Teachers training in Norway and MKTPresented at the University of Coimbra, Portugal May 31st, 2011<br />Arne Jakobsen<br /...
2<br />
Trondheim<br />Oslo<br />Bergen<br />Stavanger<br />
Educational system in Norway<br />Right to Upper secondary school<br />Compulsery 10 yearsofschooling<br />Age 1 – 5 Kinde...
Financingofeducation:<br />Central governmentsubsidisespublic and  most private educationon all levels.<br />Counties and ...
State ComprehensiveSchool System<br />Public schools: to provideequalityofopportunities for all membersofsociety<br />A de...
Ownershipofschools<br />2 % of pupils (grade 1-10) in private schools<br />5 % of pupils in private upper secondary school...
Percentage of female teachers:<br />92 % kindergarten<br />70 % grade 1- 10 in school<br />48 % upper secondary and in col...
Colleges and universities<br />7 universities , 25 university colleges, <br />20 private institutions<br />2003 Quality re...
Trondheim<br />Oslo<br />Bergen<br />Stavanger<br />
Ullandhaug Campus<br />
Norwegian Petroleum Directorate<br />IRIS<br />Rogaland Science Park: Precubator, Incubator, Start-up companies, Spinouts<...
            University of Stavanger               History and roots<br />1994: Stavanger University College <br />(mergero...
University of Stavanger<br />Merger of University Colleges in 1994, became University College of Stavanger<br />University...
University of Stavanger<br />4 Faculties:<br />Faculty of Arts and Education<br />Faculty of Science and Technology <br />...
17<br />Faculty of Arts and Education<br />National Centre for Reading Education and Research<br />National Centre for Beh...
18<br />Department of EducationFaculty of Arts and Education<br />Used to offer a 4 year general teachereducation program ...
Teacher Education for Grades 1-7<br />Math Education (30 ECTS), Norwegian (30 ECTS)<br />Pedagogy and Pupil-related skills...
Teacher Education for Grades 5-10<br />Mathematics Education OR Norwegian 60 ECTS<br />Pedagogy and Pupil-related skills (...
Main issues<br />Two differentteacher programs – directed to primary – or secondaryschoolpupils – to meetthedifferentneeds...
Graduate and Post-Graduate Programs<br />MA Special Needs Education<br />MA Mathematics Education<br />Eramus Mundus MA Mi...
Research<br />Teachers’ knowledge and capacity for teaching diverse students  (mainresearch program)<br />Severalresearchg...
24<br />UiS International<br />
25<br />International studentswww.uis.no/english<br />Open to applicants from all over the world:<br />Degree opportunitie...
               International studentswww.uis.no/english<br />Open to students whose home institution has <br />an agreemen...
Comparative Educational Studies<br />Comparative Educational Studies - A Three Month Exchange Programme for International ...
28<br />Orientation Week for International Students<br />Pick-up service<br />Air-port, train-station, etc<br />Presentati...
29<br />Orientation Week for International Students<br />Guided tours downtown and in Rogaland county<br />city walk<br />...
30<br />Student Residencies<br />
31<br />Student Residencies<br />
Photo: E. Stornes<br />
Photo: E. Stornes<br />
www.uis.nowww.uis.no/english<br />
Research at Department of Education<br />Teachers’ knowledge and capacity for teaching diverse students  (mainresearch pro...
Background Norway/Portugal:<br />Students (TIMSS, PISA,…)<br />Teachers’ knowledge is important for students achievement<b...
Mathematicalknowledge for teaching (MKT)<br /><ul><li>Classroom studies in the U.S.
Workofteaching (gravacoessalas de aula)
Tasks ofteaching (gravacoessalas de aula)
Areas of MKT (emGeometria e Medida, Otd, Algebra, NO)
MKT items
MQI - back to theclassroom (aindanao mas…)</li></li></ul><li>
Exampleofonetaskwithitems<br />Choosing and using representations<br />Representing a particular idea in multiple ways<br ...
MKT - the «egg»<br />Ball, D. L., Thames, M. H., & Phelps, G. (2008, p. 403). <br />
<ul><li>A Especificidade do Conhecimento Matemático para o Ensino Ball et al. (2008)</li></ul>CCK – Conhecimento comum do ...
<ul><li>A Especificidade do Conhecimento Matemático para o Ensino Ball et al. (2008)</li></ul>KCT – Conhecimento do Conteú...
Example item<br />
<ul><li>MKT item</li></ul>46<br />
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Presentation of UKM-Stavanger at Coimbra, Portugal

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This presentation of MKT (mathematical knowledge for teaching) was held in Coimbra, Portugal by Arne Jakobsen and Carlos Miguel Ribeiro.

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Presentation of UKM-Stavanger at Coimbra, Portugal

  1. 1. Teachers training in Norway and MKTPresented at the University of Coimbra, Portugal May 31st, 2011<br />Arne Jakobsen<br />Department of Education<br />University of Stavanger<br />arne.jakobsen@uis.no<br />C. Miguel Ribeiro<br />ESEC Universidade do Algarve <br />cmribeiro@ualg.pt<br />
  2. 2. 2<br />
  3. 3. Trondheim<br />Oslo<br />Bergen<br />Stavanger<br />
  4. 4. Educational system in Norway<br />Right to Upper secondary school<br />Compulsery 10 yearsofschooling<br />Age 1 – 5 Kindergarten (Right to kindergarten, iftheparentswant)<br />4<br />
  5. 5. Financingofeducation:<br />Central governmentsubsidisespublic and most private educationon all levels.<br />Counties and municiplitiesget a lump ofmoney from state, autonomy in use. Veryfewearmarked grants.<br />Public education from primary to university is providedfreeofcharge. <br />
  6. 6.
  7. 7. State ComprehensiveSchool System<br />Public schools: to provideequalityofopportunities for all membersofsociety<br />A democraticcommunitywhere all socialclassesofsocietymeet.<br />A commonstructure for all pupils grade 1-10<br /> (someresistance: butgraduallyunstreamedclassesreplaceddividedcourses/structure<br />Grades canstigmatisepupils, kill innermotivation to learn. No grades given to childrebefore in 8. grade.<br />
  8. 8. Ownershipofschools<br />2 % of pupils (grade 1-10) in private schools<br />5 % of pupils in private upper secondary school<br />Long tradition of public schools <br />43 % of children in private kindergarten <br />57 % of children in public kindergarten<br />
  9. 9. Percentage of female teachers:<br />92 % kindergarten<br />70 % grade 1- 10 in school<br />48 % upper secondary and in colleges<br />35 % universities<br />9<br />
  10. 10. Colleges and universities<br />7 universities , 25 university colleges, <br />20 private institutions<br />2003 Quality reform: implementationof Bologna process<br />State EducationalLoan Fund offers support to students<br />
  11. 11. Trondheim<br />Oslo<br />Bergen<br />Stavanger<br />
  12. 12. Ullandhaug Campus<br />
  13. 13. Norwegian Petroleum Directorate<br />IRIS<br />Rogaland Science Park: Precubator, Incubator, Start-up companies, Spinouts<br />
  14. 14. University of Stavanger History and roots<br />1994: Stavanger University College <br />(mergerofseven colleges)<br />Rogaland University Center (1969)<br />NorwegianSchoolof Hotel Management (1912)<br />Stavanger SchoolofNursing (1920)<br />Rogaland ConservatoryofMusic (1945)<br />Stavanger Schoolof Education (1954)<br />Stavanger Schoolof Social Studies (1966)<br />The NorwegianChurch’sSchoolofTheology (1989)<br />January 1, 2005: University status<br />
  15. 15. University of Stavanger<br />Merger of University Colleges in 1994, became University College of Stavanger<br />University of Stavanger since 2005<br />1200 faculty, administrative and service staff<br />8500 students<br />16:1 student-faculty ratio<br />34 Bachelor programmes<br />28 Master programmes <br />8 PhD programmes<br />
  16. 16. University of Stavanger<br />4 Faculties:<br />Faculty of Arts and Education<br />Faculty of Science and Technology <br />Faculty of Social Sciences<br />Museum of Archaeology<br />
  17. 17. 17<br />Faculty of Arts and Education<br />National Centre for Reading Education and Research<br />National Centre for Behavioural Research <br />Department of Music and Dance<br />Department of Cultural Studies and Languages<br />Department of Early Childhood Education <br />Department of Education<br />
  18. 18. 18<br />Department of EducationFaculty of Arts and Education<br />Used to offer a 4 year general teachereducation program for grades 1 – 10 (all schoolsubjects)<br />4 yearteachereducation, grades 1-7 <br />4 yearteachereducation program<br /> grades 5-10 – bothcan be extended to 5 years MA program<br />BA (and MA) Sports Education<br />MA Special Needs Education<br />MA Mathematics Education<br />Eramus Mundus MA Migration & <br />InterculturalRelations<br />PhD in Education<br />
  19. 19. Teacher Education for Grades 1-7<br />Math Education (30 ECTS), Norwegian (30 ECTS)<br />Pedagogy and Pupil-related skills (60 ECTS)<br />Chooseamong a lot ofelectivesubjects<br />Normallyfourschoolsubjects - must have 60 ECTS in minimum onesubject<br />Bachelor’ thesis<br />100 daysfieldpractice<br />Takeplace at partner schools, under supervision and counselling by experiencedteachers<br />With minimum 15 ECTS in counselling student teachers<br />
  20. 20. Teacher Education for Grades 5-10<br />Mathematics Education OR Norwegian 60 ECTS<br />Pedagogy and Pupil-related skills (60 ECTS)<br />Chooseamong a lot ofelectivesubjects<br />Normally 3 schoolsubjects, eachof 60 ECTS<br />Bachelor’ thesis<br />100 dayswithfieldpractice<br />Takeplace at partner schools, under supervision and counseling by experiencedteachers<br />With minimum 15 ECTS in counseling student teachers<br />
  21. 21. Main issues<br />Two differentteacher programs – directed to primary – or secondaryschoolpupils – to meetthedifferentneedsofthepupils – bothsocially and academically<br />In Mathematics, Norwegian and Pedagogycompletedifferentiationbetweenthetwo programs<br />Integrationbetweenschoolsubject, pedagogy and learning in practice<br />Link betweentheory and practice<br />
  22. 22. Graduate and Post-Graduate Programs<br />MA Special Needs Education<br />MA Mathematics Education<br />Eramus Mundus MA Migration & <br />InterculturalRelations<br />PhD in Education<br />
  23. 23. Research<br />Teachers’ knowledge and capacity for teaching diverse students (mainresearch program)<br />Severalresearchgroupsarealignedwiththistopic; for example:<br />Teachers’ mathematicalknowledge for teaching<br />Whatkindofknowledge do teachersneed to teachmatematics?<br />Teachers’ knowledge and capacity for teaching: from students to professional<br />Students development over thecourseoftheirstudy;<br />Transition to teaching<br />Mentoringnoviceteachers<br />Inclusive Education<br />To understand procceses ofinclusion and exclusion<br />
  24. 24. 24<br />UiS International<br />
  25. 25. 25<br />International studentswww.uis.no/english<br />Open to applicants from all over the world:<br />Degree opportunities<br />MSc in Petroleum Engineering<br />MSc in Biological Chemistry<br />MSc in Computer Science<br />MSc in Offshore Technology<br />MSc in Environmental Technology<br />MSc in International Hotel and Tourism Management<br />Master of Arts in Literacy Studies<br />Master Programme in Musical Performance - classical<br />Joint Master programme in Migration and Intercultural Relations<br />PhD-Programmes<br />Postgraduate courses within <br />Music production and recording, classical music, jazz, voice etc<br />For students who plan to study in Norway or students who<br />already are in Norway:<br />Norwegian Language and Culture (1 year programme which qualifies for entry to all Norwegian Higher Education)<br />
  26. 26. International studentswww.uis.no/english<br />Open to students whose home institution has <br />an agreement with the University of Stavanger:<br />Exchange programme opportunities<br />Music and Dance Performance<br />Business, Hotel- and Tourism<br />Nursing<br />Computer Science<br />Natural Science and Mathematics<br />Mechanical and Civil Engineering<br />Industrial Economics, risk management and planning<br />Petroleum Engineering<br />Foreign Languages (English)<br />Comparative Educational Studies<br />
  27. 27. Comparative Educational Studies<br />Comparative Educational Studies - A Three Month Exchange Programme for International Students<br />Offered for the first time in 2004. So far more than 150 student teachers from Austria, Belgium, the Czech Republic, Denmark, Finland, Germany, Latvia, Northern Ireland, Poland, Romania, Spain, Switzerland, The Netherlands and the USA have attended our courses<br />Student teachers (Pre-school, primary and secondary school)<br />27<br />
  28. 28. 28<br />Orientation Week for International Students<br />Pick-up service<br />Air-port, train-station, etc<br />Presentation of UiS<br />Computer room<br />Student card<br />Guided tour on campus<br />Library introduction<br />Meeting Norwegian culture<br />How to reduce the cost of living in Norway<br />Practical arrangements<br />Passport/Visa/Immigrant Office<br />Bus card<br />Bank account<br />Health check (TB)<br />
  29. 29. 29<br />Orientation Week for International Students<br />Guided tours downtown and in Rogaland county<br />city walk<br />bus trip<br />boat trip<br />daylong hike in mountain<br />barbeques<br />Note the 1000 meters drop below them into a cold fjord!<br />
  30. 30. 30<br />Student Residencies<br />
  31. 31. 31<br />Student Residencies<br />
  32. 32. Photo: E. Stornes<br />
  33. 33. Photo: E. Stornes<br />
  34. 34.
  35. 35. www.uis.nowww.uis.no/english<br />
  36. 36.
  37. 37. Research at Department of Education<br />Teachers’ knowledge and capacity for teaching diverse students (mainresearch program)<br />Severalresearchgroupsarealignedwiththistopic; for example:<br />Teachers’ mathematicalknowledge for teaching (MKT)<br />Whatkindofknowledge do teachersneed to teachmatematics?<br />Teachers’ knowledge and capacity for teaching: from students to professional<br />Students development over thecourseoftheirstudy;<br />Transition to teaching<br />Mentoringnoviceteachers<br />Inclusive Education<br />To understand procceses ofinclusion and exclusion<br />
  38. 38. Background Norway/Portugal:<br />Students (TIMSS, PISA,…)<br />Teachers’ knowledge is important for students achievement<br />Government decide to invest in Professional development (Programa de Formacão Continua emMatematica - PFCM)<br />Professional development programs to meet teachers’ needs<br />Mathematical knowledge for teaching (MKT)<br />Our project research question: What are the possibilities and challenges of using the MKT measures in Norway?<br />Que MKT possuemosprofessores (actuais e futuros), comoevoluiesse MKT e de quemodopodemoscontribuirpara o seuincremento?<br />Project so far: Translation of items Pilot: 142 (150) teachers measured and 7 focus group interviews<br />Trabalhocolaborativo com professores dos primeirosanos (reflexaosobre as aulas); questionarios e entrevistasalunosformacaoinicial<br />
  39. 39. Mathematicalknowledge for teaching (MKT)<br /><ul><li>Classroom studies in the U.S.
  40. 40. Workofteaching (gravacoessalas de aula)
  41. 41. Tasks ofteaching (gravacoessalas de aula)
  42. 42. Areas of MKT (emGeometria e Medida, Otd, Algebra, NO)
  43. 43. MKT items
  44. 44. MQI - back to theclassroom (aindanao mas…)</li></li></ul><li>
  45. 45. Exampleofonetaskwithitems<br />Choosing and using representations<br />Representing a particular idea in multiple ways<br />Interpreting a particular representation in multiple ways<br />Choosing a diagram/story/model to represent and idea/concept/expression<br />Selecting a representation to match an instructional purpose<br />
  46. 46. MKT - the «egg»<br />Ball, D. L., Thames, M. H., & Phelps, G. (2008, p. 403). <br />
  47. 47. <ul><li>A Especificidade do Conhecimento Matemático para o Ensino Ball et al. (2008)</li></ul>CCK – Conhecimento comum do conteúdo – conhecimento sobre como fazer – óptica do utilizador (adquirido nas UC de Matemática) <br />SCK – Conhecimento Especializado do Conteúdo – conhecimento sobre como ensinar a fazer/entender (apenas necessário aos professores para ensinar – adquirido tambémnas UC de Matemática (na formação de professores…))<br />HCK (Conhecimento do Horizonte Matemático) – conhecimento de como os vários tópicos matemáticos se relacionam e da forma como a aprendizagem de um determinado tópico se desenvolve ao longo da escolaridade <br />Ball, D. L., Thames, M. H., & Phelps, G. (2008, p. 403). <br />
  48. 48. <ul><li>A Especificidade do Conhecimento Matemático para o Ensino Ball et al. (2008)</li></ul>KCT – Conhecimento do Conteúdo e do Ensino – escolha da sequência das tarefas, de exemplos, ..., (Normalmente considerado “Didáctica”)<br />KCS – Conhecimento do conteúdo e dos alunos – necessidade/capacidade do professor antecipar o que os alunos pensam, suas dificuldades e motivações bem como ouvir e interpretar os seus comentários (conhecimento das possíveis concepções erróneas, motivações e interesses dos alunos, bem como das suas necessidades)<br />KCC – Conhecimento do conteúdo e do currículo – possuir uma visão completa da diversidade e variedade de materiais didácticos disponíveis<br />
  49. 49. Example item<br />
  50. 50. <ul><li>MKT item</li></ul>46<br />
  51. 51. Discutindo o MKT envolvido/relacionado com um exemplo envolvendo rectângulos <br /> A professora Maria pretende abordar o estudo de rectângulos (e a noção de fracção como parte-todo). Para isso pediu aos seus alunos do 1.º ano para dizerem o que entendem por rectângulo, desenharem um e dividirem-no em quatro partes iguais. <br /> Que conhecimento lhe cumpre ter de modo a poder “ensinar para a compreensão” e deixar a “porta aberta” para aprendizagens futuras? <br />
  52. 52. Discutindo o MKT envolvido/relacionado com um exemplo envolvendo rectângulos <br /> A professora Maria pretende abordar o estudo de rectângulos (e a noção de fracção como parte-todo). Para isso pediu aos seus alunos do 1.º ano para dizerem o que entendem por rectângulo, desenharem um e dividirem-no em quatro partes iguais. <br />Estas foram algumas das respostas (representações) dos alunos da professora Maria ao pedido para desenharem e dividirem o rectângulo em quatro partes iguais<br /> Que conhecimento lhe cumpre ter de modo a poder “ensinar para a compreensão” e deixar a “porta aberta” para aprendizagens futuras? <br />
  53. 53. (CCK) – Conhecimento Comum do Conteúdo<br />Saber identificar, de entre as respostas fornecidas, quais as representações incorrectas e “correctas” e de rectângulo e que ilustram uma sua correcta divisão em quatro partes iguais<br />?<br />?<br />?<br />?<br />
  54. 54. (SCK) – Conhecimento Especializado do Conteúdo (exemplos rectângulos) <br />Poderá a professora Maria aceitar todas estas representações de rectângulo? <br />Quais os motivos matemáticos que permitem considerar, ou não, como correcta(s), estas divisões?<br />(será possível efectuar uma tal divisão?)<br />
  55. 55.
  56. 56. www.uis.nowww.uis.no/english<br />

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