{"id":"https://openalex.org/W7214230767","doi":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","title":"Supporting critical thinking in sequences and series through a problem-solving e-module with algebraic tasks","display_name":"Supporting critical thinking in sequences and series through a problem-solving e-module with algebraic tasks","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214230767","doi":"https://doi.org/10.22460/infinity.v15i4.p1031-1060"},"language":"en","primary_location":{"id":"doi:10.22460/infinity.v15i4.p1031-1060","doi":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","is_oa":true,"landing_page_url":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","pdf_url":"https://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/download/7304/2599","source":{"id":"https://openalex.org/S2764492204","display_name":"Infinity Journal","issn_l":"2089-6867","issn":["2089-6867","2460-9285"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310314984","host_organization_name":"Mathematics Education Study Program of STKIP Siliwangi","host_organization_lineage":["https://openalex.org/P4310314984"],"host_organization_lineage_names":["Mathematics Education Study Program of STKIP Siliwangi"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Infinity Journal","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/download/7304/2599","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063398933","display_name":"Nasrun Nasrun","orcid":"https://orcid.org/0000-0003-1684-3101","observed_orcids":["https://orcid.org/0000-0003-1684-3101"]},"institutions":[{"id":"https://openalex.org/I3132802412","display_name":"Muhammadiyah University of Makassar","ror":"https://ror.org/03kc2e209","country_code":"ID","type":"education","lineage":["https://openalex.org/I3132802412"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Nasrun Nasrun","raw_affiliation_strings":["Department of Mathematics Education, Universitas Muhammadiyah Makassar"],"raw_orcid":"https://orcid.org/0000-0003-1684-3101","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Universitas Muhammadiyah Makassar","institution_ids":["https://openalex.org/I3132802412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075407230","display_name":"Irwan Akib","orcid":"https://orcid.org/0000-0003-0358-688X","observed_orcids":["https://orcid.org/0000-0003-0358-688X"]},"institutions":[{"id":"https://openalex.org/I3132802412","display_name":"Muhammadiyah University of Makassar","ror":"https://ror.org/03kc2e209","country_code":"ID","type":"education","lineage":["https://openalex.org/I3132802412"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Irwan Akib","raw_affiliation_strings":["Department of Mathematics Education, Universitas Muhammadiyah Makassar"],"raw_orcid":"https://orcid.org/0000-0003-0358-688X","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Universitas Muhammadiyah Makassar","institution_ids":["https://openalex.org/I3132802412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048015869","display_name":"Muhammad Ikram","orcid":"https://orcid.org/0000-0002-3763-4299","observed_orcids":["https://orcid.org/0000-0002-3763-4299"]},"institutions":[{"id":"https://openalex.org/I4429535","display_name":"State University of Makassar","ror":"https://ror.org/05fzw1z08","country_code":"ID","type":"education","lineage":["https://openalex.org/I4429535"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Muhammad Ikram","raw_affiliation_strings":["Department of Mathematics, Universitas Negeri Makassar"],"raw_orcid":"https://orcid.org/0000-0002-3763-4299","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitas Negeri Makassar","institution_ids":["https://openalex.org/I4429535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087683206","display_name":"Muhammad Muzaini","orcid":"https://orcid.org/0000-0003-0042-7031","observed_orcids":["https://orcid.org/0000-0003-0042-7031"]},"institutions":[{"id":"https://openalex.org/I3132802412","display_name":"Muhammadiyah University of Makassar","ror":"https://ror.org/03kc2e209","country_code":"ID","type":"education","lineage":["https://openalex.org/I3132802412"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Muhammad Muzaini","raw_affiliation_strings":["Department of Mathematics Education, Universitas Muhammadiyah Makassar"],"raw_orcid":"https://orcid.org/0000-0003-0042-7031","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, Universitas Muhammadiyah Makassar","institution_ids":["https://openalex.org/I3132802412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058974705","display_name":"Rahmat Kamaruddin","orcid":"https://orcid.org/0009-0003-5515-4576","observed_orcids":["https://orcid.org/0009-0003-5515-4576"]},"institutions":[{"id":"https://openalex.org/I4405275686","display_name":"STKIP Andi Matappa","ror":"https://ror.org/044a2pr22","country_code":"ID","type":"education","lineage":["https://openalex.org/I4405275686"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Rahmat Kamaruddin","raw_affiliation_strings":["Department of Mathematics Education, STKIP Andi Matappa Pangkep"],"raw_orcid":"https://orcid.org/0009-0003-5515-4576","affiliations":[{"raw_affiliation_string":"Department of Mathematics Education, STKIP Andi Matappa Pangkep","institution_ids":["https://openalex.org/I4405275686"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1000000,"currency":"IDR","value_usd":65},"apc_paid":{"value":1000000,"currency":"IDR","value_usd":65},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58755883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"4","first_page":"1031","last_page":"1060"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12522","display_name":"Mathematics Education and Pedagogy","score":0.9976000189781189,"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/T12522","display_name":"Mathematics Education and Pedagogy","score":0.9976000189781189,"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/T11715","display_name":"Education and Critical Thinking Development","score":0.0013000000035390258,"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/T12590","display_name":"STEM Education","score":0.0005000000237487257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/critical-thinking","display_name":"critical thinking","score":0.9869999885559082},{"id":"https://openalex.org/keywords/sequences-and-series","display_name":"sequences and series","score":0.9950000047683716},{"id":"https://openalex.org/keywords/e-module","display_name":"e-module","score":0.7559999823570251},{"id":"https://openalex.org/keywords/problem-solving","display_name":"problem solving","score":0.5080000162124634},{"id":"https://openalex.org/keywords/algebraic-thinking","display_name":"algebraic thinking","score":0.7570000290870667},{"id":"https://openalex.org/keywords/algebraic-modeling","display_name":"algebraic modeling","score":0.7879999876022339},{"id":"https://openalex.org/keywords/generalization","display_name":"generalization","score":0.8939999938011169},{"id":"https://openalex.org/keywords/scaffolding","display_name":"scaffolding","score":0.9319999814033508},{"id":"https://openalex.org/keywords/feedback","display_name":"feedback","score":0.9380000233650208},{"id":"https://openalex.org/keywords/reflection","display_name":"reflection","score":0.9660000205039978},{"id":"https://openalex.org/keywords/argument-quality","display_name":"argument quality","score":0.5230000019073486},{"id":"https://openalex.org/keywords/secondary-school-students","display_name":"high school students","score":0.7289999723434448}],"concepts":[{"id":"https://openalex.org/C533356498","wikidata":"https://www.wikidata.org/wiki/Q843894","display_name":"Critical thinking","level":2,"score":0.7312999963760376},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.631600022315979},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5602999925613403},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.5498999953269958},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.498199999332428},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.4927999973297119},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.4291999936103821},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C2986913963","wikidata":"https://www.wikidata.org/wiki/Q843894","display_name":"Critical reflection","level":2,"score":0.39640000462532043},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.3677999973297119},{"id":"https://openalex.org/C133462117","wikidata":"https://www.wikidata.org/wiki/Q4929239","display_name":"Data collection","level":2,"score":0.33809998631477356},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.3244999945163727},{"id":"https://openalex.org/C39896193","wikidata":"https://www.wikidata.org/wiki/Q380344","display_name":"Descriptive statistics","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3131999969482422},{"id":"https://openalex.org/C33566652","wikidata":"https://www.wikidata.org/wiki/Q1065927","display_name":"Theme (computing)","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.3050999939441681},{"id":"https://openalex.org/C171560490","wikidata":"https://www.wikidata.org/wiki/Q3374857","display_name":"Convergent thinking","level":4,"score":0.2678000032901764},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C7991579","wikidata":"https://www.wikidata.org/wiki/Q17955","display_name":"Criticism","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.2565000057220459}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.22460/infinity.v15i4.p1031-1060","doi":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","is_oa":true,"landing_page_url":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","pdf_url":"https://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/download/7304/2599","source":{"id":"https://openalex.org/S2764492204","display_name":"Infinity Journal","issn_l":"2089-6867","issn":["2089-6867","2460-9285"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310314984","host_organization_name":"Mathematics Education Study Program of STKIP Siliwangi","host_organization_lineage":["https://openalex.org/P4310314984"],"host_organization_lineage_names":["Mathematics Education Study Program of STKIP Siliwangi"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Infinity Journal","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:29a15c9752c749268491003f029df705","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/29a15c9752c749268491003f029df705","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,"listed_in":[],"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":"Infinity, Vol 15, Iss 4, Pp 1031-1060 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.22460/infinity.v15i4.p1031-1060","doi":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","is_oa":true,"landing_page_url":"https://doi.org/10.22460/infinity.v15i4.p1031-1060","pdf_url":"https://e-journal.stkipsiliwangi.ac.id/index.php/infinity/article/download/7304/2599","source":{"id":"https://openalex.org/S2764492204","display_name":"Infinity Journal","issn_l":"2089-6867","issn":["2089-6867","2460-9285"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":"https://openalex.org/P4310314984","host_organization_name":"Mathematics Education Study Program of STKIP Siliwangi","host_organization_lineage":["https://openalex.org/P4310314984"],"host_organization_lineage_names":["Mathematics Education Study Program of STKIP Siliwangi"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Infinity Journal","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.975600004196167,"display_name":"Quality education","id":"https://metadata.un.org/sdg/4"}],"study_designs":[{"display_name":"Clinical Trial","id":"https://openalex.org/study-designs/clinical-trial"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214230767.pdf","grobid_xml":"https://content.openalex.org/works/W7214230767.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W1997210479","https://openalex.org/W2724125522","https://openalex.org/W2790467171","https://openalex.org/W2808127062","https://openalex.org/W2809921736","https://openalex.org/W2811132917","https://openalex.org/W2886011697","https://openalex.org/W2890058064","https://openalex.org/W2890357245","https://openalex.org/W2908667500","https://openalex.org/W2912092000","https://openalex.org/W2912887158","https://openalex.org/W2913798675","https://openalex.org/W2917364997","https://openalex.org/W2943457804","https://openalex.org/W2962534509","https://openalex.org/W2990110117","https://openalex.org/W2995372184","https://openalex.org/W3006386119","https://openalex.org/W3008623236","https://openalex.org/W3010743912","https://openalex.org/W3012461893","https://openalex.org/W3032049912","https://openalex.org/W3081352638","https://openalex.org/W3082881270","https://openalex.org/W3087909215","https://openalex.org/W3091238132","https://openalex.org/W3101712325","https://openalex.org/W3108695892","https://openalex.org/W3125051199","https://openalex.org/W3137184449","https://openalex.org/W3174249584","https://openalex.org/W4200337332","https://openalex.org/W4225405071","https://openalex.org/W4228997889","https://openalex.org/W4229005528","https://openalex.org/W4229456670","https://openalex.org/W4292087209","https://openalex.org/W4294266335","https://openalex.org/W4322628681","https://openalex.org/W4361305935","https://openalex.org/W4380482809","https://openalex.org/W4382652577","https://openalex.org/W4391155020","https://openalex.org/W4410415577","https://openalex.org/W4415373047","https://openalex.org/W4415771634","https://openalex.org/W7155080373"],"related_works":["https://openalex.org/W7170205155","https://openalex.org/W2955810897","https://openalex.org/W7218547379","https://openalex.org/W7215976182","https://openalex.org/W3104010081","https://openalex.org/W4414922871","https://openalex.org/W4406977802","https://openalex.org/W4322733858","https://openalex.org/W4408689570","https://openalex.org/W4412904263"],"abstract_inverted_index":{"Examining":[0],"sequences":[1],"and":[2,17,32,51,97,99,116,131,141,156,166,177,185],"series":[3],"often":[4],"leads":[5],"students":[6,80],"to":[7,39],"rely":[8],"on":[9],"formulas,":[10],"especially":[11,28],"when":[12],"assignments":[13],"require":[14],"algebraic":[15,45,186],"modeling":[16],"generalization.":[18],"This":[19,34],"condition":[20],"may":[21],"hinder":[22],"the":[23,37,53,61,144,161],"advancement":[24],"of":[25],"critical":[26,49,58,154,180],"thinking,":[27],"in":[29,152],"evaluation,":[30],"inference,":[31],"reasoning.":[33],"study":[35,65],"examined":[36,108,137],"extent":[38],"which":[40],"a":[41,67,86,102],"problem-solving":[42],"e-module":[43,91,125],"with":[44,89,143],"challenges":[46],"enhanced":[47],"students'":[48,124],"thinking":[50,59,155],"identified":[52],"elements":[54],"that":[55],"best":[56],"facilitated":[57,179],"during":[60],"learning":[62],"process.":[63],"The":[64,72,104,134,147],"used":[66],"sequential":[68],"explanatory":[69],"mixed-methods":[70],"design.":[71],"quantitative":[73,105,145],"phase":[74],"encompassed":[75],"89":[76],"senior":[77],"high":[78],"school":[79],"from":[81,123],"three":[82],"classes.":[83],"Students":[84],"completed":[85,101],"pretest,":[87],"engaged":[88],"an":[90,150],"featuring":[92],"guiding":[93],"questions,":[94],"scaffolding,":[95,176],"feedback,":[96],"reflection,":[98],"then":[100],"posttest.":[103],"data":[106,135],"were":[107,121,136,163],"utilizing":[109],"descriptive":[110],"statistics,":[111],"normalized":[112],"gain,":[113],"pretest-posttest":[114],"comparisons,":[115],"effect":[117],"size":[118],"analysis.":[119],"Data":[120],"gathered":[122],"assignments,":[126],"classroom":[127],"observations,":[128],"written":[129],"reflections,":[130],"task-oriented":[132],"interviews.":[133],"using":[138],"theme":[139],"coding":[140],"synthesized":[142],"results.":[146],"results":[148],"indicated":[149],"improvement":[151],"overall":[153],"across":[157],"all":[158],"metrics;":[159],"however,":[160,182],"improvements":[162],"inconsistent.":[164],"Evaluation":[165],"interpretation":[167],"improved":[168],"more":[169],"significantly":[170],"than":[171],"explanation.":[172],"Feedback,":[173],"directed":[174],"inquiries,":[175],"reflection":[178],"thinking;":[181],"argument":[183],"quality":[184],"reasoning":[187],"varied":[188],"among":[189],"students.":[190]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-09-25T00:00:00"}
