{"pk":49482,"title":"Towards a curriculum for neural networks to simulate symbolic arithmetic","subtitle":null,"abstract":"Understanding and operating on multi-digit numbers is a critical step in the development of mathematical skills and concepts. Empirical and computational modeling evidence suggests that multi-digit numbers are processed decomposed into units, tens, hundreds, etc. for magnitude comparison. Yet, there is currently no computational model to simulate multi-digit number arithmetic. Accordingly, we developed a neural network model with three interconnected modules reflecting single-digit additions, recognition of a carry-over, and decision-making. We then compared model performance after following two training curricula: i) a \\textit{ step-by-step} curriculum, where single-digit addition are trained before progressing to multi-digit problems and ii) an \\textit{all-at-once} curriculum, where all modules of the model were trained simultaneously. Our results indicated that only the \\textit{step-by-step} curriculum made the model learn multi-digit addition successfully as reflected by replicating empirical effects of carry-over and problem size. These findings highlight the importance of structured, incremental learning in both cognitive modeling and education.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[{"word":"Education; Psychology; Learning; Computational Modeling; Neural Networks"}],"section":"Papers with Poster Presentation","is_remote":true,"remote_url":"https://escholarship.org/uc/item/5dt3d93g","frozenauthors":[{"first_name":"Samuel","middle_name":"","last_name":"Lozano","name_suffix":"","institution":"Complutense University of Madrid","department":""},{"first_name":"Markus","middle_name":"","last_name":"Spitzer","name_suffix":"","institution":"Martin-Luther University, Halle-Wittenberg","department":""},{"first_name":"Younes","middle_name":"","last_name":"Strittmatter","name_suffix":"","institution":"Princeton University","department":""},{"first_name":"Korbinian","middle_name":"","last_name":"Moeller","name_suffix":"","institution":"Loughborough University","department":""},{"first_name":"Miguel","middle_name":"","last_name":"Ruiz-Garcia","name_suffix":"","institution":"Complutense University de Madrid","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"2025-01-01T18:00:00Z","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/49482/galley/37444/download/"}]}