[{"ddc":["510"],"keyword":["Teacher expertise","noticing","analytical vectorial geometry"],"language":[{"iso":"eng"}],"publication":"Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education","abstract":[{"lang":"eng","text":"Selecting tasks is a typical job in everyday teaching that requires teachers to have content-specific expertise, including categories to think about and perceive conceptual understanding. This contribution investigates the activation of prospective teachers’ categories when solving tasks on the scalar product and evaluating their relevance for teaching in upper secondary school. To further investigate, whether input on content-related aspects could be helpful to promote a professional justification for the selection of tasks, two groups with and without input are to be differentiated. Different ways of dealing with underlying concept elements and evaluating the relevance of tasks are discussed by examples."}],"file":[{"content_type":"application/pdf","success":1,"relation":"main_file","date_updated":"2025-08-26T08:32:39Z","date_created":"2025-08-26T08:32:39Z","creator":"herrmann","file_size":408502,"access_level":"closed","file_name":"RR_Herrmann.pdf","file_id":"61018"}],"date_created":"2025-08-26T08:35:10Z","title":"Which categories do prospective teachers apply when selecting tasks for the scalar product?","quality_controlled":"1","year":"2025","_id":"61017","user_id":"64060","file_date_updated":"2025-08-26T08:32:39Z","type":"conference","editor":[{"first_name":"Claudia","last_name":"Cornejo","full_name":"Cornejo, Claudia"},{"first_name":"Patricio","full_name":"Felmer, Patricio","last_name":"Felmer"},{"first_name":"David M.","full_name":"Gómez, David M.","last_name":"Gómez"},{"last_name":"Dartnell","full_name":"Dartnell, Pablo","first_name":"Pablo"},{"first_name":"Paulina","full_name":"Araya, Paulina","last_name":"Araya"},{"first_name":"Armando","last_name":"Peri","full_name":"Peri, Armando"},{"full_name":"Randolph, Valeria ","last_name":"Randolph","first_name":"Valeria "}],"status":"public","date_updated":"2026-02-16T07:54:31Z","author":[{"id":"64060","full_name":"Herrmann, Janine","last_name":"Herrmann","first_name":"Janine"}],"volume":1,"main_file_link":[{"url":"https://www.igpme.org/wp-content/uploads/2025/07/PME48_ResearchReports_E-ISSN_2790-3648.zip"}],"conference":{"start_date":"2025-07-28","name":"48th PME Conference","location":"Santiago de Chile","end_date":"2025-08-02"},"has_accepted_license":"1","publication_identifier":{"unknown":["2790-3648"]},"citation":{"chicago":"Herrmann, Janine. “Which Categories Do Prospective Teachers Apply When Selecting Tasks for the Scalar Product?” In <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education</i>, edited by Claudia Cornejo, Patricio Felmer, David M. Gómez, Pablo Dartnell, Paulina Araya, Armando Peri, and Valeria  Randolph, Vol. 1, 2025.","ieee":"J. Herrmann, “Which categories do prospective teachers apply when selecting tasks for the scalar product?,” in <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education</i>, Santiago de Chile, 2025, vol. 1.","ama":"Herrmann J. Which categories do prospective teachers apply when selecting tasks for the scalar product? In: Cornejo C, Felmer P, Gómez DM, et al., eds. <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education</i>. Vol 1. ; 2025.","apa":"Herrmann, J. (2025). Which categories do prospective teachers apply when selecting tasks for the scalar product? In C. Cornejo, P. Felmer, D. M. Gómez, P. Dartnell, P. Araya, A. Peri, &#38; V. Randolph (Eds.), <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education</i> (Vol. 1).","short":"J. Herrmann, in: C. Cornejo, P. Felmer, D.M. Gómez, P. Dartnell, P. Araya, A. Peri, V. Randolph (Eds.), Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education, 2025.","mla":"Herrmann, Janine. “Which Categories Do Prospective Teachers Apply When Selecting Tasks for the Scalar Product?” <i>Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education</i>, edited by Claudia Cornejo et al., vol. 1, 2025.","bibtex":"@inproceedings{Herrmann_2025, title={Which categories do prospective teachers apply when selecting tasks for the scalar product?}, volume={1}, booktitle={Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education}, author={Herrmann, Janine}, editor={Cornejo, Claudia and Felmer, Patricio and Gómez, David M. and Dartnell, Pablo and Araya, Paulina and Peri, Armando and Randolph, Valeria }, year={2025} }"},"intvolume":"         1"},{"publication":"Beiträge zum Mathematikunterricht","type":"conference","editor":[{"full_name":"Schick, Lisa","last_name":"Schick","first_name":"Lisa"},{"first_name":"Melanie","full_name":"Platz, Melanie","last_name":"Platz"},{"first_name":"Anselm","last_name":"Lambert","full_name":"Lambert, Anselm"}],"status":"public","file":[{"file_name":"BzMU25_HERRMANN_Verstehenstypen.pdf","file_id":"64150","access_level":"closed","file_size":536533,"creator":"herrmann","date_created":"2026-02-13T09:34:08Z","date_updated":"2026-02-13T09:34:08Z","relation":"main_file","success":1,"content_type":"application/pdf"}],"_id":"64149","user_id":"64060","ddc":["370","510"],"language":[{"iso":"eng"}],"file_date_updated":"2026-02-13T09:34:08Z","has_accepted_license":"1","year":"2025","page":"483-486","citation":{"apa":"Herrmann, J., &#38; Wessel, L. (2025). Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt und ihre Vorstellungen von Verstehensprozessen. In L. Schick, M. Platz, &#38; A. Lambert (Eds.), <i>Beiträge zum Mathematikunterricht</i> (pp. 483–486). <a href=\"https://doi.org/10.37626/GA9783959872782.0\">https://doi.org/10.37626/GA9783959872782.0</a>","bibtex":"@inproceedings{Herrmann_Wessel_2025, title={Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt und ihre Vorstellungen von Verstehensprozessen}, DOI={<a href=\"https://doi.org/10.37626/GA9783959872782.0\">https://doi.org/10.37626/GA9783959872782.0</a>}, booktitle={Beiträge zum Mathematikunterricht}, author={Herrmann, Janine and Wessel, Lena}, editor={Schick, Lisa and Platz, Melanie and Lambert, Anselm}, year={2025}, pages={483–486} }","short":"J. Herrmann, L. Wessel, in: L. Schick, M. Platz, A. Lambert (Eds.), Beiträge Zum Mathematikunterricht, 2025, pp. 483–486.","mla":"Herrmann, Janine, and Lena Wessel. “Verstehenstypen von Lehrkräften Zum Konzept Skalarprodukt Und Ihre Vorstellungen von Verstehensprozessen.” <i>Beiträge Zum Mathematikunterricht</i>, edited by Lisa Schick et al., 2025, pp. 483–86, doi:<a href=\"https://doi.org/10.37626/GA9783959872782.0\">https://doi.org/10.37626/GA9783959872782.0</a>.","chicago":"Herrmann, Janine, and Lena Wessel. “Verstehenstypen von Lehrkräften Zum Konzept Skalarprodukt Und Ihre Vorstellungen von Verstehensprozessen.” In <i>Beiträge Zum Mathematikunterricht</i>, edited by Lisa Schick, Melanie Platz, and Anselm Lambert, 483–86, 2025. <a href=\"https://doi.org/10.37626/GA9783959872782.0\">https://doi.org/10.37626/GA9783959872782.0</a>.","ieee":"J. Herrmann and L. 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Scherer (Eds.), <i>Beiträge zum Mathematikunterricht 2024</i> (p. 1666). <a href=\"http://dx.doi.org/10.17877/DE290R-25188\">http://dx.doi.org/10.17877/DE290R-25188</a>","ieee":"J. Herrmann, “Ansprüche an eine Fortbildung zur analytischen Geometrie,” in <i>Beiträge zum Mathematikunterricht 2024</i>, Duisburg-Essen, p. 1666, doi: <a href=\"http://dx.doi.org/10.17877/DE290R-25188\">http://dx.doi.org/10.17877/DE290R-25188</a>.","chicago":"Herrmann, Janine. “Ansprüche an eine Fortbildung zur analytischen Geometrie.” In <i>Beiträge zum Mathematikunterricht 2024</i>, edited by Patrick Ebers, Fabian  Rösken, Bärbel Barzel, Andreas Büchter, Florian  Schacht, and Petra  Scherer, 1666, n.d. <a href=\"http://dx.doi.org/10.17877/DE290R-25188\">http://dx.doi.org/10.17877/DE290R-25188</a>.","ama":"Herrmann J. Ansprüche an eine Fortbildung zur analytischen Geometrie. In: Ebers P, Rösken F, Barzel B, Büchter A, Schacht F, Scherer P, eds. <i>Beiträge zum Mathematikunterricht 2024</i>. ; :1666. doi:<a href=\"http://dx.doi.org/10.17877/DE290R-25188\">http://dx.doi.org/10.17877/DE290R-25188</a>"},"year":"2025","user_id":"64060","_id":"61051","language":[{"iso":"ger"}],"file_date_updated":"2025-08-28T10:00:24Z","ddc":["510"],"publication":"Beiträge zum Mathematikunterricht 2024","type":"conference","status":"public","file":[{"success":1,"relation":"main_file","content_type":"application/pdf","file_size":57284,"file_name":"BzMU24_HERRMANN_Geometriefortbildungen.pdf","file_id":"61054","access_level":"closed","date_updated":"2025-08-28T10:00:24Z","date_created":"2025-08-28T10:00:24Z","creator":"herrmann"}],"editor":[{"first_name":"Patrick","full_name":"Ebers, Patrick","last_name":"Ebers"},{"last_name":"Rösken","full_name":"Rösken, Fabian ","first_name":"Fabian "},{"last_name":"Barzel","full_name":"Barzel, Bärbel","first_name":"Bärbel"},{"first_name":"Andreas","full_name":"Büchter, Andreas","last_name":"Büchter"},{"first_name":"Florian ","last_name":"Schacht","full_name":"Schacht, Florian "},{"full_name":"Scherer, Petra ","last_name":"Scherer","first_name":"Petra "}]}]