{"pk":50144,"title":"Studying Mathematical Reasoning through the Gadget Game","subtitle":null,"abstract":"Mathematicians regularly come up with multi-step solutions to difficult problems, formulating intermediate statements and subgoals, deciding which ones to attempt to prove, and judging when to start, stop, or come back to a question. What drives these and similar cognitive processes? Studying mathematical reasoning is challenging, in part because of a lack of engaging yet controlled environments in which to do so. We introduce a new game -- the Gadget Game -- for this purpose. Each level in the Gadget Game can be an encoding of a provable mathematical statement, together with hypotheses and deduction rules, that obscures the semantic content of the original problem. The resulting puzzles are enjoyable to play. We conduct a series of preliminary experiments involving a web-based crowdsourced experiment and a \"think aloud\"' deep-dive with two experienced mathematicians. We believe that the Gadget Game is a ripe domain for interesting cognitive science that engages deeply with mathematical thought.","language":"eng","license":{"name":"","short_name":"","text":null,"url":""},"keywords":[{"word":"Psychology; Problem Solving; Reasoning; Representation; Case studies; Mathematical modeling"}],"section":"Abstracts with Poster Presentation (accepted as Abstracts)","is_remote":true,"remote_url":"https://escholarship.org/uc/item/823177z7","frozenauthors":[{"first_name":"Jonas","middle_name":"","last_name":"Bayer","name_suffix":"","institution":"University of Cambridge","department":""},{"first_name":"Jacob","middle_name":"","last_name":"Loader","name_suffix":"","institution":"University of Cambridge","department":""},{"first_name":"Katherine","middle_name":"M","last_name":"Collins","name_suffix":"","institution":"MIT","department":""},{"first_name":"Simon","middle_name":"","last_name":"Frieder","name_suffix":"","institution":"University of Oxford","department":""},{"first_name":"Adrian","middle_name":"","last_name":"Weller","name_suffix":"","institution":"University of Cambridge","department":""},{"first_name":"Joshua","middle_name":"B.","last_name":"Tenenbaum","name_suffix":"","institution":"MIT","department":""},{"first_name":"Timothy","middle_name":"","last_name":"Gowers","name_suffix":"","institution":"University of Cambridge","department":""}],"date_submitted":null,"date_accepted":null,"date_published":"2025-01-01T19:00:00+01:00","render_galley":null,"galleys":[{"label":"PDF","type":"pdf","path":"https://journalpub.escholarship.org/cognitivesciencesociety/article/50144/galley/38106/download/"}]}