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Paderborn: AMA Service GmbH, 2025. <a href=\"https://doi.org/10.5162/ultrasonic2025/a18-a1\">https://doi.org/10.5162/ultrasonic2025/a18-a1</a>."}},{"language":[{"iso":"eng"}],"_id":"65812","main_file_link":[{"url":"https://hdl.handle.net/10419/315483"}],"user_id":"37953","author":[{"last_name":"Schmitz","first_name":"Hendrik","full_name":"Schmitz, Hendrik","id":"48879"},{"first_name":"Matthias","last_name":"Westphal","full_name":"Westphal, Matthias"}],"publication_identifier":{"unknown":["978-3-96973-329-5"]},"title":"Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities","year":"2025","status":"public","date_updated":"2026-06-09T09:59:43Z","date_created":"2026-06-09T07:21:34Z","department":[{"_id":"281"}],"type":"working_paper","citation":{"ama":"Schmitz H, Westphal M. <i>Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities</i>.; 2025.","bibtex":"@book{Schmitz_Westphal_2025, title={Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities}, author={Schmitz, Hendrik and Westphal, Matthias}, year={2025} }","mla":"Schmitz, Hendrik, and Matthias Westphal. <i>Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities</i>. 2025.","short":"H. Schmitz, M. Westphal, Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities, 2025.","chicago":"Schmitz, Hendrik, and Matthias Westphal. <i>Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities</i>, 2025.","apa":"Schmitz, H., &#38; Westphal, M. (2025). <i>Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities</i>.","ieee":"H. Schmitz and M. Westphal, <i>Early- and Later-Life Stimulation: How Retirement Shapes The Effect of Education on Old-Age Cognitive Abilities</i>. 2025."}},{"type":"conference","keyword":["Teacher expertise","noticing","analytical vectorial geometry"],"file":[{"content_type":"application/pdf","file_id":"61018","date_updated":"2026-06-10T07:01:02Z","relation":"main_file","file_size":408502,"access_level":"open_access","file_name":"RR_Herrmann.pdf","date_created":"2025-08-26T08:32:39Z","creator":"herrmann"}],"date_created":"2025-08-26T08:35:10Z","abstract":[{"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.","lang":"eng"}],"publication":"Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education","main_file_link":[{"url":"https://www.igpme.org/wp-content/uploads/2025/07/PME48_ResearchReports_E-ISSN_2790-3648.zip"}],"language":[{"iso":"eng"}],"date_updated":"2026-06-10T07:01:02Z","intvolume":"         1","year":"2025","title":"Which categories do prospective teachers apply when selecting tasks for the scalar product?","author":[{"full_name":"Herrmann, Janine","first_name":"Janine","last_name":"Herrmann","id":"64060"}],"publication_identifier":{"unknown":["2790-3648"]},"oa":"1","quality_controlled":"1","file_date_updated":"2026-06-10T07:01:02Z","citation":{"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.","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.","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).","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.","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} }","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."},"ddc":["510"],"user_id":"64060","editor":[{"last_name":"Cornejo","first_name":"Claudia","full_name":"Cornejo, Claudia"},{"full_name":"Felmer, Patricio","last_name":"Felmer","first_name":"Patricio"},{"full_name":"Gómez, David M.","last_name":"Gómez","first_name":"David M."},{"full_name":"Dartnell, Pablo","first_name":"Pablo","last_name":"Dartnell"},{"full_name":"Araya, Paulina","first_name":"Paulina","last_name":"Araya"},{"last_name":"Peri","first_name":"Armando","full_name":"Peri, Armando"},{"last_name":"Randolph","first_name":"Valeria ","full_name":"Randolph, Valeria "}],"volume":1,"_id":"61017","has_accepted_license":"1","status":"public","conference":{"end_date":"2025-08-02","location":"Santiago de Chile","start_date":"2025-07-28","name":"48th PME Conference"}},{"oa":"1","citation":{"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} }","ama":"Herrmann J, Wessel L. Verstehenstypen von Lehrkräften zum Konzept Skalarprodukt und ihre Vorstellungen von Verstehensprozessen. 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