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Marja van den Heuvel-Panhuizen

Introduction to Realistic Mathematics Education (RME) – with examples from primary school mathematics education. Marja van den Heuvel-Panhuizen. Freudenthal Institute. Faculty of Science. Faculty of Social and Behavioural Sciences. Faculty of Social and Behavioural Sciences. Faculty

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Marja van den Heuvel-Panhuizen

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  1. Introduction to Realistic Mathematics Education (RME) – with examples from primary school mathematics education Marja van den Heuvel-Panhuizen Freudenthal Institute Faculty of Science Faculty of Social and Behavioural Sciences

  2. Faculty of Social and Behavioural Sciences Faculty of Science Early Childhood Special Education Primary Education Vocational Education Secundary Education Freudenthal Institute

  3. Realistic Mathematics Education • “real world mathematics” • to imagine = ZICH REALISEREN • context-based • real world or fantasy world • formal world of mathematics

  4. Realistic Mathematics Education ~1968 2013 • still under construction • over the years different accentuations

  5. Realistic Mathematics Education ~1968 2013 • still under construction • over the years different accentuations

  6. (1978) 1987

  7. Realistic Mathematics Education Freudenthal Institute 1971 - .... ~1968 2013 • still under construction • over the years different accentuations

  8. (1978) 1987 1973

  9. Mechanistic mathematics education ~1968

  10. Mechanistic mathematics education Grade 3

  11. Mechanistic mathematics education New Maths ~1968

  12. Mechanistic mathematics education New Maths

  13. Realistic Mathematics Education Mechanistic mathematics education New Maths ~1968

  14. Grade 3 Grade 3 1969 (9e edition) 2013

  15. % market share RME textbooks % market share Mechanistic textbooks 1960s 1980s 1987 1992 1997 2004

  16. Mechanistic Mathematics Education • bare number calculations • - little attention applications • (especially not at start) • teaching is transmission • * atomized • * step-by-step

  17. Mechanistic Mathematics Education Realistic Mathematics Education • bare number calculations • - little attention applications • (especially not at start) • teaching is transmission • * atomized • * step-by-step - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle

  18. Mechanistic Mathematics Education Realistic Mathematics Education • bare number calculations • - little attention applications • (especially not at start) • teaching is transmission • * atomised • * step-by-step - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle

  19. Realistic Mathematics Education transmission approach to learning constructivist approach to learning

  20. Mechanistic Mathematics Education Realistic Mathematics Education • bare number calculations • - little attention applications • (especially not at start) • teaching is transmission • * atomised • * step-by-step - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle

  21. source target applications target Realistic Mathematics Education transmission approach to learning applications constructivist approach to learning applications

  22. TIMSS 2003 Study - Grade 8 International average: 38% got a full credit Dutch students: 74% got a full credit

  23. 1 1 scoop holds kg; 5 so, 1 kg is 5 scoops and 6 kg is 6 times 5, is 30 scoops. Formal strategy × 5 × 6 number 1 5 30 of scoops 1 1 6 kg 5 Informal context-connected strategy

  24. Realistic Mathematics Education - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle

  25. Freudenthal Rather than beginning with abstractions or definitions to be applied later, one must start with rich contexts that ask for mathematical organization; or, in other words, one must start with contexts that can be mathematized. “What humans have to learn is not mathematics as a closed system, but rather as an activity, the process of mathematizing reality and if possible even that of mathematizing mathematics.” (1968)

  26. “real” world mathematics 1 2 Treffers 1987 (Three Dimensions) mathematizing

  27. Realistic Mathematics Education - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle • various levels of understanding • progressive schematization • models as bridges

  28. Realistic Mathematics Education - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle • various levels of understanding • progressive schematization • models as bridges

  29. Grade 1

  30. 1 1 1 1 5 5 Grade 1 Maureen 1 1 1 1 1 1 1 1 1 1 1 1 Thijs and Nick Luuk “First, put three guilders out of the six to the seven guilders; that makes ten guilders; and three makes thirteen guilders” Hannah “Six and six is twelve; and one makes thirteen guilders”

  31. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5 Grade 1 formal calculation six and six is ... calculation by structuring cross-section calculation by counting

  32. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 5 Grade 1 formal calculation six and six is ... calculation by structuring cross-section calculation by counting calculation by structuring formal calculation longitudinal-section

  33. Realistic Mathematics Education - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle • various levels of understanding • progressive schematization • models as bridges

  34. Treffers 1987 (Three Dimensions) Progressive schematization

  35. Progressive ‘complexization’

  36. Progressive schematization 12 6394

  37. Progressive schematization

  38. whole-number-based written calculation digit-based written calculation 53 5459 103 53 15 53 5459 0 5300 100 159 159 159 159 3 0 0 103

  39. Realistic Mathematics Education - activity principle - reality principle - level principle - intertwinement principle - interactivity principle - guidance principle • various levels of understanding • progressive schematization • models as bridges

  40. Streefland 1985 (Wiskunde als activiteit en de realiteit als bron) 1996 (Learning from history for teaching in the future) Models as bridges: Model of → Model for

  41. bus stop on off on off difference 31 39 minimal or more model of 8 0 model for

  42. 3 6 4 8 15 6 12 8 On which table do you get more? model of or Which fraction is larger ? model for or

  43. “Making sense of percents” Mathematics in Context mathematics textbook series for grades 5-8 Romberg (Ed.) (1997-1998 ...) Grade 5 (- 6)

  44. Learning trajectory for percentage qualitative/informal way of working with percentage percentage as descriptors of so-many-out-of-so-many situations quantitative/formal way of working with percentage percentage as operators

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