{"id":"https://openalex.org/W4386498498","doi":"https://doi.org/10.3390/sym15091716","title":"How to Pose Problems on Periodicity and Teaching with Problem Posing","display_name":"How to Pose Problems on Periodicity and Teaching with Problem Posing","publication_year":2023,"publication_date":"2023-09-07","ids":{"openalex":"https://openalex.org/W4386498498","doi":"https://doi.org/10.3390/sym15091716"},"language":"en","primary_location":{"id":"doi:10.3390/sym15091716","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091716","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1716/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/9/1716/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083582726","display_name":"Guoqiang Dang","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guoqiang Dang","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0003-4393-9715","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101598726","display_name":"Yufeng Guo","orcid":"https://orcid.org/0000-0003-3361-7579"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yufeng Guo","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0003-3361-7579","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052701967","display_name":"Kai Li","orcid":"https://orcid.org/0000-0002-3845-3895"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Li","raw_affiliation_strings":["School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101598726"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.9146,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.78303017,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"9","first_page":"1716","last_page":"1716"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10130","display_name":"Mathematics Education and Teaching Techniques","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9696000218391418,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6742899417877197},{"id":"https://openalex.org/keywords/mathematical-problem","display_name":"Mathematical problem","score":0.6204756498336792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49616751074790955},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.47286128997802734},{"id":"https://openalex.org/keywords/mathematics-education","display_name":"Mathematics education","score":0.46266651153564453},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4516642391681671},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.43616676330566406},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4151264429092407},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3894578814506531},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.32942691445350647},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11543172597885132}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6742899417877197},{"id":"https://openalex.org/C66783780","wikidata":"https://www.wikidata.org/wiki/Q1166625","display_name":"Mathematical problem","level":2,"score":0.6204756498336792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49616751074790955},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.47286128997802734},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.46266651153564453},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4516642391681671},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.43616676330566406},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4151264429092407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3894578814506531},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.32942691445350647},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11543172597885132},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15091716","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091716","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1716/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d36589c7a9074a5887f82209140f5faa","is_oa":false,"landing_page_url":"https://doaj.org/article/d36589c7a9074a5887f82209140f5faa","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 9, p 1716 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/9/1716/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15091716","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15091716","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15091716","pdf_url":"https://www.mdpi.com/2073-8994/15/9/1716/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6600000262260437,"display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G7497301013","display_name":null,"funder_award_id":"19YJA880009","funder_id":"https://openalex.org/F4320321106","funder_display_name":"Ministry of Education of the People's Republic of China"}],"funders":[{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386498498.pdf","grobid_xml":"https://content.openalex.org/works/W4386498498.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W829001109","https://openalex.org/W1254520110","https://openalex.org/W1494563177","https://openalex.org/W1530798444","https://openalex.org/W1542746085","https://openalex.org/W1576482218","https://openalex.org/W1633315028","https://openalex.org/W1966380491","https://openalex.org/W1976196891","https://openalex.org/W1983624685","https://openalex.org/W2027922926","https://openalex.org/W2058338047","https://openalex.org/W2060480593","https://openalex.org/W2083960709","https://openalex.org/W2086673715","https://openalex.org/W2112880297","https://openalex.org/W2738327069","https://openalex.org/W2899283552","https://openalex.org/W2912396804","https://openalex.org/W2913557066","https://openalex.org/W2945862264","https://openalex.org/W2992473810","https://openalex.org/W3006490921","https://openalex.org/W3008999632","https://openalex.org/W3016216170","https://openalex.org/W3087306623","https://openalex.org/W3094783728","https://openalex.org/W3098373824","https://openalex.org/W3110553598","https://openalex.org/W3133305934","https://openalex.org/W3158426462","https://openalex.org/W3161404584","https://openalex.org/W3183290492","https://openalex.org/W3196613480","https://openalex.org/W4237970627","https://openalex.org/W4248614872","https://openalex.org/W4303987503","https://openalex.org/W4311192110","https://openalex.org/W4315486801","https://openalex.org/W4381431180","https://openalex.org/W4386412163","https://openalex.org/W6628153626","https://openalex.org/W6641896212","https://openalex.org/W6771781351","https://openalex.org/W6787016803","https://openalex.org/W6847325479"],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W4300899577","https://openalex.org/W2371138613","https://openalex.org/W3194471551","https://openalex.org/W2048963458","https://openalex.org/W4375956809","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W1581373162","https://openalex.org/W4302778552"],"abstract_inverted_index":{"Research":[0],"on":[1,133],"how":[2,187],"to":[3,47,63,77,149],"pose":[4,106],"good":[5,18],"problems":[6,19,60,155,235],"in":[7,35,50,87,137],"mathematical":[8,36,42,73,108,166,183,200,207,231],"science":[9],"is":[10,193],"rarely":[11,119],"touched.":[12],"Inspired":[13],"by":[14,33,85,180,203,210],"Kilpatrick\u2019s":[15],"\u201cWhere":[16],"do":[17],"come":[20],"from?\u201d,":[21],"the":[22,26,29,51,79,124,169,199,206],"current":[23],"research":[24,196],"investigates":[25],"problem":[27,31,201,208,243],"of":[28,44,53,55,123,165,236],"specific":[30],"posed":[32],"mathematicians":[34,86,96,181,204],"sciences.":[37],"We":[38],"select":[39],"a":[40,115,128,194],"recent":[41],"conjecture":[43],"Yang":[45],"related":[46],"periodic":[48,239],"functions":[49,54,240],"field":[52],"one":[56,242],"complex":[57,64,237,245],"variable.":[58],"These":[59],"are":[61,118,177],"extended":[62],"differential":[65],"equations,":[66,68,70],"difference":[67,246],"differential-difference":[69],"etc.":[71],"Through":[72],"analysis,":[74],"we":[75,161,227],"try":[76],"reproduce":[78],"effective":[80],"strategies":[81,189],"or":[82,182],"techniques":[83],"used":[84],"posing":[88,153,202,209],"these":[89,188],"new":[90,107],"problems.":[91,109],"The":[92,121],"results":[93,122],"show":[94],"that":[95,197],"often":[97],"use":[98],"generalization,":[99],"constraint":[100,222],"manipulation,":[101],"and":[102,113,131,139,144,156,185,205,212,217,224,241],"specialization":[103],"when":[104],"they":[105],"Conversely,":[110],"goal":[111],"manipulation":[112,223],"targeting":[114],"particular":[116],"solution":[117],"used.":[120],"study":[125],"may":[126],"have":[127],"potential":[129],"impact":[130],"promotion":[132],"implementing":[134],"problem-posing":[135,174],"teaching":[136,167],"primary":[138],"secondary":[140,213],"schools.":[141],"Accordingly,":[142],"teachers":[143,216],"students":[145],"can":[146],"be":[147],"encouraged":[148],"think":[150],"like":[151],"mathematicians,":[152],"better":[154],"learning":[157],"mathematics":[158],"better.":[159],"Then,":[160],"give":[162],"some":[163],"examples":[164],"at":[168],"high":[170],"school":[171,214],"level":[172],"using":[173],"strategies,":[175],"which":[176],"frequently":[178],"employed":[179],"researchers,":[184],"demonstrate":[186],"work.":[190],"Therefore,":[191],"this":[192],"pioneering":[195],"integrates":[198],"elementary":[211],"math":[215],"students.":[218],"In":[219],"addition,":[220],"applying":[221],"analogical":[225],"reasoning,":[226],"present":[228],"four":[229],"unsolved":[230],"problems,":[232],"including":[233],"three":[234],"difference-related":[238],"with":[244],"equations.":[247]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}