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

1. Teachers training in Norway and MKTPresented at the University of Coimbra, Portugal May 31st, 2011 Arne Jakobsen Department of Education University of Stavanger arne.jakobsen@uis.no C. Miguel Ribeiro ESEC Universidade do Algarve cmribeiro@ualg.pt

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3. Trondheim Oslo Bergen Stavanger

4. Educational system in Norway Right to Upper secondary school Compulsery 10 yearsofschooling Age 1 – 5 Kindergarten (Right to kindergarten, iftheparentswant) 4

5. Financingofeducation: Central governmentsubsidisespublic and most private educationon all levels. Counties and municiplitiesget a lump ofmoney from state, autonomy in use. Veryfewearmarked grants. Public education from primary to university is providedfreeofcharge.

7. State ComprehensiveSchool System Public schools: to provideequalityofopportunities for all membersofsociety A democraticcommunitywhere all socialclassesofsocietymeet. A commonstructure for all pupils grade 1-10 (someresistance: butgraduallyunstreamedclassesreplaceddividedcourses/structure Grades canstigmatisepupils, kill innermotivation to learn. No grades given to childrebefore in 8. grade.

8. Ownershipofschools 2 % of pupils (grade 1-10) in private schools 5 % of pupils in private upper secondary school Long tradition of public schools 43 % of children in private kindergarten 57 % of children in public kindergarten

9. Percentage of female teachers: 92 % kindergarten 70 % grade 1- 10 in school 48 % upper secondary and in colleges 35 % universities 9

10. Colleges and universities 7 universities , 25 university colleges, 20 private institutions 2003 Quality reform: implementationof Bologna process State EducationalLoan Fund offers support to students

11. Trondheim Oslo Bergen Stavanger

12. Ullandhaug Campus

13. Norwegian Petroleum Directorate IRIS Rogaland Science Park: Precubator, Incubator, Start-up companies, Spinouts

14. University of Stavanger History and roots 1994: Stavanger University College (mergerofseven colleges) Rogaland University Center (1969) NorwegianSchoolof Hotel Management (1912) Stavanger SchoolofNursing (1920) Rogaland ConservatoryofMusic (1945) Stavanger Schoolof Education (1954) Stavanger Schoolof Social Studies (1966) The NorwegianChurch’sSchoolofTheology (1989) January 1, 2005: University status

15. University of Stavanger Merger of University Colleges in 1994, became University College of Stavanger University of Stavanger since 2005 1200 faculty, administrative and service staff 8500 students 16:1 student-faculty ratio 34 Bachelor programmes 28 Master programmes 8 PhD programmes

16. University of Stavanger 4 Faculties: Faculty of Arts and Education Faculty of Science and Technology Faculty of Social Sciences Museum of Archaeology

17. 17 Faculty of Arts and Education National Centre for Reading Education and Research National Centre for Behavioural Research Department of Music and Dance Department of Cultural Studies and Languages Department of Early Childhood Education Department of Education

18. 18 Department of EducationFaculty of Arts and Education Used to offer a 4 year general teachereducation program for grades 1 – 10 (all schoolsubjects) 4 yearteachereducation, grades 1-7 4 yearteachereducation program grades 5-10 – bothcan be extended to 5 years MA program BA (and MA) Sports Education MA Special Needs Education MA Mathematics Education Eramus Mundus MA Migration & InterculturalRelations PhD in Education

19. Teacher Education for Grades 1-7 Math Education (30 ECTS), Norwegian (30 ECTS) Pedagogy and Pupil-related skills (60 ECTS) Chooseamong a lot ofelectivesubjects Normallyfourschoolsubjects - must have 60 ECTS in minimum onesubject Bachelor’ thesis 100 daysfieldpractice Takeplace at partner schools, under supervision and counselling by experiencedteachers With minimum 15 ECTS in counselling student teachers

20. Teacher Education for Grades 5-10 Mathematics Education OR Norwegian 60 ECTS Pedagogy and Pupil-related skills (60 ECTS) Chooseamong a lot ofelectivesubjects Normally 3 schoolsubjects, eachof 60 ECTS Bachelor’ thesis 100 dayswithfieldpractice Takeplace at partner schools, under supervision and counseling by experiencedteachers With minimum 15 ECTS in counseling student teachers

21. Main issues Two differentteacher programs – directed to primary – or secondaryschoolpupils – to meetthedifferentneedsofthepupils – bothsocially and academically In Mathematics, Norwegian and Pedagogycompletedifferentiationbetweenthetwo programs Integrationbetweenschoolsubject, pedagogy and learning in practice Link betweentheory and practice

22. Graduate and Post-Graduate Programs MA Special Needs Education MA Mathematics Education Eramus Mundus MA Migration & InterculturalRelations PhD in Education

23. Research Teachers’ knowledge and capacity for teaching diverse students (mainresearch program) Severalresearchgroupsarealignedwiththistopic; for example: Teachers’ mathematicalknowledge for teaching Whatkindofknowledge do teachersneed to teachmatematics? Teachers’ knowledge and capacity for teaching: from students to professional Students development over thecourseoftheirstudy; Transition to teaching Mentoringnoviceteachers Inclusive Education To understand procceses ofinclusion and exclusion

24. 24 UiS International

25. 25 International studentswww.uis.no/english Open to applicants from all over the world: Degree opportunities MSc in Petroleum Engineering MSc in Biological Chemistry MSc in Computer Science MSc in Offshore Technology MSc in Environmental Technology MSc in International Hotel and Tourism Management Master of Arts in Literacy Studies Master Programme in Musical Performance - classical Joint Master programme in Migration and Intercultural Relations PhD-Programmes Postgraduate courses within Music production and recording, classical music, jazz, voice etc For students who plan to study in Norway or students who already are in Norway: Norwegian Language and Culture (1 year programme which qualifies for entry to all Norwegian Higher Education)

26. International studentswww.uis.no/english Open to students whose home institution has an agreement with the University of Stavanger: Exchange programme opportunities Music and Dance Performance Business, Hotel- and Tourism Nursing Computer Science Natural Science and Mathematics Mechanical and Civil Engineering Industrial Economics, risk management and planning Petroleum Engineering Foreign Languages (English) Comparative Educational Studies

27. Comparative Educational Studies Comparative Educational Studies - A Three Month Exchange Programme for International Students 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 Student teachers (Pre-school, primary and secondary school) 27

28. 28 Orientation Week for International Students Pick-up service Air-port, train-station, etc Presentation of UiS Computer room Student card Guided tour on campus Library introduction Meeting Norwegian culture How to reduce the cost of living in Norway Practical arrangements Passport/Visa/Immigrant Office Bus card Bank account Health check (TB)

29. 29 Orientation Week for International Students Guided tours downtown and in Rogaland county city walk bus trip boat trip daylong hike in mountain barbeques Note the 1000 meters drop below them into a cold fjord!

30. 30 Student Residencies

31. 31 Student Residencies

32. Photo: E. Stornes

33. Photo: E. Stornes

35. www.uis.nowww.uis.no/english

37. Research at Department of Education Teachers’ knowledge and capacity for teaching diverse students (mainresearch program) Severalresearchgroupsarealignedwiththistopic; for example: Teachers’ mathematicalknowledge for teaching (MKT) Whatkindofknowledge do teachersneed to teachmatematics? Teachers’ knowledge and capacity for teaching: from students to professional Students development over thecourseoftheirstudy; Transition to teaching Mentoringnoviceteachers Inclusive Education To understand procceses ofinclusion and exclusion

38. Background Norway/Portugal: Students (TIMSS, PISA,…) Teachers’ knowledge is important for students achievement Government decide to invest in Professional development (Programa de Formacão Continua emMatematica - PFCM) Professional development programs to meet teachers’ needs Mathematical knowledge for teaching (MKT) Our project research question: What are the possibilities and challenges of using the MKT measures in Norway? Que MKT possuemosprofessores (actuais e futuros), comoevoluiesse MKT e de quemodopodemoscontribuirpara o seuincremento? Project so far: Translation of items Pilot: 142 (150) teachers measured and 7 focus group interviews Trabalhocolaborativo com professores dos primeirosanos (reflexaosobre as aulas); questionarios e entrevistasalunosformacaoinicial

40. Workofteaching (gravacoessalas de aula)

41. Tasks ofteaching (gravacoessalas de aula)

42. Areas of MKT (emGeometria e Medida, Otd, Algebra, NO)

43. MKT items

45. Exampleofonetaskwithitems Choosing and using representations Representing a particular idea in multiple ways Interpreting a particular representation in multiple ways Choosing a diagram/story/model to represent and idea/concept/expression Selecting a representation to match an instructional purpose

46. MKT - the «egg» Ball, D. L., Thames, M. H., & Phelps, G. (2008, p. 403).

49. Example item

51. Discutindo o MKT envolvido/relacionado com um exemplo envolvendo rectângulos 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. Que conhecimento lhe cumpre ter de modo a poder “ensinar para a compreensão” e deixar a “porta aberta” para aprendizagens futuras?

52. Discutindo o MKT envolvido/relacionado com um exemplo envolvendo rectângulos 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. Estas foram algumas das respostas (representações) dos alunos da professora Maria ao pedido para desenharem e dividirem o rectângulo em quatro partes iguais Que conhecimento lhe cumpre ter de modo a poder “ensinar para a compreensão” e deixar a “porta aberta” para aprendizagens futuras?

53. (CCK) – Conhecimento Comum do Conteúdo 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 ? ? ? ?

54. (SCK) – Conhecimento Especializado do Conteúdo (exemplos rectângulos) Poderá a professora Maria aceitar todas estas representações de rectângulo? Quais os motivos matemáticos que permitem considerar, ou não, como correcta(s), estas divisões? (será possível efectuar uma tal divisão?)

56. www.uis.nowww.uis.no/english