{"corpus_id":118957506,"paper_sha":"697d0e8b4f4de16d7e18ed4dadf516bfe6bed476","doi":"10.1080/24727466.2010.11790298","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":1610642340,"dblp_id":null,"acl_id":null,"title":"Undergraduates’ Example Use in Proof Construction: Purposes and Effectiveness","year":2010,"publication_date":"2010-09-01","venue":"","journal":{"name":"Investigations in Mathematics Learning","pages":"1 - 22","volume":"3"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":47,"citation_count":40,"influential_citation_count":2,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"https://figshare.com/articles/journal_contribution/Undergraduates_example_use_in_proof_construction_purposes_and_effectiveness/9370826/1/files/16981442.pdf","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/697d0e8b4f4de16d7e18ed4dadf516bfe6bed476","s2_open_access_license":"CCBYNCND","s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully constructing proofs, and that these purposes are consistent with those described by mathematicians. We then examine other cases in which students used examples ineffectively. We note that in these cases, the purposes for which the students attempted to use examples are again appropriate, but the implementation of their strategies is inadequate in one of two specific ways. On this basis we identify points that should be borne in mind by a university teacher who wishes to teach students to use examples effectively in proof-based mathematics courses.","claims":[{"public_id":"cl_fac673cc0c97e325a0f50b33965bb194","status":"active","text":"In ineffective cases, the purposes for using examples are appropriate, but the implementation of the strategies is inadequate in one of two specific ways.","confidence":0.93,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_fac673cc0c97e325a0f50b33965bb194"},{"public_id":"cl_06b2e04892b38b1c160887c247d9fa98","status":"active","text":"Points are identified for university teachers who want to teach students to use examples effectively in proof-based mathematics courses.","confidence":0.83,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_06b2e04892b38b1c160887c247d9fa98"},{"public_id":"cl_690baebc540878ddba2fae995e89f277","status":"active","text":"Undergraduates in a transition-to-proof course use examples for specific purposes while successfully constructing proofs, and those purposes align with purposes described by mathematicians.","confidence":0.94,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_690baebc540878ddba2fae995e89f277"}],"concepts":[{"public_id":"co_1af69de6b46e477f174d8ee760252c5c","status":"active","name":"exploratory study","description":"An investigation aimed at examining how students use examples in proof attempts.","types":["study design"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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