Realistic Mathematics Education (RME) is an approach to teaching mathematics that is based on several key principles: 1) Starting with real-life contexts that are meaningful to students and using them as a source for mathematical concepts. 2) Encouraging the use of various problem-solving strategies over rote memorization of procedures. 3) Promoting the use of models and diagrams to help students understand mathematical relationships. 4) Emphasizing interaction between teacher and students, and among students, rather than just instruction from teacher to students. 5) Utilizing structured teaching materials to help build students' conceptual understanding of quantities.

1. Presentatie titel What is Realistic Mathematics Education? Rotterdam, 00 januari 2007 Swakopmund, May 2011

2. Europe The Netherlands Holland Rotterdam

4. Rotterdam primary schools

6. April 12th, 1961

8. ‘Mathematics must be connected to reality, stay close to children and be relevant to society, in order to be of human value. Instead of seeing mathematics as subject matter that has to be transmitted, I see the idea of mathematics as a ‘human activity’. Education should give students the “guided” opportunity to “re-invent” mathematics by doing it. This means that in mathematics education, the focal point should not be on mathematics as a closed system but on the activity, on the process of mathematization, going from the world of life into the world of symbols’ (Freudenthal, 1968).

9. 1960 Mechanisticmathematics Education in 95% of the Dutch primary schools MME Context problems as a field of application, Procedure-focusedwayof teaching in which the learning content is split up in meaningless small parts, Students are offered fixed solving procedures to be trained by exercises. 2011 Realisticmathematics Education in 95% of the Dutch primary schools RME Context problems as a sourcefor the learningprocessand to apply mathematicalconcepts, Complex and meaningful conceptualization of teaching and learning, Students are considered to be active participants in the teaching learning process, in which they develop mathematical tools and insights.

10. What is realistic mathematics education? You enter a classroom. The teacher of this classroom gives her lessons according the basic principles of RME. How do you recognize this? What is the influence of teaching according RME on the learning of the learners? What can you expect of the learning proceeds by teaching mathematics education according to the principles of RME? Does RME make the maths lessons more interesting, more attractive for the learners? What does a lessonplan look like for a maths lesson according RME?

13. Use of smart strategies

14. Learning by use of models and diagrams

15. Learning in interaction

17. Learning from the learners’ experiences

18. Learning from useful materials

19. Learning from pair and group activities

20. Learning by doing

22. Interaction

23. Models and diagrams

24. Strategies

25. Use of characteristic, structured teaching materials

27. Strategies

28. Models and diagrams

29. Interaction

31. Contexts in Dutch maths books

33. What experience do they have?

35. By doing so, the child will certainly be motivated to learn.

36. Why do we use contexts? The child sees that you can use mathematics in daily life, that is to say, in your life.

37. What is a context for you? How numerated are you?

39. Right

47. Strategies

48. Models and diagrams

49. Interaction

51. Do we know how children think?

54. Strategies (5) A book with 92 pages. You are reading at the bottom of page 27. How many pages to read when page 27 is finished?

55. Solutions Algorithm calculation: Addingbystringing, the ‘cashiersstrategy’: 27 + 3 = 30, 30 + 60 = 90, 90 + 2 = 92, So: 3 + 60 + 2 = 65

56. Solutions Stringing: Splitting: deficit Combination of splitting and stringing:

57. Scale strategy: Jumping toofar and back: Smart strategies 92 – 27 = 92 – 30 + 3 = 65

58. Strategiescalculation up to 20 (1) 8 + 7 9, 10, 11, 12, 13, 14, 15 8 + 2 = 10, 10 + 5 = 15 5 + 3 + 5 + 2 = 10 + 5 = 15 7 + 7 + 1 = 14 + 1 = 15 8 + 8 – 1 = 16 – 1 = 15 etc

59. Strategies calculation up to 20 (2) Maureen: Thijs: Luuk: “First, put three euro’s out of the six to the seven euro’s; thatmakes ten euro’s, and threemakesthirteen euro’s.” Hannah: “Six and six is twelve; and one makes thirteen euro’s.”

60. Strategieslearning the times tables (1)

61. Strategies learning the times tables (2)

62. Strategies learning the times tables (3) ‘Stepping stones’

63. Reflection Do you present various strategies in maths class? Do children have preferences for strategies? Is the children’s numberconcept sufficient to apply various strategies? Do children choose their own strategy? Do all children have to learn various strategies?

65. Strategies

66. Models and diagrams

67. Interaction

69. Difference between € 54.- and € 37.-?

72. Strategies

73. Models and diagrams

74. Interaction

76. Verticalinteraction

78. HorizontalInteraction

81. Strategies

82. Models and diagrams

83. Interaction

86. Numeric cards

87. Number snake

88. Numbers in love

89. Sun game

92. The levels of concept based mathematics education formal level model level contextlevel

94. Because of the direct link to daily life, children get the possibility to use the matter they learned at school in their environment.

95. Children will be able to solve real problems based on what they learned at school. Not only with maths!

97. Strategies

98. Models and diagrams

99. Interaction

101. ‘How can we teach our learners in the way of Realistic Mathematics Education?’

103. Jaap de Waard, j.de.waard@hro.nl