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Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the\u003Cjats:italic>mixture Rasch model\u003C\u002Fjats:italic>that allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. 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Kết quả từ mô hình tâm lý lượng giác và bằng chứng từ các buổi phỏng vấn ghi hình và các buổi đào tạo chuyên môn cho thấy có 2 phân nhóm giáo viên trung học cơ sở, 1 nhóm có khả năng lý luận tốt hơn với các cấu trúc đơn vị 3 cấp và 1 nhóm bị giới hạn ở các cấu trúc đơn vị 2 cấp. 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Number concepts and operations in the middle grades, 119",{},{"id":24,"text":461,"url":24,"identifiers":462},"Steffe L., 1994, The development of multiplicative reasoning in the learning of mathematics, 3",{},{"id":24,"text":464,"url":24,"identifiers":465},"10.1016\u002FS0732-3123(02)00075-5",{"doi":464},{"id":24,"text":467,"url":24,"identifiers":468},"10.1016\u002FS0732-3123(03)00022-1",{"doi":467},{"id":24,"text":470,"url":24,"identifiers":471},"10.1207\u002Fs15327833mtl0602_4",{"doi":470},{"id":24,"text":473,"url":24,"identifiers":474},"10.2307\u002F749817",{"doi":473},{"id":24,"text":476,"url":24,"identifiers":477},"10.2307\u002F749137",{"doi":476},{"id":24,"text":479,"url":24,"identifiers":480},"10.2307\u002F749339",{"doi":479},{"id":24,"text":482,"url":24,"identifiers":483},"10.2307\u002F749707",{"doi":482},{"id":24,"text":485,"url":24,"identifiers":486},"10.1016\u002FS0732-3123(99)00025-5",{"doi":485},{"id":24,"text":488,"url":24,"identifiers":489},"10.1016\u002Fj.jmathb.2003.12.006",{"doi":488},{"id":24,"text":491,"url":24,"identifiers":492},"Vergnaud G., 1983, Acquisition of mathematics concepts and processes, 127",{},{"id":24,"text":494,"url":24,"identifiers":495},"Vergnaud G., 1988, Research agenda for mathematics education: Vol. 2. Number concepts and operations in the middle grades, 141",{},{"id":24,"text":497,"url":24,"identifiers":498},"Wilkins J. L. M., 2011, Journal for Research in Mathematics Education, 42, 386, 10.5951\u002Fjresematheduc.42.4.0386",{"doi":499},"10.5951\u002Fjresematheduc.42.4.0386",false,{"id":502,"createTime":503,"updateTime":504,"relativeEntities":505,"slug":506,"properties":507,"entityType":147,"verifyStatus":148,"verifyTime":503,"verifyNote":149,"languages":522,"translateLanguages":523,"viewCount":25,"primaryUrl":524,"fullTextUrl":24,"authors":525,"publicationType":233,"publisherRelationship":564,"citationCount":619,"citationInfo":620,"publishDate":625,"publishYear":621,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":626,"openAccess":24,"references":627,"isForceReanalyzing":500},"5c0e5fc1-24f2-4198-959c-2b696201ca5d","2024-09-30T23:59:50.156+00:00","2025-01-25T03:01:49.080+00:00",[],"Relationships-Between-Students-Fractional-Knowledge-and-Equation-Writing",{"openalex":508,"mag":510,"abstract":512,"title":515,"keywords":518,"doi":520},{"VOID":509},"W2232428287",{"VOID":511},"2232428287",{"VI":513,"EN":514},"\u003Cjats:p>Để hiểu rõ mối quan hệ giữa kiến thức phân số của học sinh và lý luận đại số trong bối cảnh viết phương trình, một nghiên cứu phỏng vấn đã được thực hiện với 12 học sinh trung học cơ sở, trong đó có 6 học sinh hoạt động với mỗi một trong 2 khái niệm nhân khác nhau. Các khái niệm này được xây dựng dựa trên cách mà học sinh phối hợp các đơn vị phức hợp. Học sinh đã tham gia vào hai buổi phỏng vấn kéo dài 45 phút và hoàn thành một bài kiểm tra phân số bằng văn bản. Học sinh hoạt động với khái niệm nhân thứ hai chưa xây dựng được các số phân số, trong khi học sinh hoạt động với khái niệm nhân thứ ba thì đã có; học sinh hoạt động với khái niệm nhân thứ hai biểu diễn các đại lượng không xác định có mối quan hệ nhân với cách thức chất lượng khác so với học sinh hoạt động với khái niệm nhân thứ ba. Một liên kết tiện lợi được đề xuất giữa việc xây dựng các số phân số và cách mà học sinh biểu diễn các đại lượng không xác định có mối quan hệ nhân.","\u003Cjats:p>To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.\u003C\u002Fjats:p>",{"EN":516,"VI":517},"Relationships Between Students' Fractional Knowledge and Equation Writing","Mối Quan Hệ Giữa Kiến Thức Phân Số Của Học Sinh Và Việc Viết Phương Trình",{"VI":519},"",{"VOID":521},"10.5951\u002Fjresematheduc.46.2.0196",[151],[153],"https:\u002F\u002Fpubs.nctm.org\u002Fview\u002Fjournals\u002Fjrme\u002F46\u002F2\u002Farticle-p196.xml",[526,545],{"id":527,"sortIndex":25,"researcher":24,"roles":528,"affiliations":529,"properties":538,"displayName":542,"givenName":24,"familyName":24},"1a86f47c-b14a-4963-a56c-a54ecb4ad233",[],[530],{"id":531,"sortIndex":25,"affiliation":532,"properties":24},"af647964-70d8-48b9-9b86-85786117a394",{"id":531,"createTime":24,"updateTime":24,"relativeEntities":533,"slug":24,"properties":534,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":537,"statistic":24},[],{"title":535},{"EN":536},"1 Indiana University",[],{"orcid":539,"title":541,"openalex":543},{"VOID":540},"https:\u002F\u002Forcid.org\u002F0000-0002-3406-4761",{"EN":542},"Amy J. Hackenberg",{"VOID":544},"A5087473719",{"id":546,"sortIndex":100,"researcher":24,"roles":547,"affiliations":548,"properties":557,"displayName":561,"givenName":24,"familyName":24},"069616ee-490b-4c5b-8af2-8b3dfeae10c5",[],[549],{"id":550,"sortIndex":25,"affiliation":551,"properties":24},"fa17a314-f5d1-42bb-905d-ab6a951bfb00",{"id":550,"createTime":24,"updateTime":24,"relativeEntities":552,"slug":24,"properties":553,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":556,"statistic":24},[],{"title":554},{"EN":555},"2 Arizona State University",[],{"orcid":558,"title":560,"openalex":562},{"VOID":559},"https:\u002F\u002Forcid.org\u002F0000-0003-3937-8695",{"EN":561},"Mi Yeon Lee",{"VOID":563},"A5101423253",{"url":24,"publisher":565,"properties":612},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":566,"slug":10,"properties":567,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":572,"manageAffiliations":581,"indexDatabases":592,"url":91,"thumbnailPath":24,"statistic":607,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":568,"eissn":569,"issn":570,"title":571},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[573,577],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":574,"label":575,"description":576,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":578,"label":579,"description":580,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37,"VI":38},{},[582,587],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":583,"slug":24,"properties":584,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":586,"statistic":24},[],{"title":585},{"EN":46},[],{"id":49,"createTime":24,"updateTime":24,"relativeEntities":588,"slug":24,"properties":589,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":591,"statistic":24},[],{"title":590},{"EN":53},[],[593,600],{"id":57,"indexDatabase":594,"url":70,"indexYears":24,"academicFieldIds":599,"indexDatabaseRanking":24},{"id":59,"createTime":24,"updateTime":24,"relativeEntities":595,"label":596,"description":597,"key":66,"publicationTags":598,"standard":24},[],{"EN":62,"VI":62},{"EN":64,"VI":65},[68,69],[72],{"id":74,"indexDatabase":601,"url":85,"indexYears":86,"academicFieldIds":606,"indexDatabaseRanking":90},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":602,"label":603,"description":604,"key":82,"publicationTags":605,"standard":24},[],{"EN":79,"VI":79},{"EN":79,"VI":81},[84],[88,89],{"impactFactor":25,"impactFactorByYear":608,"i10Index":99,"i10IndexLast5Year":100,"totalPublication":101,"totalPublicationByYear":609,"totalCitation":104,"totalCitationByYear":610,"totalCitationPerPublication":115,"totalCitationPerPublicationByYear":611,"hindexLast5Year":99,"hindex":99},{"2012":94,"2013":95,"2014":96,"2015":97,"2023":98},{"1993":100,"1996":103,"1997":100,"2004":100,"2008":100,"2010":100,"2011":103,"2013":100,"2022":103},{"1993":106,"1996":107,"1997":108,"2004":109,"2008":110,"2010":111,"2011":112,"2013":113,"2022":114},{"1993":106,"1996":117,"1997":108,"2004":109,"2008":110,"2010":111,"2011":118,"2013":113,"2022":119},{"issue":613,"pages":615,"volume":617},{"VOID":614},"2",{"VOID":616},"196-243",{"VOID":618},"46",101,{"total":619,"publishYear":621,"statisticByYear":622},2015,{"2013":100,"2015":97,"2016":97,"2017":99,"2018":99,"2019":623,"2020":623,"2021":96,"2022":101,"2023":624,"2024":101},14,6,"2015-03-01",[68,90],[],{"id":629,"createTime":630,"updateTime":631,"relativeEntities":632,"slug":633,"properties":634,"entityType":147,"verifyStatus":148,"verifyTime":649,"verifyNote":149,"languages":650,"translateLanguages":651,"viewCount":25,"primaryUrl":652,"fullTextUrl":24,"authors":653,"publicationType":233,"publisherRelationship":671,"citationCount":726,"citationInfo":727,"publishDate":732,"publishYear":728,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":733,"openAccess":24,"references":734,"isForceReanalyzing":500},"f8e984a8-489c-496c-8cd9-4e7088e9ab56","2024-10-10T14:02:44.682+00:00","2025-01-25T03:00:53.071+00:00",[],"Brief-Report-The-Role-of-Mathematics-Teaching-in-Fostering-Student-Growth-Mindset",{"openalex":635,"mag":637,"abstract":639,"title":642,"keywords":645,"doi":647},{"VOID":636},"W2801034469",{"VOID":638},"2801034469",{"VI":640,"EN":641},"\u003Cjats:p>Niềm tin rằng khả năng toán học là một đặc điểm cố định rất phổ biến và có thể là một lý do chính cho sự không quan tâm và hiệu suất kém của nhiều học sinh trong môn toán. Nghiên cứu này điều tra cách mà các phương pháp giảng dạy toán học có thể góp phần vào niềm tin của học sinh về khả năng toán học là một đặc điểm cố định hoặc có thể thay đổi (tư duy). Thông qua việc tổng hợp tài liệu hiện có và phân tích dữ liệu từ các quan sát lớp học, bài báo này trình bày một khung phương pháp giảng dạy và xác định cách thực hiện khác nhau của các phương pháp này có thể được phân loại dọc theo một continuum từ việc truyền tải thông điệp tư duy cố định đến việc truyền tải thông điệp tư duy phát triển liên quan đến khả năng toán học.\u003C\u002Fjats:p>","\u003Cjats:p>The belief that mathematics ability is a fixed trait is particularly common and may be a key reason for many students' disinterest and underperformance in mathematics. This study investigates how mathematics teaching practices might contribute to students' beliefs about mathematics ability being a fixed or malleable trait (mindset). Through a synthesis of existing literature and an analysis of data from classroom observations, this article presents a framework of teaching practices and identifies how varying implementations of these practices can be classified along a continuum from conveying fixed-mindset messages to conveying growth-mindset messages related to mathematics ability.\u003C\u002Fjats:p>",{"EN":643,"VI":644},"Brief Report: The Role of Mathematics Teaching in Fostering Student Growth Mindset","Báo cáo ngắn: Vai trò của giảng dạy toán học trong việc thúc đẩy tư duy phát triển của học sinh",{"VI":646},"Tư duy phát triển, giảng dạy toán học, khả năng toán học, thực hành giảng dạy, tư duy cố định",{"VOID":648},"10.5951\u002Fjresematheduc.49.3.0330","2024-10-10T14:02:44.681+00:00",[151],[153],"https:\u002F\u002Fpubs.nctm.org\u002Fview\u002Fjournals\u002Fjrme\u002F49\u002F3\u002Farticle-p330.xml",[654],{"id":655,"sortIndex":25,"researcher":24,"roles":656,"affiliations":657,"properties":666,"displayName":668,"givenName":24,"familyName":24},"a36db2de-f9ab-4ede-9c15-e396dbb0689a",[],[658],{"id":659,"sortIndex":25,"affiliation":660,"properties":24},"fc13834a-ff5c-4c22-97f6-ea6238224af2",{"id":659,"createTime":24,"updateTime":24,"relativeEntities":661,"slug":24,"properties":662,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":665,"statistic":24},[],{"title":663},{"EN":664},"1 Santa Clara University",[],{"title":667,"openalex":669},{"EN":668},"Kathy Liu 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this article, I investigate the influence of the dominant culture characterizing mathematics education—which I term the \u003Cjats:italic>culture of exclusion\u003C\u002Fjats:italic>—on efforts to teach for equity. Analyzing a year of observations in an urban high school mathematics department, I found that this culture structured everyday instruction even for teachers who expressed strong commitment to equity and who participated in ongoing equityoriented professional development. Through their classroom practice, the 4 focal teachers in this study often framed mathematics as a fixed body of knowledge to be received, and they positioned students as deficient, unintentionally excluding many students from rich learning opportunities. However, these teachers also asserted alternatives to the culture of exclusion, showing how resistance to this culture might take shape in everyday mathematics instruction.\u003C\u002Fjats:p>","\u003Cjats:p>Trong bài viết này, tôi điều tra ảnh hưởng của nền văn hóa chiếm ưu thế trong giáo dục toán học—mà tôi gọi là \u003Cjats:italic>văn hóa loại trừ\u003C\u002Fjats:italic>—đối với những nỗ lực giảng dạy với mục tiêu công bằng. Thông qua việc phân tích một năm quan sát tại một phòng toán của trường trung học ở đô thị, tôi phát hiện ra rằng nền văn hóa này đã cấu trúc việc giảng dạy hàng ngày ngay cả đối với những giáo viên thể hiện cam kết mạnh mẽ đối với công bằng và tham gia vào quá trình phát triển chuyên môn định hướng công bằng. Qua thực hành lớp học của họ, 4 giáo viên trọng tâm trong nghiên cứu này thường khung toán học như một khối kiến thức cố định cần được tiếp nhận, và họ đã định vị học sinh như những người thiếu thốn, vô tình loại trừ nhiều học sinh khỏi những cơ hội học tập phong phú. Tuy nhiên, những giáo viên này cũng đã khẳng định các phương án thay thế cho văn hóa loại trừ, cho thấy cách thức kháng cự lại văn hóa này có thể phát triển trong việc giảng dạy toán học hàng ngày.\u003C\u002Fjats:p>",{"EN":750,"VI":751},"The Culture of Exclusion in Mathematics Education and Its Persistence in Equity-Oriented Teaching","Văn hóa loại trừ trong giáo dục toán học và sự bền bỉ của nó trong giảng dạy định hướng công bằng",{"VI":753},"văn hóa loại trừ, giáo dục toán học, công bằng trong giáo dục, giảng dạy định hướng công bằng",{"VOID":755},"10.5951\u002Fjresematheduc.48.5.0488",[151],[153],"https:\u002F\u002Fpubs.nctm.org\u002Fview\u002Fjournals\u002Fjrme\u002F48\u002F5\u002Farticle-p488.xml",[760],{"id":761,"sortIndex":25,"researcher":24,"roles":762,"affiliations":763,"properties":772,"displayName":776,"givenName":24,"familyName":24},"9d0f8bbf-29e1-4fc3-b81e-3dfced1cbfef",[],[764],{"id":765,"sortIndex":25,"affiliation":766,"properties":24},"fcaafe0c-7475-4df5-8822-8ea05ee5b187",{"id":765,"createTime":24,"updateTime":24,"relativeEntities":767,"slug":24,"properties":768,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":771,"statistic":24},[],{"title":769},{"EN":770},"1 The University of Wisconsin–Madison",[],{"orcid":773,"title":775,"openalex":777},{"VOID":774},"https:\u002F\u002Forcid.org\u002F0000-0001-6080-325X",{"EN":776},"Nicole Louie",{"VOID":778},"A5050676854",{"url":24,"publisher":780,"properties":827},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":781,"slug":10,"properties":782,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":787,"manageAffiliations":796,"indexDatabases":807,"url":91,"thumbnailPath":24,"statistic":822,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":783,"eissn":784,"issn":785,"title":786},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[788,792],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":789,"label":790,"description":791,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":793,"label":794,"description":795,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37,"VI":38},{},[797,802],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":798,"slug":24,"properties":799,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":801,"statistic":24},[],{"title":800},{"EN":46},[],{"id":49,"createTime":24,"updateTime":24,"relativeEntities":803,"slug":24,"properties":804,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":806,"statistic":24},[],{"title":805},{"EN":53},[],[808,815],{"id":57,"indexDatabase":809,"url":70,"indexYears":24,"academicFieldIds":814,"indexDatabaseRanking":24},{"id":59,"createTime":24,"updateTime":24,"relativeEntities":810,"label":811,"description":812,"key":66,"publicationTags":813,"standard":24},[],{"EN":62,"VI":62},{"EN":64,"VI":65},[68,69],[72],{"id":74,"indexDatabase":816,"url":85,"indexYears":86,"academicFieldIds":821,"indexDatabaseRanking":90},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":817,"label":818,"description":819,"key":82,"publicationTags":820,"standard":24},[],{"EN":79,"VI":79},{"EN":79,"VI":81},[84],[88,89],{"impactFactor":25,"impactFactorByYear":823,"i10Index":99,"i10IndexLast5Year":100,"totalPublication":101,"totalPublicationByYear":824,"totalCitation":104,"totalCitationByYear":825,"totalCitationPerPublication":115,"totalCitationPerPublicationByYear":826,"hindexLast5Year":99,"hindex":99},{"2012":94,"2013":95,"2014":96,"2015":97,"2023":98},{"1993":100,"1996":103,"1997":100,"2004":100,"2008":100,"2010":100,"2011":103,"2013":100,"2022":103},{"1993":106,"1996":107,"1997":108,"2004":109,"2008":110,"2010":111,"2011":112,"2013":113,"2022":114},{"1993":106,"1996":117,"1997":108,"2004":109,"2008":110,"2010":111,"2011":118,"2013":113,"2022":119},{"issue":828,"pages":830,"volume":832},{"VOID":829},"5",{"VOID":831},"488-519",{"VOID":833},"48",90,{"total":834,"publishYear":836,"statisticByYear":837},2017,{"2018":215,"2019":838,"2020":99,"2021":839,"2022":840,"2023":841,"2024":842},5,16,25,19,7,"2017-11-01",[68,90],[],{"id":847,"createTime":848,"updateTime":849,"relativeEntities":850,"slug":851,"properties":852,"entityType":147,"verifyStatus":148,"verifyTime":848,"verifyNote":149,"languages":866,"translateLanguages":867,"viewCount":25,"primaryUrl":868,"fullTextUrl":24,"authors":869,"publicationType":233,"publisherRelationship":921,"citationCount":110,"citationInfo":975,"publishDate":990,"publishYear":976,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":991,"openAccess":24,"references":992,"isForceReanalyzing":500},"9a45b318-08ec-4891-b11a-404a5dba2837","2024-09-13T02:01:35.827+00:00","2024-12-25T08:00:32.160+00:00",[],"Unpacking-Pedagogical-Content-Knowledge-Conceptualizing-and-Measuring-Teachers-Topic-Specific-Knowledge-of-Students",{"openalex":853,"mag":855,"abstract":857,"title":860,"keywords":863,"doi":865},{"VOID":854},"W15859922",{"VOID":856},"15859922",{"EN":858,"VI":859},"\u003Cjats:p>There is widespread agreement that effective teachers have unique knowledge of students' mathematical ideas and thinking. However, few scholars have focused on conceptualizing this domain, and even fewer have focused on measuring this knowledge. In this article, we describe an effort to conceptualize and develop measures of teachers' combined knowledge of content and students by writing, piloting, and analyzing results from multiple-choice items. Our results suggest partial success in measuring this domain among practicing teachers but also identify key areas around which the field must achieve conceptual and empirical clarity. Although this is ongoing work, we believe that the lessons learned from our efforts shed light on teachers' knowledge in this domain and can inform future attempts to develop measures.\u003C\u002Fjats:p>","\u003Cjats:p>Có sự đồng thuận rộng rãi rằng giáo viên hiệu quả có kiến thức đặc biệt về ý tưởng và tư duy toán học của học sinh. Tuy nhiên, ít học giả tập trung vào việc khái niệm hóa lĩnh vực này, và thậm chí còn ít người hơn tập trung vào việc đo lường kiến thức này. Trong bài viết này, chúng tôi mô tả một nỗ lực để khái niệm hóa và phát triển các biện pháp đo lường kiến thức kết hợp giữa nội dung và học sinh của giáo viên thông qua việc viết, thử nghiệm và phân tích kết quả từ các câu hỏi trắc nghiệm. Kết quả của chúng tôi cho thấy một phần thành công trong việc đo lường lĩnh vực này giữa các giáo viên đang hành nghề, nhưng cũng xác định được các khu vực chủ chốt mà ngành cần đạt được sự rõ ràng về mặt khái niệm và thực nghiệm. Mặc dù đây là công việc đang tiến hành, chúng tôi tin rằng những bài học từ những nỗ lực của chúng tôi làm sáng tỏ kiến thức của giáo viên trong lĩnh vực này và có thể cung cấp thông tin cho các nỗ lực phát triển các biện pháp trong tương lai.\u003C\u002Fjats:p>",{"EN":861,"VI":862},"Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students","Khám Phá Kiến Thức Nội Dung Sư Phạm: Khái Niệm và Đo Lường Kiến Thức Cụ Thể Về Học Sinh của Giáo Viên",{"VI":864},"khả năng sư phạm, đo lường kiến thức giáo viên, lĩnh vực toán học, bài học từ thực tiễn, kiến thức nội dung",{"VOID":382},[151],[153],"https:\u002F\u002Fpubs.nctm.org\u002Fview\u002Fjournals\u002Fjrme\u002F39\u002F4\u002Farticle-p372.xml",[870,889,906],{"id":871,"sortIndex":25,"researcher":24,"roles":872,"affiliations":873,"properties":882,"displayName":886,"givenName":24,"familyName":24},"9e525912-240c-441a-96b4-41d55ad6c618",[],[874],{"id":875,"sortIndex":25,"affiliation":876,"properties":24},"184ebf01-a670-4617-8c4b-5d6f126ef1a6",{"id":875,"createTime":24,"updateTime":24,"relativeEntities":877,"slug":24,"properties":878,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":881,"statistic":24},[],{"title":879},{"EN":880},"Harvard Graduate School of Education",[],{"orcid":883,"title":885,"openalex":887},{"VOID":884},"https:\u002F\u002Forcid.org\u002F0000-0001-5181-1573",{"EN":886},"Heather C. 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Schilling",{"VOID":920},"A5042499201",{"url":24,"publisher":922,"properties":969},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":923,"slug":10,"properties":924,"entityType":22,"verifyStatus":23,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":25,"subjectFields":929,"manageAffiliations":938,"indexDatabases":949,"url":91,"thumbnailPath":24,"statistic":964,"gsStatistic":24,"type":24,"analyzePriority":24},[],{"country":925,"eissn":926,"issn":927,"title":928},{"VOID":13},{"VOID":15},{"VOID":17},{"EN":19},[930,934],{"id":28,"createTime":24,"updateTime":24,"relativeEntities":931,"label":932,"description":933,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":31},{},{"id":34,"createTime":24,"updateTime":24,"relativeEntities":935,"label":936,"description":937,"parentId":24,"standard":24,"scholarHubFieldId":24},[],{"EN":37,"VI":38},{},[939,944],{"id":42,"createTime":24,"updateTime":24,"relativeEntities":940,"slug":24,"properties":941,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":943,"statistic":24},[],{"title":942},{"EN":46},[],{"id":49,"createTime":24,"updateTime":24,"relativeEntities":945,"slug":24,"properties":946,"entityType":24,"verifyStatus":24,"verifyTime":24,"verifyNote":24,"languages":24,"translateLanguages":24,"viewCount":24,"url":24,"parentIds":948,"statistic":24},[],{"title":947},{"EN":53},[],[950,957],{"id":57,"indexDatabase":951,"url":70,"indexYears":24,"academicFieldIds":956,"indexDatabaseRanking":24},{"id":59,"createTime":24,"updateTime":24,"relativeEntities":952,"label":953,"description":954,"key":66,"publicationTags":955,"standard":24},[],{"EN":62,"VI":62},{"EN":64,"VI":65},[68,69],[72],{"id":74,"indexDatabase":958,"url":85,"indexYears":86,"academicFieldIds":963,"indexDatabaseRanking":90},{"id":76,"createTime":24,"updateTime":24,"relativeEntities":959,"label":960,"description":961,"key":82,"publicationTags":962,"standard":24},[],{"EN":79,"VI":79},{"EN":79,"VI":81},[84],[88,89],{"impactFactor":25,"impactFactorByYear":965,"i10Index":99,"i10IndexLast5Year":100,"totalPublication":101,"totalPublicationByYear":966,"totalCitation":104,"totalCitationByYear":967,"totalCitationPerPublication":115,"totalCitationPerPublicationByYear":968,"hindexLast5Year":99,"hindex":99},{"2012":94,"2013":95,"2014":96,"2015":97,"2023":98},{"1993":100,"1996":103,"1997":100,"2004":100,"2008":100,"2010":100,"2011":103,"2013":100,"2022":103},{"1993":106,"1996":107,"1997":108,"2004":109,"2008":110,"2010":111,"2011":112,"2013":113,"2022":114},{"1993":106,"1996":117,"1997":108,"2004":109,"2008":110,"2010":111,"2011":118,"2013":113,"2022":119},{"issue":970,"pages":971,"volume":973},{"VOID":284},{"VOID":972},"372-400",{"VOID":974},"39",{"total":110,"publishYear":976,"statisticByYear":977},2008,{"2012":978,"2013":979,"2014":980,"2015":981,"2016":982,"2017":983,"2018":983,"2019":984,"2020":985,"2021":986,"2022":987,"2023":988,"2024":989},96,118,108,149,123,99,132,109,106,94,82,39,"2008-07-01",[68,90],[],{"id":994,"createTime":995,"updateTime":996,"relativeEntities":997,"slug":998,"properties":999,"entityType":147,"verifyStatus":148,"verifyTime":995,"verifyNote":149,"languages":1014,"translateLanguages":1015,"viewCount":25,"primaryUrl":1016,"fullTextUrl":24,"authors":1017,"publicationType":233,"publisherRelationship":1054,"citationCount":1108,"citationInfo":1109,"publishDate":1119,"publishYear":1110,"citationAnalyzeStatus":23,"lastCitationAnalyze":24,"indexDatabases":1120,"openAccess":24,"references":1121,"isForceReanalyzing":500},"c1cbd5cd-d0e5-472b-974c-15c64bb7ff30","2024-09-13T02:01:36.808+00:00","2024-12-24T07:08:11.609+00:00",[],"Sociomathematical-Norms-Argumentation-and-Autonomy-in-Mathematics",{"openalex":1000,"mag":1002,"abstract":1004,"title":1007,"keywords":1010,"doi":1012},{"VOID":1001},"W2046790558",{"VOID":1003},"2046790558",{"EN":1005,"VI":1006},"\u003Cjats:p>This paper sets forth a way of interpreting mathematics classrooms that aims to account for how students develop mathematical beliefs and values and, consequently, how they become intellectually autonomous in mathematics. To do so, we advance the notion of \u003Cjats:italic>sociomathematical\u003C\u002Fjats:italic> norms, that is, normative aspects of mathematical discussions that are specific to students' mathematical activity. The explication of sociomathematical norms extends our previous work on general classroom social norms that sustain inquiry-based discussion and argumentation. Episodes from a second-grade classroom where mathematics instruction generally followed an inquiry tradition are used to clarify the processes by which sociomathematical norms are interactively constituted and to illustrate how these norms regulate mathematical argumentation and influence learning opportunities for both the students and the teacher. In doing so, we both clarify how students develop a mathematical disposition and account for students' development of increasing intellectual autonomy in mathematics. In the process, the teacher's role as a representative of the mathematical community is elaborated.\u003C\u002Fjats:p>","Bài báo này trình bày một phương pháp giải thích các lớp học toán nhằm lý giải làm thế nào học sinh phát triển các tín ngưỡng và giá trị toán học, và do đó, làm thế nào họ trở nên tự chủ trí tuệ trong toán học. Để làm điều đó, chúng tôi phát triển khái niệm chuẩn tắc xã hội hóa toán học, cụ thể là, các khía cạnh chuẩn tắc của các cuộc thảo luận toán học có đặc điểm riêng biệt trong hoạt động toán học của học sinh. Việc giải thích các chuẩn tắc xã hội hóa toán học mở rộng công trình trước đây của chúng tôi về các chuẩn tắc xã hội chung trong lớp học, giúp duy trì các cuộc thảo luận và lập luận dựa trên điều tra. Các tập phim từ một lớp hai, nơi mà giáo dục toán học thường theo truyền thống điều tra, được sử dụng để làm rõ các quá trình tạo dựng tương tác các chuẩn tắc xã hội hóa toán học và minh họa cách các chuẩn tắc này điều chỉnh lập luận toán học và ảnh hưởng đến cơ hội học tập cho cả học sinh và giáo viên. Trong quá trình này, chúng tôi vừa làm rõ cách học sinh phát triển thái độ toán học vừa lý giải quá trình học sinh phát triển sự tự chủ trí tuệ ngày càng cao trong toán học. Đồng thời, vai trò của giáo viên như là một đại diện của cộng đồng toán học cũng được mô tả rõ ràng.",{"EN":1008,"VI":1009},"Sociomathematical Norms, Argumentation, and Autonomy in Mathematics","Các Chuẩn Tắc Xã Hội Hóa Toán Học, Lý Luận và Tự Trị Trong Toán Học",{"VI":1011},"chuẩn tắc xã hội hóa, lý luận toán học, tự trị trí tuệ, hoạt động toán học, lớp học toán, giáo dục dựa trên điều 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