[{"page":"81-119","publisher":"Cellule MathDoc/CEDRAM","_id":"31263","user_id":"49063","volume":4,"status":"public","external_id":{"arxiv":["1803.06717"]},"citation":{"ama":"Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>. 2021;4:81-119. doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>","bibtex":"@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for invariant Ruelle densities}, volume={4}, DOI={<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>}, journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }","mla":"Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i>, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119, doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>.","short":"C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.","chicago":"Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i> 4 (2021): 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>.","apa":"Guillarmou, C., Hilgert, J., &#38; Weich, T. (2021). High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>, <i>4</i>, 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>","ieee":"C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant Ruelle densities,” <i>Annales Henri Lebesgue</i>, vol. 4, pp. 81–119, 2021, doi: <a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>."},"language":[{"iso":"eng"}],"doi":"10.5802/ahl.67","title":"High frequency limits for invariant Ruelle densities","year":"2021","author":[{"full_name":"Guillarmou, Colin","last_name":"Guillarmou","first_name":"Colin"},{"full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert","id":"220"},{"id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias","full_name":"Weich, Tobias"}],"publication_identifier":{"issn":["2644-9463"]},"publication_status":"published","date_updated":"2024-02-19T06:27:43Z","intvolume":"         4","date_created":"2022-05-17T12:05:17Z","type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"publication":"Annales Henri Lebesgue"},{"citation":{"chicago":"Brennecken, Dominik, Joachim Hilgert, and Lorenzo Ciardo. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i> 31, no. 2 (2021): 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>.","short":"D. Brennecken, J. Hilgert, L. Ciardo, Journal of Lie Theory 31 (2021) 459--468.","ieee":"D. Brennecken, J. Hilgert, and L. Ciardo, “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R),” <i>Journal of Lie Theory</i>, vol. 31, no. 2, pp. 459--468, 2021, doi: <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>.","apa":"Brennecken, D., Hilgert, J., &#38; Ciardo, L. (2021). Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>, <i>31</i>(2), 459--468. <a href=\"https://doi.org/10.48550/arXiv.2008.07479\">https://doi.org/10.48550/arXiv.2008.07479</a>","bibtex":"@article{Brennecken_Hilgert_Ciardo_2021, title={Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)}, volume={31}, DOI={<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>}, number={2}, journal={Journal of Lie Theory}, publisher={Heldermann Verlag}, author={Brennecken, Dominik and Hilgert, Joachim and Ciardo, Lorenzo}, year={2021}, pages={459--468} }","ama":"Brennecken D, Hilgert J, Ciardo L. Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R). <i>Journal of Lie Theory</i>. 2021;31(2):459--468. doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>","mla":"Brennecken, Dominik, et al. “Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R).” <i>Journal of Lie Theory</i>, vol. 31, no. 2, Heldermann Verlag, 2021, pp. 459--468, doi:<a href=\"https://doi.org/10.48550/arXiv.2008.07479\">10.48550/arXiv.2008.07479</a>."},"issue":"2","publication":"Journal of Lie Theory","department":[{"_id":"555"},{"_id":"91"}],"type":"journal_article","date_created":"2023-01-12T08:23:28Z","intvolume":"        31","date_updated":"2024-02-19T06:27:09Z","publication_status":"published","author":[{"id":"55911","first_name":"Dominik","last_name":"Brennecken","full_name":"Brennecken, Dominik"},{"full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert","id":"220"},{"last_name":"Ciardo","first_name":"Lorenzo","full_name":"Ciardo, Lorenzo"}],"title":"Algebraically Independent Generators for the Algebra of Invariant Differential Operators on SLn(R)/SOn(R)","year":"2021","status":"public","volume":31,"doi":"10.48550/arXiv.2008.07479","user_id":"49063","_id":"36271","language":[{"iso":"eng"}],"publisher":"Heldermann Verlag","page":"459--468"},{"publication":"Mathematische Semesterberichte","citation":{"ieee":"J. Hilgert, “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019,” <i>Mathematische Semesterberichte</i>, vol. 68. pp. 171–173, 2021, doi: <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>.","apa":"Hilgert, J. (2021). Philip Ording: 99 Variations on a Proof. Princeton University Press 2019. In <i>Mathematische Semesterberichte</i> (Vol. 68, pp. 171–173). <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">https://doi.org/10.1007/s00591-021-00295-7</a>","short":"J. Hilgert, Mathematische Semesterberichte 68 (2021) 171–173.","chicago":"Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019.” <i>Mathematische Semesterberichte</i>, 2021. <a href=\"https://doi.org/10.1007/s00591-021-00295-7\">https://doi.org/10.1007/s00591-021-00295-7</a>.","mla":"Hilgert, Joachim. “Philip Ording: 99 Variations on a Proof. Princeton University Press 2019.” <i>Mathematische Semesterberichte</i>, vol. 68, 2021, pp. 171–173, doi:<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>.","bibtex":"@article{Hilgert_2021, title={Philip Ording: 99 Variations on a Proof. Princeton University Press 2019}, volume={68}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021}, pages={171–173} }","ama":"Hilgert J. Philip Ording: 99 Variations on a Proof. Princeton University Press 2019. <i>Mathematische Semesterberichte</i>. 2021;68:171–173. doi:<a href=\"https://doi.org/10.1007/s00591-021-00295-7\">10.1007/s00591-021-00295-7</a>"},"type":"review","department":[{"_id":"91"}],"date_created":"2024-02-20T09:52:08Z","publication_status":"published","date_updated":"2024-02-20T10:03:43Z","intvolume":"        68","year":"2021","status":"public","title":"Philip Ording: 99 Variations on a Proof. Princeton University Press 2019","author":[{"id":"220","last_name":"Hilgert","first_name":"Joachim","full_name":"Hilgert, Joachim"}],"user_id":"49063","doi":"10.1007/s00591-021-00295-7","volume":68,"page":"171–173","language":[{"iso":"eng"}],"_id":"51556"},{"publication":"Mathematische Semesterberichte","citation":{"ama":"Hilgert J. Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020. <i>Mathematische Semesterberichte</i>. 2021;68:175–177. doi:<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>","bibtex":"@article{Hilgert_2021, title={Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020}, volume={68}, DOI={<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>}, journal={Mathematische Semesterberichte}, author={Hilgert, Joachim}, year={2021}, pages={175–177} }","mla":"Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.” <i>Mathematische Semesterberichte</i>, vol. 68, 2021, pp. 175–177, doi:<a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>.","short":"J. Hilgert, Mathematische Semesterberichte 68 (2021) 175–177.","chicago":"Hilgert, Joachim. “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020.” <i>Mathematische Semesterberichte</i>, 2021. <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">https://doi.org/10.1007/s00591-021-00296-6</a>.","apa":"Hilgert, J. (2021). Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020. In <i>Mathematische Semesterberichte</i> (Vol. 68, pp. 175–177). <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">https://doi.org/10.1007/s00591-021-00296-6</a>","ieee":"J. Hilgert, “Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020,” <i>Mathematische Semesterberichte</i>, vol. 68. pp. 175–177, 2021, doi: <a href=\"https://doi.org/10.1007/s00591-021-00296-6\">10.1007/s00591-021-00296-6</a>."},"date_created":"2024-02-20T09:50:31Z","type":"review","department":[{"_id":"91"}],"year":"2021","status":"public","title":"Georg Glaeser (Hrsg.): 77-mal Mathematik für zwischendurch – Unterhaltsame Kuriositäten und unorthodoxe Anwendungen. Springer Spektrum 2020","author":[{"id":"220","full_name":"Hilgert, Joachim","first_name":"Joachim","last_name":"Hilgert"}],"date_updated":"2024-02-20T10:14:56Z","publication_status":"published","intvolume":"        68","page":"175–177","_id":"51555","language":[{"iso":"ger"}],"doi":"10.1007/s00591-021-00296-6","user_id":"49063","volume":68},{"publication":"arXiv","citation":{"apa":"Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for mean curvature flow in higher codimension. <i>ArXiv</i>.","ieee":"T. Binz and B. Kovács, “A convergent finite element algorithm for mean curvature flow in higher codimension,” <i>arXiv</i>, 2021.","short":"T. Binz, B. Kovács, ArXiv (2021).","chicago":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.","mla":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Mean Curvature Flow in Higher Codimension.” <i>ArXiv</i>, 2021.","ama":"Binz T, Kovács B. A convergent finite element algorithm for mean curvature flow in higher codimension. <i>arXiv</i>. Published online 2021.","bibtex":"@article{Binz_Kovács_2021, title={A convergent finite element algorithm for mean curvature flow in higher codimension}, journal={arXiv}, author={Binz, Tim and Kovács, Balázs}, year={2021} }"},"date_created":"2023-07-10T11:46:16Z","type":"journal_article","department":[{"_id":"841"}],"status":"public","year":"2021","title":"A convergent finite element algorithm for mean curvature flow in higher codimension","author":[{"first_name":"Tim","last_name":"Binz","full_name":"Binz, Tim"},{"id":"100441","full_name":"Kovács, Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474","first_name":"Balázs"}],"date_updated":"2024-04-03T09:16:19Z","language":[{"iso":"eng"}],"_id":"45967","user_id":"100441"},{"volume":42,"user_id":"100441","publisher":"Oxford University Press (OUP)","_id":"45962","page":"2545-2588","status":"public","citation":{"ama":"Binz T, Kovács B. A convergent finite element algorithm for generalized mean curvature flows of closed surfaces. <i>IMA Journal of Numerical Analysis</i>. 2021;42(3):2545-2588. doi:<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>","bibtex":"@article{Binz_Kovács_2021, title={A convergent finite element algorithm for generalized mean curvature flows of closed surfaces}, volume={42}, DOI={<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>}, number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Binz, Tim and Kovács, Balázs}, year={2021}, pages={2545–2588} }","mla":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2545–88, doi:<a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>.","short":"T. Binz, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2545–2588.","chicago":"Binz, Tim, and Balázs Kovács. “A Convergent Finite Element Algorithm for Generalized Mean Curvature Flows of Closed Surfaces.” <i>IMA Journal of Numerical Analysis</i> 42, no. 3 (2021): 2545–88. <a href=\"https://doi.org/10.1093/imanum/drab043\">https://doi.org/10.1093/imanum/drab043</a>.","apa":"Binz, T., &#38; Kovács, B. (2021). A convergent finite element algorithm for generalized mean curvature flows of closed surfaces. <i>IMA Journal of Numerical Analysis</i>, <i>42</i>(3), 2545–2588. <a href=\"https://doi.org/10.1093/imanum/drab043\">https://doi.org/10.1093/imanum/drab043</a>","ieee":"T. Binz and B. Kovács, “A convergent finite element algorithm for generalized mean curvature flows of closed surfaces,” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, pp. 2545–2588, 2021, doi: <a href=\"https://doi.org/10.1093/imanum/drab043\">10.1093/imanum/drab043</a>."},"doi":"10.1093/imanum/drab043","language":[{"iso":"eng"}],"intvolume":"        42","publication_status":"published","date_updated":"2024-04-03T09:18:40Z","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"first_name":"Tim","last_name":"Binz","full_name":"Binz, Tim"},{"id":"100441","full_name":"Kovács, Balázs","first_name":"Balázs","last_name":"Kovács","orcid":"0000-0001-9872-3474"}],"title":"A convergent finite element algorithm for generalized mean curvature flows of closed surfaces","year":"2021","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"type":"journal_article","date_created":"2023-07-10T11:44:41Z","abstract":[{"text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow and powers of mean and inverse mean curvature flow. Error estimates are proved for semidiscretizations and full discretizations for the generalized flow. The algorithm proposed and studied here combines evolving surface finite elements, whose nodes determine the discrete surface, and linearly implicit backward difference formulae for time integration. The numerical method is based on a system coupling the surface evolution to nonlinear second-order parabolic evolution equations for the normal velocity and normal vector. A convergence proof is presented in the case of finite elements of polynomial degree at least 2 and backward difference formulae of orders 2 to 5. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector, normal velocity and therefore for the mean curvature. The stability analysis is performed in the matrix–vector formulation and is independent of geometric arguments, which only enter the consistency analysis. Numerical experiments are presented to illustrate the convergence results and also to report on monotone quantities, e.g. Hawking mass for inverse mean curvature flow, and complemented by experiments for nonconvex surfaces.</jats:p>","lang":"eng"}],"publication":"IMA Journal of Numerical Analysis","issue":"3"},{"doi":"10.1093/imanum/drab045","language":[{"iso":"eng"}],"date_updated":"2024-04-03T09:20:15Z","publication_status":"published","intvolume":"        42","year":"2021","title":"Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions","publication_identifier":{"issn":["0272-4979","1464-3642"]},"author":[{"first_name":"Paula","last_name":"Harder","full_name":"Harder, Paula"},{"orcid":"0000-0001-9872-3474","first_name":"Balázs","last_name":"Kovács","full_name":"Kovács, Balázs","id":"100441"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics","General Mathematics"],"department":[{"_id":"841"}],"date_created":"2023-07-10T11:43:28Z","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>A proof of convergence is given for a bulk–surface finite element semidiscretisation of the Cahn–Hilliard equation with Cahn–Hilliard-type dynamic boundary conditions in a smooth domain. The semidiscretisation is studied in an abstract weak formulation as a second-order system. Optimal-order uniform-in-time error estimates are shown in the $L^2$- and $H^1$-norms. The error estimates are based on a consistency and stability analysis. The proof of stability is performed in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system. Numerical experiments illustrate the theoretical results.</jats:p>"}],"issue":"3","publication":"IMA Journal of Numerical Analysis","user_id":"100441","volume":42,"page":"2589-2620","publisher":"Oxford University Press (OUP)","_id":"45957","status":"public","citation":{"ama":"Harder P, Kovács B. Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>. 2021;42(3):2589-2620. doi:<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>","bibtex":"@article{Harder_Kovács_2021, title={Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions}, volume={42}, DOI={<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>}, number={3}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University Press (OUP)}, author={Harder, Paula and Kovács, Balázs}, year={2021}, pages={2589–2620} }","mla":"Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, Oxford University Press (OUP), 2021, pp. 2589–620, doi:<a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>.","chicago":"Harder, Paula, and Balázs Kovács. “Error Estimates for the Cahn–Hilliard Equation with Dynamic Boundary Conditions.” <i>IMA Journal of Numerical Analysis</i> 42, no. 3 (2021): 2589–2620. <a href=\"https://doi.org/10.1093/imanum/drab045\">https://doi.org/10.1093/imanum/drab045</a>.","short":"P. Harder, B. Kovács, IMA Journal of Numerical Analysis 42 (2021) 2589–2620.","apa":"Harder, P., &#38; Kovács, B. (2021). Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions. <i>IMA Journal of Numerical Analysis</i>, <i>42</i>(3), 2589–2620. <a href=\"https://doi.org/10.1093/imanum/drab045\">https://doi.org/10.1093/imanum/drab045</a>","ieee":"P. Harder and B. Kovács, “Error estimates for the Cahn–Hilliard equation with dynamic boundary conditions,” <i>IMA Journal of Numerical Analysis</i>, vol. 42, no. 3, pp. 2589–2620, 2021, doi: <a href=\"https://doi.org/10.1093/imanum/drab045\">10.1093/imanum/drab045</a>."}},{"publication":"Numerische Mathematik","issue":"4","department":[{"_id":"841"}],"type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"date_created":"2023-07-10T11:44:25Z","intvolume":"       147","publication_status":"published","date_updated":"2024-04-03T09:18:52Z","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"full_name":"Nick, Jörg","first_name":"Jörg","last_name":"Nick"},{"id":"100441","last_name":"Kovács","first_name":"Balázs","orcid":"0000-0001-9872-3474","full_name":"Kovács, Balázs"},{"full_name":"Lubich, Christian","first_name":"Christian","last_name":"Lubich"}],"year":"2021","title":"Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations","doi":"10.1007/s00211-021-01196-6","language":[{"iso":"eng"}],"citation":{"ama":"Nick J, Kovács B, Lubich C. Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>. 2021;147(4):997-1000. doi:<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>","bibtex":"@article{Nick_Kovács_Lubich_2021, title={Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations}, volume={147}, DOI={<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>}, number={4}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Nick, Jörg and Kovács, Balázs and Lubich, Christian}, year={2021}, pages={997–1000} }","mla":"Nick, Jörg, et al. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i>, vol. 147, no. 4, Springer Science and Business Media LLC, 2021, pp. 997–1000, doi:<a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>.","short":"J. Nick, B. Kovács, C. Lubich, Numerische Mathematik 147 (2021) 997–1000.","chicago":"Nick, Jörg, Balázs Kovács, and Christian Lubich. “Correction to: Stable and Convergent Fully Discrete Interior–Exterior Coupling of Maxwell’s Equations.” <i>Numerische Mathematik</i> 147, no. 4 (2021): 997–1000. <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">https://doi.org/10.1007/s00211-021-01196-6</a>.","apa":"Nick, J., Kovács, B., &#38; Lubich, C. (2021). Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations. <i>Numerische Mathematik</i>, <i>147</i>(4), 997–1000. <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">https://doi.org/10.1007/s00211-021-01196-6</a>","ieee":"J. Nick, B. Kovács, and C. Lubich, “Correction to: Stable and convergent fully discrete interior–exterior coupling of Maxwell’s equations,” <i>Numerische Mathematik</i>, vol. 147, no. 4, pp. 997–1000, 2021, doi: <a href=\"https://doi.org/10.1007/s00211-021-01196-6\">10.1007/s00211-021-01196-6</a>."},"status":"public","volume":147,"user_id":"100441","_id":"45961","publisher":"Springer Science and Business Media LLC","page":"997-1000"},{"issue":"3","publication":"Numerische Mathematik","date_created":"2023-07-10T11:43:59Z","department":[{"_id":"841"}],"keyword":["Applied Mathematics","Computational Mathematics"],"type":"journal_article","publication_identifier":{"issn":["0029-599X","0945-3245"]},"author":[{"full_name":"Kovács, Balázs","last_name":"Kovács","first_name":"Balázs"},{"full_name":"Li, Buyang","first_name":"Buyang","last_name":"Li"},{"last_name":"Lubich","first_name":"Christian","full_name":"Lubich, Christian"}],"year":"2021","title":"A convergent evolving finite element algorithm for Willmore flow of closed surfaces","intvolume":"       149","publication_status":"published","date_updated":"2024-04-03T09:19:20Z","language":[{"iso":"eng"}],"doi":"10.1007/s00211-021-01238-z","citation":{"mla":"Kovács, Balázs, et al. “A Convergent Evolving Finite Element Algorithm for Willmore Flow of Closed Surfaces.” <i>Numerische Mathematik</i>, vol. 149, no. 3, Springer Science and Business Media LLC, 2021, pp. 595–643, doi:<a href=\"https://doi.org/10.1007/s00211-021-01238-z\">10.1007/s00211-021-01238-z</a>.","bibtex":"@article{Kovács_Li_Lubich_2021, title={A convergent evolving finite element algorithm for Willmore flow of closed surfaces}, volume={149}, DOI={<a href=\"https://doi.org/10.1007/s00211-021-01238-z\">10.1007/s00211-021-01238-z</a>}, number={3}, journal={Numerische Mathematik}, publisher={Springer Science and Business Media LLC}, author={Kovács, Balázs and Li, Buyang and Lubich, Christian}, year={2021}, pages={595–643} }","ama":"Kovács B, Li B, Lubich C. A convergent evolving finite element algorithm for Willmore flow of closed surfaces. <i>Numerische Mathematik</i>. 2021;149(3):595-643. doi:<a href=\"https://doi.org/10.1007/s00211-021-01238-z\">10.1007/s00211-021-01238-z</a>","ieee":"B. Kovács, B. Li, and C. Lubich, “A convergent evolving finite element algorithm for Willmore flow of closed surfaces,” <i>Numerische Mathematik</i>, vol. 149, no. 3, pp. 595–643, 2021, doi: <a href=\"https://doi.org/10.1007/s00211-021-01238-z\">10.1007/s00211-021-01238-z</a>.","apa":"Kovács, B., Li, B., &#38; Lubich, C. (2021). A convergent evolving finite element algorithm for Willmore flow of closed surfaces. <i>Numerische Mathematik</i>, <i>149</i>(3), 595–643. <a href=\"https://doi.org/10.1007/s00211-021-01238-z\">https://doi.org/10.1007/s00211-021-01238-z</a>","chicago":"Kovács, Balázs, Buyang Li, and Christian Lubich. “A Convergent Evolving Finite Element Algorithm for Willmore Flow of Closed Surfaces.” <i>Numerische Mathematik</i> 149, no. 3 (2021): 595–643. <a href=\"https://doi.org/10.1007/s00211-021-01238-z\">https://doi.org/10.1007/s00211-021-01238-z</a>.","short":"B. Kovács, B. Li, C. Lubich, Numerische Mathematik 149 (2021) 595–643."},"status":"public","_id":"45959","publisher":"Springer Science and Business Media LLC","page":"595-643","volume":149,"user_id":"100441"},{"_id":"34629","publisher":"Elsevier BV","user_id":"49063","volume":382,"status":"public","citation":{"mla":"Hesse, Kerstin, et al. “Local RBF-Based Penalized Least-Squares Approximation on the Sphere with Noisy Scattered Data.” <i>Journal of Computational and Applied Mathematics</i>, vol. 382, 113061, Elsevier BV, 2021, doi:<a href=\"https://doi.org/10.1016/j.cam.2020.113061\">10.1016/j.cam.2020.113061</a>.","bibtex":"@article{Hesse_Sloan_Womersley_2021, title={Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data}, volume={382}, DOI={<a href=\"https://doi.org/10.1016/j.cam.2020.113061\">10.1016/j.cam.2020.113061</a>}, number={113061}, journal={Journal of Computational and Applied Mathematics}, publisher={Elsevier BV}, author={Hesse, Kerstin and Sloan, Ian H. and Womersley, Robert S.}, year={2021} }","ama":"Hesse K, Sloan IH, Womersley RS. Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data. <i>Journal of Computational and Applied Mathematics</i>. 2021;382. doi:<a href=\"https://doi.org/10.1016/j.cam.2020.113061\">10.1016/j.cam.2020.113061</a>","ieee":"K. Hesse, I. H. Sloan, and R. S. Womersley, “Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data,” <i>Journal of Computational and Applied Mathematics</i>, vol. 382, Art. no. 113061, 2021, doi: <a href=\"https://doi.org/10.1016/j.cam.2020.113061\">10.1016/j.cam.2020.113061</a>.","apa":"Hesse, K., Sloan, I. H., &#38; Womersley, R. S. (2021). Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data. <i>Journal of Computational and Applied Mathematics</i>, <i>382</i>, Article 113061. <a href=\"https://doi.org/10.1016/j.cam.2020.113061\">https://doi.org/10.1016/j.cam.2020.113061</a>","chicago":"Hesse, Kerstin, Ian H. Sloan, and Robert S. Womersley. “Local RBF-Based Penalized Least-Squares Approximation on the Sphere with Noisy Scattered Data.” <i>Journal of Computational and Applied Mathematics</i> 382 (2021). <a href=\"https://doi.org/10.1016/j.cam.2020.113061\">https://doi.org/10.1016/j.cam.2020.113061</a>.","short":"K. Hesse, I.H. Sloan, R.S. Womersley, Journal of Computational and Applied Mathematics 382 (2021)."},"article_number":"113061","language":[{"iso":"eng"}],"doi":"10.1016/j.cam.2020.113061","title":"Local RBF-based penalized least-squares approximation on the sphere with noisy scattered data","year":"2021","publication_identifier":{"issn":["0377-0427"]},"author":[{"full_name":"Hesse, Kerstin","orcid":"0000-0003-4125-1941","first_name":"Kerstin","last_name":"Hesse","id":"42608"},{"first_name":"Ian H.","last_name":"Sloan","full_name":"Sloan, Ian H."},{"last_name":"Womersley","first_name":"Robert S.","full_name":"Womersley, Robert S."}],"publication_status":"published","date_updated":"2024-04-03T11:04:23Z","intvolume":"       382","date_created":"2022-12-20T17:26:44Z","type":"journal_article","keyword":["Applied Mathematics","Computational Mathematics"],"department":[{"_id":"10"}],"publication":"Journal of Computational and Applied Mathematics"},{"doi":"10.1007/s00023-021-01068-7","language":[{"iso":"eng"}],"intvolume":"        22","publication_status":"published","date_updated":"2024-04-11T12:39:23Z","author":[{"full_name":"Guillarmou, Colin","first_name":"Colin","last_name":"Guillarmou"},{"full_name":"Küster, Benjamin","first_name":"Benjamin","last_name":"Küster"}],"publication_identifier":{"issn":["1424-0637","1424-0661"]},"year":"2021","title":"Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds","department":[{"_id":"548"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"type":"journal_article","date_created":"2022-06-20T08:37:52Z","publication":"Annales Henri Poincaré","issue":"11","volume":22,"user_id":"70575","publisher":"Springer Science and Business Media LLC","_id":"32006","page":"3565-3617","status":"public","citation":{"short":"C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617.","chicago":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i> 22, no. 11 (2021): 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>.","ieee":"C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds,” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, pp. 3565–3617, 2021, doi: <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>.","apa":"Guillarmou, C., &#38; Küster, B. (2021). Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>, <i>22</i>(11), 3565–3617. <a href=\"https://doi.org/10.1007/s00023-021-01068-7\">https://doi.org/10.1007/s00023-021-01068-7</a>","bibtex":"@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}, volume={22}, DOI={<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>}, number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021}, pages={3565–3617} }","ama":"Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. <i>Annales Henri Poincaré</i>. 2021;22(11):3565-3617. doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>","mla":"Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” <i>Annales Henri Poincaré</i>, vol. 22, no. 11, Springer Science and Business Media LLC, 2021, pp. 3565–617, doi:<a href=\"https://doi.org/10.1007/s00023-021-01068-7\">10.1007/s00023-021-01068-7</a>."}},{"status":"public","volume":53,"user_id":"31132","_id":"53363","publisher":"Springer Science and Business Media LLC","page":"1189-1206","citation":{"short":"S. Rezat, L. Fan, B. Pepin, ZDM – Mathematics Education 53 (2021) 1189–1206.","ama":"Rezat S, Fan L, Pepin B. Mathematics textbooks and curriculum resources as instruments for change. <i>ZDM – Mathematics Education</i>. 2021;53(6):1189-1206. doi:<a href=\"https://doi.org/10.1007/s11858-021-01309-3\">10.1007/s11858-021-01309-3</a>","chicago":"Rezat, Sebastian, Lianghuo Fan, and Birgit Pepin. “Mathematics Textbooks and Curriculum Resources as Instruments for Change.” <i>ZDM – Mathematics Education</i> 53, no. 6 (2021): 1189–1206. <a href=\"https://doi.org/10.1007/s11858-021-01309-3\">https://doi.org/10.1007/s11858-021-01309-3</a>.","bibtex":"@article{Rezat_Fan_Pepin_2021, title={Mathematics textbooks and curriculum resources as instruments for change}, volume={53}, DOI={<a href=\"https://doi.org/10.1007/s11858-021-01309-3\">10.1007/s11858-021-01309-3</a>}, number={6}, journal={ZDM – Mathematics Education}, publisher={Springer Science and Business Media LLC}, author={Rezat, Sebastian and Fan, Lianghuo and Pepin, Birgit}, year={2021}, pages={1189–1206} }","apa":"Rezat, S., Fan, L., &#38; Pepin, B. (2021). Mathematics textbooks and curriculum resources as instruments for change. <i>ZDM – Mathematics Education</i>, <i>53</i>(6), 1189–1206. <a href=\"https://doi.org/10.1007/s11858-021-01309-3\">https://doi.org/10.1007/s11858-021-01309-3</a>","mla":"Rezat, Sebastian, et al. “Mathematics Textbooks and Curriculum Resources as Instruments for Change.” <i>ZDM – Mathematics Education</i>, vol. 53, no. 6, Springer Science and Business Media LLC, 2021, pp. 1189–206, doi:<a href=\"https://doi.org/10.1007/s11858-021-01309-3\">10.1007/s11858-021-01309-3</a>.","ieee":"S. Rezat, L. Fan, and B. Pepin, “Mathematics textbooks and curriculum resources as instruments for change,” <i>ZDM – Mathematics Education</i>, vol. 53, no. 6, pp. 1189–1206, 2021, doi: <a href=\"https://doi.org/10.1007/s11858-021-01309-3\">10.1007/s11858-021-01309-3</a>."},"intvolume":"        53","publication_status":"published","date_updated":"2024-04-18T07:51:53Z","author":[{"full_name":"Rezat, Sebastian","last_name":"Rezat","first_name":"Sebastian","id":"31132"},{"first_name":"Lianghuo","last_name":"Fan","full_name":"Fan, Lianghuo"},{"full_name":"Pepin, Birgit","first_name":"Birgit","last_name":"Pepin"}],"publication_identifier":{"issn":["1863-9690","1863-9704"]},"title":"Mathematics textbooks and curriculum resources as instruments for change","year":"2021","doi":"10.1007/s11858-021-01309-3","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title><jats:p>In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources as instruments for change from a theoretical perspective; (2) The design of curriculum resources to mediate the implementation of reform ideas and innovative practice; (3) Teachers’ influence on the implementation of change through curriculum resources; (4) Students’ influence on the implementation of change through curriculum resources; and (5) Evidence of curriculum resources yielding changes in student-related factors or variables. We claim that, whilst textbooks and curriculum resources are influential, they alone cannot change teachers’ teaching nor students’ learning practices in times of curricular change. Moreover, more knowledge is needed about features of curriculum resources that support the implementation of change. We contend that curriculum innovations are likely to be successful, if teachers and students are supported to co- and re-design the relevant curriculum trajectories and materials in line with the reform efforts and their own individual needs.</jats:p>"}],"publication":"ZDM – Mathematics Education","issue":"6","department":[{"_id":"360"}],"type":"journal_article","keyword":["General Mathematics","Education"],"date_created":"2024-04-09T06:50:36Z"},{"type":"book_chapter","department":[{"_id":"360"},{"_id":"543"}],"place":"London","date_created":"2022-11-30T08:33:27Z","related_material":{"link":[{"relation":"other","url":"https://doi.org/10.4324/9781003137580"}]},"publication":"Mathematics Education in the Digital Age. Learning, Practice and Theory","citation":{"bibtex":"@inbook{Rezat_Schacht_Häsel-Weide_2021, place={London}, title={Challenges of making sense of tasks and automated feedback in digital mathematics textbooks}, DOI={<a href=\"https://doi.org/10.4324/9781003137580\">10.4324/9781003137580</a>}, booktitle={Mathematics Education in the Digital Age. Learning, Practice and Theory}, publisher={Routledge}, author={Rezat, Sebastian and Schacht, Florian and Häsel-Weide, Uta}, editor={Clark-Wilson, A. and Donevska-Todorova, A. and Faggiano, E. and Trgalová , J. and Weigang, H.-G.}, year={2021}, pages={168–184} }","ama":"Rezat S, Schacht F, Häsel-Weide U. Challenges of making sense of tasks and automated feedback in digital mathematics textbooks. In: Clark-Wilson A, Donevska-Todorova A, Faggiano E, Trgalová  J, Weigang H-G, eds. <i>Mathematics Education in the Digital Age. Learning, Practice and Theory</i>. Routledge; 2021:168-184. doi:<a href=\"https://doi.org/10.4324/9781003137580\">10.4324/9781003137580</a>","mla":"Rezat, Sebastian, et al. “Challenges of Making Sense of Tasks and Automated Feedback in Digital Mathematics Textbooks.” <i>Mathematics Education in the Digital Age. Learning, Practice and Theory</i>, edited by A. Clark-Wilson et al., Routledge, 2021, pp. 168–84, doi:<a href=\"https://doi.org/10.4324/9781003137580\">10.4324/9781003137580</a>.","short":"S. Rezat, F. Schacht, U. Häsel-Weide, in: A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalová , H.-G. Weigang (Eds.), Mathematics Education in the Digital Age. Learning, Practice and Theory, Routledge, London, 2021, pp. 168–184.","chicago":"Rezat, Sebastian, Florian Schacht, and Uta Häsel-Weide. “Challenges of Making Sense of Tasks and Automated Feedback in Digital Mathematics Textbooks.” In <i>Mathematics Education in the Digital Age. Learning, Practice and Theory</i>, edited by A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalová , and H.-G. Weigang, 168–84. London: Routledge, 2021. <a href=\"https://doi.org/10.4324/9781003137580\">https://doi.org/10.4324/9781003137580</a>.","ieee":"S. Rezat, F. Schacht, and U. Häsel-Weide, “Challenges of making sense of tasks and automated feedback in digital mathematics textbooks,” in <i>Mathematics Education in the Digital Age. Learning, Practice and Theory</i>, A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalová , and H.-G. Weigang, Eds. London: Routledge, 2021, pp. 168–184.","apa":"Rezat, S., Schacht, F., &#38; Häsel-Weide, U. (2021). Challenges of making sense of tasks and automated feedback in digital mathematics textbooks. In A. Clark-Wilson, A. Donevska-Todorova, E. Faggiano, J. Trgalová , &#38; H.-G. Weigang (Eds.), <i>Mathematics Education in the Digital Age. Learning, Practice and Theory</i> (pp. 168–184). Routledge. <a href=\"https://doi.org/10.4324/9781003137580\">https://doi.org/10.4324/9781003137580</a>"},"doi":"10.4324/9781003137580","user_id":"31132","editor":[{"first_name":"A.","last_name":"Clark-Wilson","full_name":"Clark-Wilson, A."},{"full_name":"Donevska-Todorova, A.","last_name":"Donevska-Todorova","first_name":"A."},{"full_name":"Faggiano, E.","first_name":"E.","last_name":"Faggiano"},{"full_name":"Trgalová , J.","first_name":"J.","last_name":"Trgalová "},{"full_name":"Weigang, H.-G.","last_name":"Weigang","first_name":"H.-G."}],"page":"168-184","_id":"34161","language":[{"iso":"eng"}],"publisher":"Routledge","date_updated":"2024-04-18T08:11:39Z","year":"2021","status":"public","title":"Challenges of making sense of tasks and automated feedback in digital mathematics textbooks","author":[{"last_name":"Rezat","first_name":"Sebastian","full_name":"Rezat, Sebastian","id":"31132"},{"full_name":"Schacht, Florian","last_name":"Schacht","first_name":"Florian"},{"id":"60267","first_name":"Uta","last_name":"Häsel-Weide","full_name":"Häsel-Weide, Uta"}]},{"page":"1433-1445","publisher":"Springer","_id":"44683","user_id":"31132","volume":53,"status":"public","citation":{"ieee":"S. Rezat, “How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies,” <i>ZDM Mathematics Education</i>, vol. 53, no. 6, pp. 1433–1445, 2021, doi: <a href=\"https://doi.org/10.1007/s11858-021-01263-0\">10.1007/s11858-021-01263-0</a>.","apa":"Rezat, S. (2021). How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies. <i>ZDM Mathematics Education</i>, <i>53</i>(6), 1433–1445. <a href=\"https://doi.org/10.1007/s11858-021-01263-0\">https://doi.org/10.1007/s11858-021-01263-0</a>","short":"S. Rezat, ZDM Mathematics Education 53 (2021) 1433–1445.","chicago":"Rezat, Sebastian. “How Automated Feedback from a Digital Mathematics Textbook Affects Primary Students’ Conceptual Development: Two Case Studies.” <i>ZDM Mathematics Education</i> 53, no. 6 (2021): 1433–45. <a href=\"https://doi.org/10.1007/s11858-021-01263-0\">https://doi.org/10.1007/s11858-021-01263-0</a>.","mla":"Rezat, Sebastian. “How Automated Feedback from a Digital Mathematics Textbook Affects Primary Students’ Conceptual Development: Two Case Studies.” <i>ZDM Mathematics Education</i>, vol. 53, no. 6, Springer, 2021, pp. 1433–45, doi:<a href=\"https://doi.org/10.1007/s11858-021-01263-0\">10.1007/s11858-021-01263-0</a>.","bibtex":"@article{Rezat_2021, title={How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies}, volume={53}, DOI={<a href=\"https://doi.org/10.1007/s11858-021-01263-0\">10.1007/s11858-021-01263-0</a>}, number={6}, journal={ZDM Mathematics Education}, publisher={Springer}, author={Rezat, Sebastian}, year={2021}, pages={1433–1445} }","ama":"Rezat S. How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies. <i>ZDM Mathematics Education</i>. 2021;53(6):1433-1445. doi:<a href=\"https://doi.org/10.1007/s11858-021-01263-0\">10.1007/s11858-021-01263-0</a>"},"quality_controlled":"1","language":[{"iso":"eng"}],"doi":"10.1007/s11858-021-01263-0","title":"How automated feedback from a digital mathematics textbook affects primary students’ conceptual development: two case studies","year":"2021","author":[{"first_name":"Sebastian","last_name":"Rezat","full_name":"Rezat, Sebastian","id":"31132"}],"publication_identifier":{"issn":["1863-9690","1863-9704"]},"date_updated":"2024-04-18T08:23:20Z","publication_status":"published","intvolume":"        53","date_created":"2023-05-09T13:01:30Z","type":"journal_article","keyword":["General Mathematics","Education"],"department":[{"_id":"360"}],"issue":"6","publication":"ZDM Mathematics Education","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>One of the most prevalent features of digital mathematics textbooks, compared to traditional ones, is the provision of automated feedback on students’ solutions. Since feedback is regarded as an important factor that influences learning, this is often seen as an affordance of digital mathematics textbooks. While there is a large body of mainly quantitative research on the effectiveness of feedback in general, very little is known about how feedback actually affects students’ individual content specific learning processes and conceptual development. A theoretical framework based on Rabardel’s theory of the instrument and Vergnaud’s theory of conceptual fields is developed to study qualitatively how feedback actually functions in the learning process. This framework was applied in a case study of two elementary school students’ learning processes when working on a probability task from a German 3rd grade digital textbook. The analysis allowed detailed reconstruction of how students made sense of the information provided by the feedback and adjusted their behavior accordingly. This in-depth analysis unveiled that feedback does not necessarily foster conceptual development in the desired way, and a correct solution does not always coincide with conceptual understanding. The results point to some obstacles that students face when working individually on tasks from digital mathematics textbooks with automated feedback, and indicate that feedback needs to be developed in design-based research cycles in order to yield the desired effects.</jats:p>","lang":"eng"}]},{"citation":{"bibtex":"@inbook{Hochmuth_Biehler_Blum_Achmetli_Rode_Krawitz_Schukajlow_Bender_Haase_2021, place={Berlin, Heidelberg}, title={Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation}, DOI={<a href=\"https://doi.org/10.1007/978-3-662-62854-6_24\">10.1007/978-3-662-62854-6_24</a>}, booktitle={Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik}, publisher={Springer Spektrum}, author={Hochmuth, Reinhard and Biehler, Rolf and Blum, Werner and Achmetli, Kay and Rode, Jana and Krawitz, Janina and Schukajlow, Stanislaw and Bender, Peter and Haase, Jürgen}, editor={Biehler, Rolf and Eichler, Andreas and Hochmuth, Reinhard and Rach, Stefanie and Schaper, Niclas}, year={2021}, pages={611–644} }","ama":"Hochmuth R, Biehler R, Blum W, et al. Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation. In: Biehler R, Eichler A, Hochmuth R, Rach S, Schaper N, eds. <i>Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>. 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Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik</i>, edited by Rolf Biehler, Andreas Eichler, Reinhard Hochmuth, Stefanie Rach, and Niclas Schaper, 611–44. Berlin, Heidelberg: Springer Spektrum, 2021. <a href=\"https://doi.org/10.1007/978-3-662-62854-6_24\">https://doi.org/10.1007/978-3-662-62854-6_24</a>.","short":"R. Hochmuth, R. Biehler, W. Blum, K. Achmetli, J. Rode, J. Krawitz, S. Schukajlow, P. Bender, J. Haase, in: R. Biehler, A. Eichler, R. Hochmuth, S. Rach, N. Schaper (Eds.), Lehrinnovationen in der Hochschulmathematik . Konzepte und Studien zur Hochschuldidaktik und Lehrerbildung Mathematik, Springer Spektrum, Berlin, Heidelberg, 2021, pp. 611–644.","ieee":"R. Hochmuth <i>et al.</i>, “Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden – Entwicklung im ersten Semester und Veränderungen durch eine Lehrinnovation,” in <i>Lehrinnovationen in der Hochschulmathematik . 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