Stylianides, G. (2012). Principles of task design for conjecturing and proving. In G. Hanna & M. de Villiers (Eds.), Proof and proving in mathematics education. the 19th ICMI study (pp. 305\u2013325). Berlin: Springer."},{"issue":"6","key":"9213_CR26","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1080\/00207390600712539","volume":"37","author":"F Lopez-Real","year":"2006","unstructured":"Lopez-Real, F., & Leung, A. (2006). Dragging as a conceptual tool in dynamic geometry environments. International Journal of Mathematical Education in Science and Technology, 37(6), 665\u2013679.","journal-title":"International Journal of Mathematical Education in Science and Technology"},{"issue":"1","key":"9213_CR27","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1023\/A:1012785106627","volume":"44","author":"R Marrades","year":"2000","unstructured":"Marrades, R., & Gutierrez, A. (2000). Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44(1), 87\u2013125.","journal-title":"Educational Studies in Mathematics"},{"key":"9213_CR28","volume-title":"Thinking mathematically","author":"J Mason","year":"2010","unstructured":"Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Dorchester: Pearson Education.","edition":"2"},{"issue":"2","key":"9213_CR29","first-page":"96","volume":"19","author":"C Mogetta","year":"1999","unstructured":"Mogetta, C., Olivero, F., & Jones, K. (1999). Providing the motivation to prove in a dynamic geometry environment. Proceedings of the British Society for Research into Learning Mathematics, 19(2), 96.","journal-title":"Proceedings of the British Society for Research into Learning Mathematics"},{"issue":"2","key":"9213_CR30","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/s10758-007-9115-1","volume":"12","author":"F Olivero","year":"2007","unstructured":"Olivero, F., & Robutti, O. (2007). Measuring in dynamic geometry environments as a tool for conjecturing and proving. International Journal of Computers for Mathematical Learning, 12(2), 135\u2013156.","journal-title":"International Journal of Computers for Mathematical Learning"},{"issue":"3","key":"9213_CR31","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s11412-008-9043-7","volume":"3","author":"D \u00d6ner","year":"2008","unstructured":"\u00d6ner, D. (2008). Supporting students\u2019 participation in authentic proof activities in computer supported collaborative learning (CSCL) environments. International Journal of Computer Supported Collaborative Learning, 3(3), 343\u2013359.","journal-title":"International Journal of Computer Supported Collaborative Learning"},{"issue":"3","key":"9213_CR32","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1007\/s10649-008-9177-6","volume":"71","author":"R Pierce","year":"2009","unstructured":"Pierce, R., & Ball, L. (2009). Perceptions that may affect teachers\u2019 intention to use technology in secondary mathematics classes. Educational Studies in Mathematics, 71(3), 299\u2013317.","journal-title":"Educational Studies in Mathematics"},{"key":"9213_CR33","doi-asserted-by":"crossref","DOI":"10.1515\/9781400828678","volume-title":"How to solve it","author":"G P\u00f3lya","year":"1945","unstructured":"P\u00f3lya, G. (1945). How to solve it. Princton: Princeton University Press."},{"issue":"3","key":"9213_CR34","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1023\/A:1024360204239","volume":"52","author":"M Raman","year":"2003","unstructured":"Raman, M. (2003). Key ideas: What are they and how can they help us understand how people view proof? Educational Studies in Mathematics, 52(3), 319\u2013325.","journal-title":"Educational Studies in Mathematics"},{"issue":"1","key":"9213_CR35","doi-asserted-by":"crossref","first-page":"131","DOI":"10.4000\/educationdidactique.434","volume":"3","author":"K Ruthven","year":"2009","unstructured":"Ruthven, K. (2009). Towards a naturalistic conceptualisation of technology integration in classroom practice: The example of school mathematics. Education & Didactique, 3(1), 131\u2013159.","journal-title":"Education & Didactique"},{"issue":"1","key":"9213_CR36","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.compedu.2007.05.013","volume":"51","author":"K Ruthven","year":"2008","unstructured":"Ruthven, K., Hennessy, S., & Deaney, R. (2008). Constructions of dynamic geometry: A study of the interpretative flexibility of educational software in classroom practice. Computers & Education, 51(1), 297\u2013317.","journal-title":"Computers & Education"},{"issue":"1","key":"9213_CR37","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1080\/00207390110087129","volume":"33","author":"M Santos-Trigo","year":"2002","unstructured":"Santos-Trigo, M., & Espinosa-Perez, H. (2002). Searching and exploring properties of geometric configurations using dynamic software. International Journal of Mathematical Education in Science and Technology, 33(1), 37\u201350.","journal-title":"International Journal of Mathematical Education in Science and Technology"},{"issue":"3","key":"9213_CR38","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1023\/A:1024305603330","volume":"52","author":"MP Sinclair","year":"2003","unstructured":"Sinclair, M. P. (2003). Some implications of the results of a case study for the design of pre-constructed, dynamic geometry sketches and accompanying materials. Educational Studies in Mathematics, 52(3), 289\u2013317.","journal-title":"Educational Studies in Mathematics"},{"issue":"4","key":"9213_CR39","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1007\/s10857-008-9077-9","volume":"11","author":"AJ Stylianides","year":"2008","unstructured":"Stylianides, A. J., & Ball, D. L. (2008). Understanding and describing mathematical knowledge for teaching: Knowledge about proof for engaging students in the activity of proving. Journal of Mathematics Teacher Education, 11(4), 307\u2013332.","journal-title":"Journal of Mathematics Teacher Education"},{"issue":"3\u20134","key":"9213_CR40","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.jmathb.2005.09.005","volume":"24","author":"K Weber","year":"2005","unstructured":"Weber, K. (2005). Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction. The Journal of Mathematical Behavior, 24(3\u20134), 351\u2013360.","journal-title":"The Journal of Mathematical Behavior"},{"issue":"2","key":"9213_CR41","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1023\/B:EDUC.0000040410.57253.a1","volume":"56","author":"K Weber","year":"2004","unstructured":"Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(2), 209\u2013234.","journal-title":"Educational Studies in Mathematics"},{"key":"9213_CR42","first-page":"57","volume-title":"The geometric supposer: What is it a case of?","author":"M Yerushalmy","year":"1993","unstructured":"Yerushalmy, M. (1993). Generalization in geometry. In J. L. Schwartz, M. J. Yerushalmy, & B. Wilson (Eds.), The geometric supposer: What is it a case of? (pp. 57\u201384). USA: Lawrence Erlbaum."},{"issue":"2","key":"9213_CR43","first-page":"153","volume":"16","author":"N Zehavi","year":"2011","unstructured":"Zehavi, N., & Mann, G. (2011). Development process of a praxeology for supporting the teaching of proofs in a CAS environment based on teachers\u2019 experience in a professional development course. Technology Knowledge and Learning, 16(2), 153\u2013181.","journal-title":"Technology Knowledge and Learning"}],"container-title":["Technology, Knowledge and Learning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10758-014-9213-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10758-014-9213-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10758-014-9213-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,3,24]],"date-time":"2022-03-24T16:18:01Z","timestamp":1648138681000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10758-014-9213-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,1,29]]},"references-count":42,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,10]]}},"alternative-id":["9213"],"URL":"https:\/\/doi.org\/10.1007\/s10758-014-9213-9","relation":{},"ISSN":["2211-1662","2211-1670"],"issn-type":[{"value":"2211-1662","type":"print"},{"value":"2211-1670","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,1,29]]}}}